Characterization of the dynamic damping properties of a fiber-reinforced metaconcrete

1 Equation Chapter 1 Section 1 Trabajo Fin de Grado Grado en Ingeniería Civil “Characterization of the dynamic damping properties of a fiber-reinforced metaconcrete” Autora: Violeta González Villegas Tutor: Héctor Cifuentes Bulté Miguel Molinos Pérez Dpto. de Mecánica de Medios Continuos y Teoría de Estructuras Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla, 2024 iii Trabajo Fin de Grado Grado en Ingeniería Civil “Characterization of the dynamic damping properties of a fiber-reinforced metaconcrete” Autora: Violeta González Villegas Tutor: Héctor Cifuentes Bulté Catedrático de Universidad Miguel Molinos Pérez Contrato Juan de la Cierva Formación Dpto. de Mecánica de Medios Continuos y Teoría de Estructuras Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla, 2024 v Trabajo Fin de Grado: “Characterization of the dynamic damping properties of a fiber-reinforced metaconcrete” Autora: Violeta González Villegas Tutor: Héctor Cifuentes Bulté Miguel Molinos Pérez El tribunal nombrado para juzgar el Proyecto arriba indicado, compuesto por los siguientes miembros: Presidente: Vocales: Secretario: Acuerdan otorgarle la calificación de: Sevilla, 2024 El Secretario del Tribunal vii Agradecimientos A mi familia, por haberme permitido seguir haciendo lo que más valoro en este mundo, formarme y enriquecer mi saber. A mi madre, por haber sido mi mayor apoyo y ayuda, y haber estado ahí cuando más falta me hacía sacrificándose siempre por mí. A mi hermano, por haber sido mi modelo a seguir y preocuparse porque no hiciera más de lo que podía. A mi padre, por haber hecho esos momentos duros menos pesados con sus bromas y sus palabras de ánimos. A mi abuela, por ser la que más se ilusiona con mis aprobados, por verse todos los programas de ingeniería que salen en la tele, porque “quién le iba a decir a ella que iba a tener una nieta Ingeniera de Caminos”. A Pedro, por haberme ayudado siempre con todo lo que podía y haberme dado fuerza cuando la necesitaba. A mi tutor Héctor, por confiar en mí y por impartirme Estructuras de Hormigón I tan admirablemente que me hizo decantarme por la que ahora es mi especialidad. Violeta González Villegas Sevilla, 2024 ix Resumen Este trabajo se centra en la caracterización de las propiedades dinámicas de amortiguación de un material reforzado con distintos tipos de fibras llamado metahormigón. Los metahormigones son un tipo de metamaterial diseñado para tener propiedades específicas que no se encuentran en los materiales convencionales. Estas propiedades se logran mediante la agregación de fibras que controlan la propagación de ondas, y en consecuencia, amortiguan las vibraciones producidas en el hormigón. El objetivo de este Trabajo Fin de Grado es la validación experimental de las propiedades amortiguadoras de varios especímenes de metahormigón reforzado con distintos tipos de fibras sometidos a ondas de alta frecuencia. Para la campaña experimental se utilizaron 4 tipos distintos de especímenes de metahormigón de ultra alta resistencia reforzado con diferentes fibras: un hormigón convencional sin fibras (D0), un metahormigón reforzado con fibras cortas (DS), un metahormigón reforzado con fibras largas (DL) y un metahormigón híbrido reforzado con una proporción 50/50 de fibras cortas y largas (DSL). De cada tipo de espécimen se sacaron a su vez 4 probetas cúbicas para poder promediar las medidas registradas. De esta forma, las 16 probetas fueron sometidas a un rango de frecuencias de 0 Hz hasta 25,000 Hz generadas por un altavoz colocado en la cara superior de la probeta. A su vez, se recogieron datos de aceleraciones con 2 acelerómetros, uno en la cara superior de la probeta (RW) y otro en la cara inferior (DW). Las aceleraciones recogidas se pasaron al dominio de la frecuencia a través de la Transformada Rápida de Fourier (FFT) para su análisis, obteniendo la respuesta promediada de todos los especímenes para cada frecuencia. Los resultados de las aceleraciones en el dominio de la frecuencia muestran un comportamiento amortiguador de los metahormigones para un cierto rango de frecuencias, obteniendo para otros rangos un comportamiento contrario. Para obtener una mejor discusión de los resultados se hizo uso de un parámetro denominado transmisibilidad, el cual cuantifica la disminución de aceleraciones en comparación con otra de referencia. En este caso se ha estudiado las transmisibilidades de los metahormigones (DS, DL y DSL) con respecto al espécimen convencional sin fibras (D0). Los resultados obtenidos muestran para ciertos rangos de frecuencias una clara atenuación de las vibraciones registradas, cumpliendo así la hipótesis contemplada. Para otros rangos su análisis es un poco más complejo y se observan aumentos de las aceleraciones registradas. De esta forma, con este trabajo se contribuye a la compresión de las capacidades de amortiguación de los metahormigones de ultra alta resistencia reforzados con fibras y su potencial para mejorar la resistencia de las estructuras frente a cargas dinámicas, lo cual resulta de gran relevancia para aplicaciones en la Ingeniería Civil donde la reducción de vibraciones es crucial. 1 1 INTRODUCTION n the past few years, researchers have started studying artificial composite materials with enhanced properties. These materials, known as metamaterials, have potential uses in various engineering applications. This project explores metaconcrete, a metamaterial made of ultra-high-strength concrete with steel fiber inclusions. In this chapter, the current state of the art is discussed, the objectives are outlined, and a summary of the content is provided. 1.1 Motivation Metamaterials are innovative materials whose properties depend on both the properties of their constituent materials and their engineered microstructure, based on simple mechanical models. These metamaterials can be designed to control the effect of external forces on systems that exhibit wave diffusion. They take advantage of unusual properties such as a negative refractive index, negative shear modulus, or negative effective mass [1]. These properties are achieved by introducing specially designed and arranged inclusions, which help recreate and control desired behaviors when the composite interacts with waves. Initially, metamaterials were developed to control the propagation of electromagnetic waves and manipulate fields visible to the human eye. However, their study has expanded to various engineering fields, leading to numerous investigations into applying the same concepts to waves of different frequencies. One example of metamaterials is metaconcrete, which consists of a cementitious matrix with aggregates of different nature. Studies and experimental validations have been conducted using spherical bi-material inclusions, with one particular study serving as a reference for continued research. This thesis experimentally verifies the attenuation capabilities of metaconcrete under sonic field stresses. An experimental campaign was conducted on cylindrical specimens with arranged heterogeneous inclusions. The results show that attenuation occurs at frequencies close to the resonance frequencies of the inclusions [2]. This leads to the possibility of studying the damping capacity of different metaconcretes with different inclusions, like fiber-reinforced concrete. This type of concrete is already used in Civil Engineering and offers advantages over regular concrete. 1.2 Objectives of the study This study aims to enhance the understanding of the attenuation properties of fibers in metaconcrete by using ultra-high-strength concrete with various types of fiber reinforcement. Two types of fibers will be tested to evaluate their effects and achieve more conclusive results. To conduct the experiment, the specimens will be excited across a wide range of frequencies to induce resonance in the fibers. Ultrasound from a speaker will be used to excite the specimens, and accelerations will be measured on both faces of the cube. The data will be analyzed in the frequency domain using a Fast Fourier Transform (FFT) made with Dewesoft software. The objective is to verify if the accelerations recorded in the specimens with fibers decrease compared to a specimen without any inclusions. To achieve this, a parameter called transmissibility will be used, which relates these accelerations from the FFTs. This parameter is obtained by applying a similar method to other used by researchers for photonic and acoustic crystals [3]. I Introduction 2 1.3 Project structure This project is organized as follows: ▪ Chapter 1 introduces metamaterials and metaconccrete, discussing briefly the state of the art and the objectives of this project. ▪ Chapter 2 provides a more complete review of existing literature in metamaterials and metaconcrete, focusing on their properties and applications. ▪ Chapter 3 describes the specimens used, the experimental setup, and the experimental and data processing procedures. ▪ Chapter 4 presents the results from the wave transmission tests and analyzes the dynamic behavior of the specimens. ▪ Chapter 5 discusses the results of the experimental analysis. ▪ Chapter 6 offers conclusions on the effectiveness of fiber-reinforced metaconcrete and suggests potential directions for future research based on the study’s results and conclusions. ▪ Appendix includes additional information on frequency sweeps, FFT averages, and transmissibility data. 3 2 BACKGROUND n this chapter, existing literature and studies related to this new type of materials, specifically metaconcrete, are examined. To continue the line of research, a comprehensive literature review has been conducted to establish the current state of knowledge. The following essential studies have been used as references: ▪ Several articles on metamaterials and metaconcrete, covering investigations into elastic wave transmission and its mitigation properties. ▪ A master’s thesis exploring metaconcrete reinforce with bi-material inclusions. 2.1 Metamaterials As discussed in section 1.1 of Chapter 1, “Introduction”, there have been significant advancements in designing metamaterials engineered to demonstrate unconventional properties. These complex composites derive their unique characteristics from carefully designed microstructures [4]. Early studies began exploring the use of metamaterials to manipulate electromagnetic waves, influencing the development of sonic and phononic crystals, which are the acoustic counterparts of photonic crystals. Basic phononic crystals, consisting of periodic arrays of cylinders, have demonstrated effective wave filtering capabilities [5], [6]. These crystals enable the creation of frequency bands where incident energy disperses or scatters, leading to partial or complete absorption of elastic waves propagating through the medium and subsequently reducing the waves detected exiting the body. Such materials often use the periodic arrangement of their internal structure to create Bragg-type bandgaps [7]. For instance, an investigation into sound attenuation by a sculpture in Madrid was introduced and formally presented with experimental analysis a few years later [8]. This led to the development of a new composite material consisting of an inner sphere made of high-density material (lead) coated with a soft material (silicone), immersed in an epoxy matrix. As sonic waves pass through the material, resonance of the heavy core can be activated at selected frequencies, resulting in resonance-induced band gaps [9]. Materials incorporating resonant inclusions exhibit wave attenuation properties due to their unique characteristics, such as negative effective mass. Normally, mass density is defined as the volume average of constituent masses. However, during dynamic excitation with resonant inclusions, relative motion between the constituents and the matrix alters the dynamic effective mass density compared to its static counterpart [10], [11]. This modification can lead to a significantly large and negative effective mass when the resonance of the heavy internal mass is activated, allowing these structures to effectively manipulate and reduce wave energy. Metaconcrete, recently introduced by Mitchell et al. [4], illustrates this concept. 2.2 Metaconcrete Metaconcrete is introduced as a modified concrete designed to reduce damage and energy propagation caused by dynamic loading, such as blast loading from explosions. Traditional aggregates in concrete are replaced with bi-material inclusions that alter the dynamic response of the system across typical frequency spectra for rapid dynamic actions [4]. These new aggregates consist of spherical inclusions with a heavy metal core coated with a layer of soft material, possibly enclosed within a thin steel protective shell. At specific frequencies, these aggregates exhibit resonant behavior, oscillating around their equilibrium position and thereby absorbing a portion of the mechanical energy supplied to the system. I Background 4 The beneficial energy transfer and the implications of resonance-induced negative effective mass highlight the importance of studying metaconcrete cubes under fixed frequencies of applied loading. Transmission ratio plots, commonly used to evaluate bandgaps and resonance-induced behaviors in phononic crystals with similar layered structures [3], can also be applied to metaconcrete. These plots evaluate the change in wave amplitude across a material in relation to input wave frequency. Analyzing these ratios for metaconcrete provides insights into its transmission characteristics and the activation of resonance at various excitation frequencies. This method enables a more precise determination of aggregate properties suited for specific loading applications. Several experimental validations have been conducted. In a 2017 article, a non-destructive dynamic test was performed on metaconcrete specimens using a wide range of ultrasound frequencies [1]. The transmitted amplitude through the cube was measured, revealing a reduction of two orders of magnitude compared to conventional concrete. Additionally, a subsequent thesis extended this research [2], conducting a more detailed study and confirming the effective mitigation of transmitted waves. These experiments lay the groundwork for future research, as experimental validation of other types of metaconcrete is still unavailable. This study provides an initial experimental validation of the attenuating properties of ultra-high-strength fiberreinforced metaconcrete. The research is motivated by the recent integration of metamaterials in civil engineering, specifically in dynamics and elastic wave transmission. Our objective is to assess the practical functionality of using this concrete, which has already found application in this field, to determine its competitiveness compared to traditional construction materials. 2.3 Application in Civil Engineering The possibility of achieving attenuations in the ultrasonic range suggests that metaconcrete could be used for mitigating explosions or impacts caused by impulsive external forces that activate a wide range of frequencies. Metaconcrete could be employed in the field of Civil Engineering as explosive blast shielding structures, protective slabs against impacts, and tuned damping foundations to mitigate seismic actions in buildings. Figure 2.1: inclusions used in the thesis “Metaconcrete: Experimental Investigation on Samples with Inhomogeneous Inclusions” [2] 5 3 MATERIALS AND METHODS he specimens used in this experiment consist of randomly arranged ultra-high-strength fiber-reinforced concrete. These specimens were prepared for investigation under the title “Analysis of the tensile fracture properties of ultra-high-strength fiber-reinforced concrete with different types of steel fibers using X-ray tomography” [12]. This chapter explains the detailed composition of the specimens, along with the execution of the experiment, the equipment utilized, and the processing of the results obtained. 3.1 Specimens: concrete mix and fibers Four mixes of ultra-high-strength fiber-reinforced concrete (UHSFRC) were prepared. The mortar in all four mixes was the same, with variations only in the type and proportion of fibers used for reinforcement. Two different types of fibers were used, show in Figure 3.1: ▪ Micro-fibers: straight and short fibers of OL 13/.20, 13 mm in length and 0.20 mm in diameter [12]. ▪ Macro-fibers: long and hooked-end Dramix RC80/30CP, 35 mm in length and 0.55 mm in diameter [12]. T (a) (a) (b) (b) Figure 3.1: fibers used as reinforcement in the specimens; (a) short fibers, (b) long fibers Materials and methods 6 The concrete matrix mix is detailed in Table 3.1, designed to achieve self-compacting mixes with a high density of silica fume, resulting in a dark color. Further information on the fabrication of the specimens and their components can be found in the referenced article. The four types of specimens achieved compression strengths ranging approximately between 130 and 150 MPa, with Young's modulus values ranging from 43 to 50 GPa. Constituent kg/m3 Cement (cm) 544 Silica fume (0,1µm) 214 Ground granulated blag slag furnace (ggbs) 312 Water (w) 188 Quartz sand (< 315 m) 470 Quartzsand (< 800 m) 470 Superplasticizer (BASF Masterglenium) 42 w/ cm 0.34 w/ binder 0.17 Table 3.1: Constituents of the matrix for the different UHSFRC mixes [12] The four mixes prepared were labeled based on the type of fibers used, as reported in Table 3.2. Mix D0 represents concrete without fibers and serves as the reference specimen. Mixes DS and DL contain 2.5% by volume of short and long fibers, respectively. The specimen labeled DSL is a hybrid mix with a 50% - 50% ratio of short and long fibers. All inclusions were randomly arranged. Regarding the fiber dosage for each type of specimen, it is detailed in Table 3.2 as well. Specimen Fiber type Fiber dosage (kg/m3) D0 No fibers 0 DS Micro-fibers 196 DL Macro-fibers 196 DSL Micro- (50%) and macro-fibers (50%) 98 / 98 Table 3.2: UHSFRC mixes and fiber dosage [12] 7 Each of these specimens was further divided into four pieces to allow for a statistical evaluation of their behavior. Thus, a total of 16 cubic samples were obtained (Figure 3.2). 3.2 Experimental Setup The experimental campaign involves subjecting four different types of specimens to high-frequency vibrations to observe their damping behavior and determine if resonance occurs in the fibers. The setup includes: ▪ Two wooden supports for the concrete specimens (Figure 3.3 (a)); ▪ A Duokon vibration speaker used as an actuator (Figure 3.3 (b)); ▪ Two high frequency, ceramic shear ICP® accel., 10 mV/g, 5 to 60k Hz, 5-44 top conn. (Figure 3.3 (c)); ▪ Two low-noise coaxial cable, 10-ft, micro 5-44 plug to BNC plug (Figure 3.3 (d)); ▪ A SIRIUS-8xACC-8xAO acquisition board (Figure 3.3 (e)); ▪ A laptop running Dewesoft software for data reception and management (Figure 3.3 (f)); Figure 3.2: samples of the four types of specimens (D0, DS, DL an DSL) (a) (b) (c) (d) (e) (f) Figure 3.3: equipment used during the experimental campaign; (a) wooden support, (b) speaker, (c) piezoelectric accelerometer, (d) low-noise cable, (e) acquisition board, (f) laptop with Dewesoft software Materials and methods 8 In Figure 3.4, the hardware used is shown, including accelerometers, cables, bonding putty, wooden supports, and a specimen. The wooden supports isolate the specimens from the desk. Two accelerometer readings were collected: one from the bottom surface of the cube opposite to the speaker, labeled as the direct wave (DW), and another from the surface where the speaker was placed, known as the reflected wave (RW). Figure 3.5 shows the arrangement of both accelerometers. To ensure proper adhesion between the accelerometers and the specimen, a special anchoring wax was used to facilitate wave transmission. Figure 3.4: picture of equipment used (a) (b) (c) Figure 3.5: experimental setup arrangements; (a) and (b) placement of upper and lower accelerometer, (c) complete overlook of the analog input 9 Due to the pioneering nature of this study, we aimed to sweep through a wide range of frequencies. However, we were limited by the speaker's capability, which can only reach up to 25 kHz. To ensure accurate data collection and prevent aliasing, we selected a sampling frequency of 100,000 Hz, which is more than twice the maximum experimental frequency of 25,000 Hz required by the Nyquist sampling theorem. The choice of 100 kHz was determined by the options available in the software used, resulting in a sampling time interval of 1-5 seconds. The frequency sweeps were executed using a Matlab script, where the starting and ending frequencies, along with the time interval, were defined. They were segmented into 5 sweeps, each spanning 10 kHz and lasting 30 seconds to ensure a quasi-static response [13]. Segmentation of the frequency spectrum was necessary due to the large file sizes generated by the high sample rate, which posed challenges for data exportation. The Matlab script mentioned can be found in section 1.1 of Appendix. A schematic representation of the conducted sweeps, including their start and end frequencies, is detailed in Table 3.3. Sweep fe [Hz] fs [Hz] T [s] B1 0 10000 30 B2 5000 15000 30 B3 10000 20000 30 B4 15000 25000 30 B5 20000 30000 30 Table 3.3: frequency sweeps Each specimen of each type (totaling 16 samples) underwent testing with all frequency sweeps. The computer, connected to the equipment, was positioned on a separate chair to avoid interfering with accelerometer measurements during the start and end of the sweeps. This setup is illustrated from Figure 3.6 to Figure 3.9. Subsequently, the accelerations will be transformed into the frequency domain using the software explained in the following sections. Figure 3.6: laptop placement Figure 3.7: experimental setup Experimental analysis 16 Figure 4.4: frequency domain for the direct and reflected wave of DSL specimen Figure 4.5: frequency domain for the direct wave of all specimens 17 It was observed that the measured reflected waves are of greater magnitude than the direct waves. This could be due to the proximity of the accelerometer to the speaker. It could also be influenced by the fact that the samples are quite small compared to other studies conducted. Also, due to the heterogeneous nature of the material, wave propagation can complex, causing the reflected wave to reach the upper accelerometer (RW) before the lower one (DW). For the analysis of the results, since there is no numerical study backing it up, all frequency ranges and possible effects for all specimens will be discussed. Up to 5,000 Hz, no response is observed for either the specimen without inclusions or the metaconcrete specimens (Figure 4.5 and Figure 4.6). Between 5,000 Hz and 10,000 Hz, there is a slight acceleration observed in both the D0 specimen and the metaconcretes, all showing very similar values. In the next chapter, these results will be discussed in more detail and better illustrated. Between 10,000 Hz and 15,000 Hz, there is a distinction between direct and reflected waves. The direct wave shows minimal response (Figure 4.5). However, in the reflected wave around 12,500 Hz, the metaconcrete specimens exhibit excitation (Figure 4.6). The DS specimen experiences the highest acceleration (Figure 4.2), followed by DL (Figure 4.3) and DSL (Figure 4.4). Specimen D0 maintains some acceleration throughout this range (Figure 4.1). For frequencies around 11,000 Hz and 14,000 Hz, a decrease in accelerations is observed compared to the specimen without fibers. Between 15,000 Hz and 20,000 Hz, there is a significant increase in accelerations for both direct and reflected waves. The direct wave accelerations increase steadily, reaching their peak at 20,000 Hz (Figure 4.5). DSL generally experiences the highest accelerations in this range for the direct wave. Specimen D0 also increases its accelerations in this range, peaking at 20,000 Hz but to a smaller value. In the reflected wave, D0 shows peaks near 15,000 Hz and around 17,500 Hz, reaching its global maximum at this point (Figure 4.6). Metaconcrete specimens show an increase up to 17,500 Hz, with DS experiencing the highest accelerations. There is also an increase at 20,000 Hz, similar in magnitude to that at 17,500 Hz. For the reflected wave near 15,000 Hz, a significant decrease in accelerations is observed in the metaconcrete specimens compared to specimen D0. Direct wave also shows a decrease in accelerations for metaconcretes between 15,000 Hz and 17,500 Hz, although not as drastic as in the reflected wave. R Figure 4.6: frequency domain for the reflected wave of all specimens Experimental analysis 18 Between 20,000 Hz and 22,500 Hz, there is a decrease in accelerations for both waves and all specimens (Figure 4.5 and Figure 4.6). Around 22,500 Hz, there is a slight but minor increase observed. Comparing the metaconcretes specimens with the D0 specimen, there is not a significant decrease in accelerations observed. 4.2 Transmissibility The quantitative observations are possible with the parameter of transmissibility. This parameter captures the mitigation on the accelerations compares to another of reference. In this case, the homogeneous specimen (D0) with no inclusions was used. The significance of the parameter requires an appropriate discussion, which will be presented following the results. Transmissibility is calculated for each type of specimen and for direct and reflected wave; therefore, we have three graphics (Figure 4.7, Figure 4.8 and Figure 4.9). Subsequently, all types of fibers are represented together to facilitate easier comparison of the results between them. (Figure 4.10 and Figure 4.11). ransmissibi it Figure 4.7: transmissibility of the direct and reflected wave of DS specimen 19 ransmissibi it ransmissibi it Figure 4.8: transmissibility of the direct and reflected wave of DL specimen Figure 4.9: transmissibility of the direct and reflected wave of DSL specimen Experimental analysis 20 ransmissibi it R ransmissibi it Figure 4.10: transmissibility of the direct wave of all metaconcrete specimen Figure 4.11: transmissibility of the reflected wave of all metaconcrete specimen 21 As indicated in the thesis of reference [2], transmissibility represents a significant index of signal attenuation only if the frequency range considered is not affected by global resonance phenomena of the specimens. However, since there are no clear data on global resonance ranges, the entire frequency range is being analyzed. For the range up to 5,000 Hz, no remarkable effects were observed, attributing the initial turbulences to possible effects of the experimental setup (Figure 4.10 and Figure 4.11). In the range between 5,000 Hz and 10,000 Hz, inconsistent decreases in transmissibility were observed, with specimen DS showing the highest value. (Figure 4.7). In the range between 10,000 Hz and 15,000 Hz, different responses were observed for the reflected and direct waves. For the direct wave, a slight decrease in transmissibility was noticed. (Figure 4.10). However, for the reflected wave, the most significant decrease occurred around 11,000 Hz. This abrupt decrease is attributed to the hybrid specimen with short and long fibers. This effect was also visible in Figure 4.6. For values between approximately 14,000 Hz and 17,000 Hz, significant decreases in transmissibility were also observed. For the direct wave, these occur closer to 17,000 Hz, with DS showing the highest value followed by DSL. For the reflected wave, the decrease is centered more around 15,000 Hz, with DSL showing the largest decrease followed by DS. From 20,000 Hz onwards, decreases in transmissibility are observed, but they are more inconsistent and of lesser magnitude. However, around 25,000 Hz, the direct wave experiences a noticeable decrease, with DS showing the highest value. Similar decreases in transmissibility are also observed for the reflected wave around this frequency range. Discussion of Results 22 5 DISCUSSION OF RESULTS n this chapter, the analyzed results will be discussed. Additionally, close-ups of the graphs will be provided within the frequency ranges of interest to facilitate better interpretation. In the frequency domain, two ranges of interest were identified: from 5,000 Hz to 10,000 Hz and from 15,000 Hz to 20,000 Hz. Below is presented the first range for direct and reflected waves of all specimens. I R Figure 5.1: frequency domain for the reflected wave of all specimens between 5,000 Hz and 10,000 Hz Figure 5.2: frequency domain for the direct wave of all specimens between 5,000 Hz and 10,000 Hz 23 For both waves, a similar trend is observed. As the frequencies increase, the reduction of accelerations associated with the metaconcretes also increases. For accelerations near 5,500 Hz and 6,000 Hz, no attenuation is observed in the metaconcretes, and there is even an increase in accelerations (Figure 5.1 and Figure 5.2). For frequencies around 7,750 Hz and 8,250 Hz, a slight decrease in accelerations is observed in the metaconcrete specimens. In this range, greater attenuation is achieved at 8,250 Hz in the specimens with short fiber and hybrid (DS and DSL). R Figure 5.3: frequency domain for the reflected wave of all specimens between 15,000 Hz and 20,000 Hz Figure 5.4: frequency domain for the direct wave of all specimens between 15,000 Hz and 20,000 Hz Discussion of Results 24 For the range between 15,000 Hz and 20,000 Hz, different responses are observed for the direct and reflected waves. Regarding the reflected wave, a trend is observed up to 17,500 Hz where the metaconcretes register lower accelerations than conventional concrete (D0). This trend continues up to approximately 19,000 Hz, despite a change around 17,750 Hz where an increase in accelerations is recorded in the short and long fiber metaconcrete (DS and DL) compared to conventional concrete. Between 19,000 Hz and 20,000 Hz, significantly higher accelerations are observed in the metaconcretes (DS, DL, and DSL) compared to the D0 specimen. Regarding the direct wave, slight decreases in accelerations are observed for all metaconcretes up to 18,250 Hz. Beyond this frequency, higher accelerations start to be recorded in the DSL specimen. At 18,500 Hz, the DL specimen also begins to show increased accelerations, followed by the DS specimen at 19,250 Hz. This trend, where the metaconcretes register higher accelerations than the reference concrete, continues up to approximately 21,000 Hz (Figure 4.5 and Figure 4.6). As previously explained, the project aims to assess whether metaconcrete specimens exhibit an attenuating effect compared to traditional concrete specimens without reinforcing fibers. Significant reductions in transmissibility have been observed at various frequencies. At lower frequencies (between 5,000 Hz and 10,000 Hz), it is observed that the specimen with short fibers attenuates both the reflected and direct waves the most. As shown in Figure 5.5, the reflected wave reaches an attenuation of -10 dB around 6,000 Hz. A similar value is also reached for both waves between 8,000 Hz and 8,500 Hz. Given that a response is observed in all specimens, including the one without fibers, it cannot be confirmed that these frequencies are not a global mode of vibration. However, it is observed that metaconcrete slightly attenuates the accelerations at these frequencies. For the reflected wave, a significant attenuation is clearly observed around 11,000 Hz (Figure 5.6). In this case, the greatest attenuation is provided by the specimen with both short and long fibers (DSL), followed by the specimen with only short fibers (DS). The attenuations achieved reach nearly -25 dB, making them the highest attenuations recorded in the entire experiment. The attenuations caused by the specimens with only one type of fiber range between -10 dB and -15 dB. ransmissibi it Figure 5.5: transmissibility of the reflected and direct wave in DS specimen between 5,000 Hz and 10,000 Hz 25 Around 15,000 Hz, attenuations are observed in both waves. For the reflected wave, the largest attenuations are observed at approximately 15,500 Hz (Figure 5.7). As observed at previous frequencies, the greatest attenuation is provided by DSL, reaching just over -20 dB. DS and DL show similar values of around -15 dB. Regarding the direct wave, attenuations reach a maximum at 16,500 Hz, with -20 dB (Figure 5.8). In this case, the specimen with short fibers shows the highest attenuation. At that frequency, DSL exhibits a response similar to DS, but with an attenuation reaching -12 dB. ransmissibi it R ransmissibi it R Figure 5.6: transmissibility of the reflected wave in all specimens at around 11,000 Hz Figure 5.7: transmissibility of the reflected wave in all specimens between 13,000 Hz and 20,000 Hz Appendix 32 find(B2_P2_fft_data_nan==1); B2_P2_fft_data(:,end)=[]; B2_P2_fft_freq=B2_P2_fft_data(1,:); B2_P2_fft_A1=B2_P2_fft_data(2,:); B2_P2_fft_A2=B2_P2_fft_data(3,:); B2_P3_fft_data=import_fft_B2_P3.data; B2_P3_fft_data_nan=isnan(B2_P3_fft_data); find(B2_P3_fft_data_nan==1); B2_P3_fft_data(:,end)=[]; B2_P3_fft_freq=B2_P3_fft_data(1,:); B2_P3_fft_A1=B2_P3_fft_data(2,:); B2_P3_fft_A2=B2_P3_fft_data(3,:); B2_P4_fft_data=import_fft_B2_P4.data; B2_P4_fft_data_nan=isnan(B2_P4_fft_data); find(B2_P4_fft_data_nan==1); B2_P4_fft_data(:,end)=[]; B2_P4_fft_freq=B2_P4_fft_data(1,:); B2_P4_fft_A1=B2_P4_fft_data(2,:); B2_P4_fft_A2=B2_P4_fft_data(3,:); % Barrido 3 B3_P1_fft_data=import_fft_B3_P1.data; B3_P1_fft_data_nan=isnan(B3_P1_fft_data); find(B3_P1_fft_data_nan==1); B3_P1_fft_data(:,end)=[]; B3_P1_fft_freq=B3_P1_fft_data(1,:); B3_P1_fft_A1=B3_P1_fft_data(2,:); B3_P1_fft_A2=B3_P1_fft_data(3,:); B3_P2_fft_data=import_fft_B3_P2.data; B3_P2_fft_data_nan=isnan(B3_P2_fft_data); find(B3_P2_fft_data_nan==1); B3_P2_fft_data(:,end)=[]; B3_P2_fft_freq=B3_P2_fft_data(1,:); B3_P2_fft_A1=B3_P2_fft_data(2,:); B3_P2_fft_A2=B3_P2_fft_data(3,:); B3_P3_fft_data=import_fft_B3_P3.data; B3_P3_fft_data_nan=isnan(B3_P3_fft_data); find(B3_P3_fft_data_nan==1); B3_P3_fft_data(:,end)=[]; B3_P3_fft_freq=B3_P3_fft_data(1,:); B3_P3_fft_A1=B3_P3_fft_data(2,:); B3_P3_fft_A2=B3_P3_fft_data(3,:); B3_P4_fft_data=import_fft_B3_P4.data; B3_P4_fft_data_nan=isnan(B3_P4_fft_data); find(B3_P4_fft_data_nan==1); B3_P4_fft_data(:,end)=[]; B3_P4_fft_freq=B3_P4_fft_data(1,:); 33 B3_P4_fft_A1=B3_P4_fft_data(2,:); B3_P4_fft_A2=B3_P4_fft_data(3,:); % Barrido 4 B4_P1_fft_data=import_fft_B4_P1.data; B4_P1_fft_data_nan=isnan(B4_P1_fft_data); find(B4_P1_fft_data_nan==1); B4_P1_fft_data(:,end)=[]; B4_P1_fft_freq=B4_P1_fft_data(1,:); B4_P1_fft_A1=B4_P1_fft_data(2,:); B4_P1_fft_A2=B4_P1_fft_data(3,:); B4_P2_fft_data=import_fft_B4_P2.data; B4_P2_fft_data_nan=isnan(B4_P2_fft_data); find(B4_P2_fft_data_nan==1); B4_P2_fft_data(:,end)=[]; B4_P2_fft_freq=B4_P2_fft_data(1,:); B4_P2_fft_A1=B4_P2_fft_data(2,:); B4_P2_fft_A2=B4_P2_fft_data(3,:); B4_P3_fft_data=import_fft_B4_P3.data; B4_P3_fft_data_nan=isnan(B4_P3_fft_data); find(B4_P3_fft_data_nan==1); B4_P3_fft_data(:,end)=[]; B4_P3_fft_freq=B4_P3_fft_data(1,:); B4_P3_fft_A1=B4_P3_fft_data(2,:); B4_P3_fft_A2=B4_P3_fft_data(3,:); B4_P4_fft_data=import_fft_B4_P4.data; B4_P4_fft_data_nan=isnan(B4_P4_fft_data); find(B4_P4_fft_data_nan==1); B4_P4_fft_data(:,end)=[]; B4_P4_fft_freq=B4_P4_fft_data(1,:); B4_P4_fft_A1=B4_P4_fft_data(2,:); B4_P4_fft_A2=B4_P4_fft_data(3,:); % Barrido 5 B5_P1_fft_data=import_fft_B5_P1.data; B5_P1_fft_data_nan=isnan(B5_P1_fft_data); find(B5_P1_fft_data_nan==1); B5_P1_fft_data(:,end)=[]; B5_P1_fft_freq=B5_P1_fft_data(1,:); B5_P1_fft_A1=B5_P1_fft_data(2,:); B5_P1_fft_A2=B5_P1_fft_data(3,:); B5_P2_fft_data=import_fft_B5_P2.data; B5_P2_fft_data_nan=isnan(B5_P2_fft_data); find(B5_P2_fft_data_nan==1); B5_P2_fft_data(:,end)=[]; B5_P2_fft_freq=B5_P2_fft_data(1,:); B5_P2_fft_A1=B5_P2_fft_data(2,:); B5_P2_fft_A2=B5_P2_fft_data(3,:); Appendix 34 B5_P3_fft_data=import_fft_B5_P3.data; B5_P3_fft_data_nan=isnan(B5_P3_fft_data); find(B5_P3_fft_data_nan==1); B5_P3_fft_data(:,end)=[]; B5_P3_fft_freq=B5_P3_fft_data(1,:); B5_P3_fft_A1=B5_P3_fft_data(2,:); B5_P3_fft_A2=B5_P3_fft_data(3,:); B5_P4_fft_data=import_fft_B5_P4.data; B5_P4_fft_data_nan=isnan(B5_P4_fft_data); find(B5_P4_fft_data_nan==1); B5_P4_fft_data(:,end)=[]; B5_P4_fft_freq=B5_P4_fft_data(1,:); B5_P4_fft_A1=B5_P4_fft_data(2,:); B5_P4_fft_A2=B5_P4_fft_data(3,:); % PROMEDIADO % Barrido 1 Pmean_fft_B1_A1=mean([B1_P1_fft_A1;B1_P2_fft_A1;B1_P3_fft_A1;B1_ P4_fft_A1]); Pmean_fft_B1_A2=mean([B1_P1_fft_A2;B1_P2_fft_A2;B1_P3_fft_A2;B1_ P4_fft_A2]); % Barrido 2 Pmean_fft_B2_A1=mean([B2_P1_fft_A1;B2_P2_fft_A1;B2_P3_fft_A1;B2_ P4_fft_A1]); Pmean_fft_B2_A2=mean([B2_P1_fft_A2;B2_P2_fft_A2;B2_P3_fft_A2;B2_ P4_fft_A2]); % Barrido 3 Pmean_fft_B3_A1=mean([B3_P1_fft_A1;B3_P2_fft_A1;B3_P3_fft_A1;B3_ P4_fft_A1]); Pmean_fft_B3_A2=mean([B3_P1_fft_A2;B3_P2_fft_A2;B3_P3_fft_A2;B3_ P4_fft_A2]); % Barrido 4 Pmean_fft_B4_A1=mean([B4_P1_fft_A1;B4_P2_fft_A1;B4_P3_fft_A1;B4_ P4_fft_A1]); Pmean_fft_B4_A2=mean([B4_P1_fft_A2;B4_P2_fft_A2;B4_P3_fft_A2;B4_ P4_fft_A2]); % Barrido 5 Pmean_fft_B5_A1=mean([B5_P1_fft_A1;B5_P2_fft_A1;B5_P3_fft_A1;B5_ P4_fft_A1]); Pmean_fft_B5_A2=mean([B5_P1_fft_A2;B5_P2_fft_A2;B5_P3_fft_A2;B5_ P4_fft_A2]); 35 % SOLAPAMIENTO DE LAS FFT % Borramos las frecuencias de cada barrido fuera de la region de interes Pmean_fft_B1_A1(10e3:30e3)=0; Pmean_fft_B2_A1([1:5000,15e3:30e3])=0; Pmean_fft_B3_A1([1:10e3,20e3:30e3])=0; Pmean_fft_B4_A1([1:15e3,25e3:30e3])=0; Pmean_fft_B5_A1(1:20e3)=0; % Sumamos todos los barridos, se solapan en toda la region menos en los extremos Pmean_fft_BX_A1=Pmean_fft_B1_A1+Pmean_fft_B2_A1+Pmean_fft_B3_A1+ Pmean_fft_B4_A1+Pmean_fft_B5_A1; % Hacemos la media de los valores en la region central donde hubo solapamiento Pmean_fft_BX_A1(5000:25000)=Pmean_fft_BX_A1(5000:25000)/2; % Repetimos con A2 Pmean_fft_B1_A2(10e3:30e3)=0; Pmean_fft_B2_A2([1:5000,15e3:30e3])=0; Pmean_fft_B3_A2([1:10e3,20e3:30e3])=0; Pmean_fft_B4_A2([1:15e3,25e3:30e3])=0; Pmean_fft_B5_A2(1:20e3)=0; Pmean_fft_BX_A2=Pmean_fft_B1_A2+Pmean_fft_B2_A2+Pmean_fft_B3_A2+ Pmean_fft_B4_A2+Pmean_fft_B5_A2; Pmean_fft_BX_A2(5000:25000)=Pmean_fft_BX_A2(5000:25000)/2; % Pasamos las graficas finales por una media movil para suavizarlas Pmean_fft_BX_A1_smoothed_D0=mediamovil(Pmean_fft_BX_A1,25); Pmean_fft_BX_A2_smoothed_D0=mediamovil(Pmean_fft_BX_A2,25); % close all figure handle=gca handle.XAxis.Exponent=0 hold on plot(B1_P1_fft_freq,Pmean_fft_BX_A1_smoothed_D0) plot(B1_P1_fft_freq,Pmean_fft_BX_A2_smoothed_D0) ylabel('A [m/s^2]') xlabel('Frequency [Hz]') xlim([0,30e3]) grid on grid minor legend('RW','DW') title('FFT-D0') Appendix 36 1.2.2 Moving average %{ FUNCION PARA LA MEDIA MOVIL ENRTRADAS input: vector con los datos a los que se les hace la media movil N: numero de puntos que se toman a izquierda y derecha para la media móvil SALIDA out: vector con la media móvil de la entrada %} function out = mediamovil (input,N) meanrange=zeros(length(input),1); for index=1:length(input) lowrange=max(index-N,1); highrange=min(index+N,length(input)); range=[lowrange:highrange]; meanrange(index)=mean(input(range)); end out=meanrange; 37 1.3 Transmissibility % TRANSMISIBILIDAD transmisibilidad_D0_A_dB=20*log10(Pmean_fft_BX_A1_smoothed_D0./P mean_fft_BX_A1_smoothed_D0); transmisibilidad_DS_A1_dB=20*log10(Pmean_fft_BX_A1_smoothed_DS./ Pmean_fft_BX_A1_smoothed_D0); transmisibilidad_DS_A2_dB=20*log10(Pmean_fft_BX_A2_smoothed_DS./ Pmean_fft_BX_A2_smoothed_D0); transmisibilidad_DL_A1_dB=20*log10(Pmean_fft_BX_A1_smoothed_DL./ Pmean_fft_BX_A1_smoothed_D0); transmisibilidad_DL_A2_dB=20*log10(Pmean_fft_BX_A2_smoothed_DL./ Pmean_fft_BX_A2_smoothed_D0); transmisibilidad_DSL_A1_dB=20*log10(Pmean_fft_BX_A1_smoothed_DSL ./Pmean_fft_BX_A1_smoothed_D0); transmisibilidad_DSL_A2_dB=20*log10(Pmean_fft_BX_A2_smoothed_DSL ./Pmean_fft_BX_A2_smoothed_D0); figure handle=gca handle.XAxis.Exponent=0 hold on plot(B1_P1_fft_freq,transmisibilidad_DS_A1_dB) plot(B1_P1_fft_freq,transmisibilidad_DS_A2_dB) plot(B1_P1_fft_freq,transmisibilidad_D0_A_dB) ylabel('Transmissibility [dB]') xlabel('Frequency [Hz]') xlim([0,30e3]) grid on grid minor legend('RW','DW','D0') title('Transmissibility DS-D0') figure handle=gca handle.XAxis.Exponent=0 hold on plot(B1_P1_fft_freq,transmisibilidad_DL_A1_dB) plot(B1_P1_fft_freq,transmisibilidad_DL_A2_dB) plot(B1_P1_fft_freq,transmisibilidad_D0_A_dB) ylabel('Transmissibility [dB]') xlabel('Frequency [Hz]') xlim([0,30e3]) grid on grid minor legend('RW','DW','D0') Appendix 38 title('Transmissibility DL-D0') figure handle=gca handle.XAxis.Exponent=0 hold on plot(B1_P1_fft_freq,transmisibilidad_DSL_A1_dB) plot(B1_P1_fft_freq,transmisibilidad_DSL_A2_dB) plot(B1_P1_fft_freq,transmisibilidad_D0_A_dB) ylabel('Transmissibility [dB]') xlabel('Frequency [Hz]') xlim([0,30e3]) grid on grid minor legend('RW','DW','D0') title('Transmissibility DSL-D0') figure handle=gca handle.XAxis.Exponent=0 hold on plot(B1_P1_fft_freq,transmisibilidad_DS_A1_dB) plot(B1_P1_fft_freq,transmisibilidad_DL_A1_dB) plot(B1_P1_fft_freq,transmisibilidad_DSL_A1_dB) yline(0) ylabel('Transmissibility [dB]') xlabel('Frequency [Hz]') xlim([0,30e3]) grid on grid minor legend('DS','DL','DSL') title('Transmissibility RW') figure handle=gca handle.XAxis.Exponent=0 hold on plot(B1_P1_fft_freq,transmisibilidad_DS_A2_dB) plot(B1_P1_fft_freq,transmisibilidad_DL_A2_dB) plot(B1_P1_fft_freq,transmisibilidad_DSL_A2_dB) yline(0) ylabel('Transmissibility [dB]') xlabel('Frequency [Hz]') xlim([0,30e3]) grid on grid minor legend('DS','DL','DSL') title('Transmissibility DW') 39 figure handle=gca handle.XAxis.Exponent=0 hold on plot(B1_P1_fft_freq,Pmean_fft_BX_A1_smoothed_D0) plot(B1_P1_fft_freq,Pmean_fft_BX_A1_smoothed_DS) plot(B1_P1_fft_freq,Pmean_fft_BX_A1_smoothed_DL) plot(B1_P1_fft_freq,Pmean_fft_BX_A1_smoothed_DSL) yline(0) ylabel('A [m/s^2]') xlabel('Frequency [Hz]') xlim([0,30e3]) grid on grid minor legend('D0','DS','DL','DSL') title('FFT-RW') figure handle=gca handle.XAxis.Exponent=0 hold on plot(B1_P1_fft_freq,Pmean_fft_BX_A2_smoothed_D0) plot(B1_P1_fft_freq,Pmean_fft_BX_A2_smoothed_DS) plot(B1_P1_fft_freq,Pmean_fft_BX_A2_smoothed_DL) plot(B1_P1_fft_freq,Pmean_fft_BX_A2_smoothed_DSL) yline(0) ylabel('A [m/s^2]') xlabel('Frequency [Hz]') xlim([0,30e3]) grid on grid minor legend('D0','DS','DL','DSL') title('FFT-DW')