A novel excitation method for pyroshock simulation [original]

Article

A novel excitation method for

pyroshock simulation

Behnam Houshmand

, Alexander Lacher

, Nikolas Juengel

Lukas Prasol

, Utz von Wagner

and Eckart Uhlmann

Abstract

Pyroshocks are structural responses to transient excitation caused by the essential use of pyrotechnic devices in aero-

space applications. In order to avoid damage in aerospace structures due to pyroshocks, tests are performed on earth

prior to launching space modules. In these tests, explosive loads are often replaced by alternative excitation methods

such as hammer pendulums or shakers simulating on earth the impact taking place in space. However, there does not yet

exist an adequate excitation method satisfying all requirements of a fast, reliable, predictable and repeatable test setup.

Whereas hammers are poorely controllable in terms of generating desired shock spectra, shakers show limitations in

terms of the bandwidths of up to 10 kHz which are prescribed in the test specifications.

The authors present a novel contactless and non-destructive excitation method for pyroshock test devices based on a

mechatronic coupling by applying Lorentz forces to the carrying structure. For generating the corresponding magnetic

field, the capacitor of a Resistor-Inductor-Capacitor RLC resonator circuit is initially charged and then discharged leading

to high currents in the coil which is placed close to the carrying structure. Latter is then inducing a counter current in the

aluminum structure which reacts with high multidirectional Lorentz forces. Any adjustments are done by tuning the

properties of the circuit such as initial charge, capacitance and inductance. By connecting several different coils, frequency

modulation and by splitting the currents more complex signals can be generated matching the natural frequencies of the

structure. Almost all disadvantages of common excitation methods are eliminated by the proposed mechanism.

Keywords

Pyroshock, simulation, excitation, wave propagation, SRS, magnetic field, Lorentz force, RLC resonator

1. Introduction

Common existing pyroshock test facilities are described

in various references such as Bernaudin et al. (2008),

Davie and Bateman (1995), Henderson and Piersol

(2003) and Lalanne (2005). The most recent develop-

ments are found in Ba

¨ger (2009), Dwyer and Moul

(1988), Filippi et al. (1999), Kiryenko et al. (2005),

Schweickert (1997) and Smith (1986) which all have

the goal of simulating far and mid ﬁeld pyroshocks in

order to meet the strict requirements of the pyroshock

test speciﬁcations in terms of the shock response spec-

trum (SRS), see e.g. Bernaudin et al. (2008). An over-

view of further articles concerning pyroshock themes

can be found in Lee et al. (2012). Far and mid ﬁeld

pyroshocks address signal bandwidths of up to

10 kHz whereas all devices presented are based on a

mechanical impact between a striker and a structure

carrying the test specimen which is either performed

in-plane or out-of-plane. The approximate maximum

acceleration levels reach up to 5000 g resulting in very

high amounts of energy which have to be transferred to

the structure within very small time periods. In the

AneCom AeroTest GmbH, Design and Analysis Department, Wildau,

Germany

Rolls-Royce Deutschland, Rotatives Department, Blankenfelde-Mahlow,

Germany

Department of Applied Mechanics, Technische Universita

¨t Berlin,

Germany

Institute for Machine Tools and Factory Management, Technische

Universita

¨t Berlin, Germany

Corresponding author:

Alexander Lacher, Rolls-Royce Deutschland, Rotatives Department,

Blankenfelde-Mahlow, Germany.

Email: alexander.lacher@rolls-royce.com

Received: 25 March 2014; accepted: 19 November 2014

Journal of Vibration and Control

2016, Vol. 22(20) 4247–4258

!The Author(s) 2015

Reprints and permissions:

sagepub.co.uk/journalsPermissions.nav

DOI: 10.1177/1077546315573904

jvc.sagepub.com

existing test, setups based on mechanical impact are

categorized into four diﬀerent groups which are (a)

sphere against rod, (b) sphere against plate, (c) sphere

against disk and (d) rod against disk. Cases (a) and (c)

have been investigated by developing a semi-analytical

solution procedure, see Lacher et al. (2012a), whereas

computation algorithms of cases (b) and (d) can be

found in Lacher et al. (2011) and Lacher (2011).

Additionally, a recently published detailed analytical

study of diﬀerent impact scenarios based on a CPU

time saving asymptotic approach can be found in

Caresta et al. (2014). The corresponding algorithms

allow for a rough prediction of accelerations and result-

ing SRS on carrying structures at arbitrary points in

terms of the impact by a striker. FE based investiga-

tions of pyroshock tests can be found in e.g. Barboni

et al. (2003), Lacher (2012b) and Kiryenko et al. (2005).

Next to the mentioned passive mechanical strikers,

also electrodynamic shakers and (based on inves-

tigations conducted at Chair of Mechatronics and

Machine Dynamics at TU Berlin) piezoelectric staple

actuators can be used in order to transfer shocks into

carrying structures, see Houshmand (2010) and Roggan

(2012). In both methods, signals can be designed by

using input voltages in terms of wavelets, see e.g.

Bernaudin et al. (2008). In some applications, explo-

sives are used in order to achieve high acceleration

levels. The range of presently existing excitation meth-

ods for pyroshock simulation can thus be written as (1)

explosives, (2) mechanical strikers, (3) electrodynamic

shakers and (4) piezoelectric staple actuators. In Jang

and Lee (2014) a laser-induced shock excitation gives

ﬁrst promising results in terms of a new non-destructive

excitation method but has to be further expanded for

test application purposes. Also, in Stewart et al. (2014)

a hydraulic blast simulator is presented as an alterna-

tive way to common explosives. However, the degree of

destruction of the involved materials is non negligible.

Whereas case (1) is delimited by the controllability

and repeatability of the test procedure, case (3) shows

its limitations at frequencies higher than 3kHz where

shakers tend to demand extremely high power.

Although as well controlable as shakers, piezoactuators

(4) are limited with respect to the acceleration ampli-

tude in the SRS graph. So far, no excitation method

other than a mechanical striker (2) is able to meet the

common requirements of reliable test setups for reach-

ing the high acceleration levels at high frequency band-

widths up to 10kHz. However, its main disadvantages

are the poor controllability caused by its laborious

handling and the fact that inﬂuencing the shock

signal is related to change hammer head materials,

radius of curvature impact velocity and so on.

Therefore, the authors present a novel contactless

excitation method combining advantages of all

methods mentioned before. Its working principle is

inspired by high speed forming technology, see

Uhlmann and Zieﬂe (2010), Unger et al. (2006) and

Xu et al. (2008), based on a simple RLC resonator

circuit charged at a speciﬁc voltage. During the dischar-

ging process, the resonator’s coil transfers a transient

magnetic pressure to a carrying metal plate leading to a

Lorentz volume force. This very high dynamic load

results in the propagation of transversal and longitu-

dinal waves in the carrying structure and the test spe-

cimen. First tests revealed that, as an example, SRS

peak levels of up to 5000 g are obtained on a 80 kg

carrying plate by charging a capacitor bank by an

energy amount of 1 kJ. In fact, the plate stayed entirely

unaﬀected and no evidence of plastic deformation in

terms of indentation or damage could be found after-

wards. In addition, the magnetic ﬁeld produced during

the electrical impact is, due to its strong spatial decay-

ing characteristics (order of r

3

in terms of the distance

r from the coil), not assumed to aﬀect any electrical

components of the test specimen.

Further reﬁnements of the technology are investi-

gated such as connecting higher numbers of RLC res-

onator circuits additionally switched by ﬁeld-eﬀect

transistors in order to produce wavelets.

2. Experimental setup and

working principle

In order to achieve high acceleration levels on the car-

rying plate, the experimental setup (see Figure 1)

requires a power electronic pulse generator (here: FA-

1440-60-SW from Chair of Machine Tools and Factory

Management, TU Berlin, see Figure 2) based on an

RLC. The pulse-like excitation of the aluminum plate

(placed on non-locating bearings) is realized by a ﬂat

axis-symmetric coil, see Figure 2. The coil is located

outside the device on a rigid foundation beneath the

aluminium plate (Figures 1 and 3(a)). In a ﬁrst step,

the capacitor banks are charged by an arbitrary

Figure 1. Setup of the proposed pyroshock test facility

(top view).

4248 Journal of Vibration and Control 22(20)

amount of energy (which can be used to control the force

amplitude), see Figure 3(a). By the use of a high-current

switch, the capacitors are discharged leading to large cur-

rents (up to several hundred kA) that generate an intense

magnetic ﬁeld inside the tool coil (Figure 3(b)).

This magnetic ﬁeld induces eddy currents at the sur-

face of the plate which are running in the opposite dir-

ection compared to the primary currents in the tool

coil. Due to the current, inside the coil a Lorentz

volume force distribution is generated acting on the

aluminum plate. A Rogowski coil and a vibrometer

are used for process measurement. The Rogowski coil

measures induced sinusiodal currents during the

discharging process whereas the vibrometer detects

the velocity at a point on the carrying plate (or speci-

men) occurring during the excitation process. Because

of the modular arrangement of the pulse generator’s

capacitors, it is possible to vary the system’s capacity.

Hence, beside the amplitude also the discharging fre-

quency of the excitation process can be controlled.

3. Magneto - thermo - structural

modeling

Developing a multiﬁeld model making pyroshock test

results predictable according to the proposed method

Figure 3. Working principle of the proposed pyroshock test facility (side view), (a) charging and (b) discharging process.

Figure 2. Instrumentation utilized, pulse generator (left) and coil (right). Reproduced with kind permission from the Institute for

Machine Tools and Factory Management (IWF), TU-Berlin.

Houshmand et al. 4249

requires the complex interaction of multiple ﬁelds in

physics. In the presented excitation technique the coil

of a discharge circuit is exciting an aluminium carrying

plate by repulsive transient Lorentz volume forces

which are produced by the discharged current. The

Lorentz volume forces result in the propagation of

mechanical waves through the carrying structure lead-

ing to an acceleration ﬁeld. In terms of the purpose of

pyroshock testing, the setup can be used as a test facil-

ity at which the input parameters are basically electrical

ones such as the charging voltage and the circuit char-

acteristics, ﬁnally leading to a mechanical ﬁeld output

in terms of the SRS. A multiﬁeld FE-model has been

developed which actively couples the electromagnetic,

thermal and structural ﬁelds. The model deals with

quasi-static Maxwell equations, impulse and energy

balances instantly. The discharging process takes

about 200 ms which is slow enough to allow for the

assumption of quasi-static electromagnetism. For

describing the wave propagation, dynamic momentum

balances are considered. The resistive heat generated

due to induction propagates in the medium according

to Fourier’s heat transfer law. Thermal analysis ﬁnds its

importance in the fact that material softening may

appear locally in the vicinity of the exciting electro-

dynamic coil if the testing object is large compared to

the coil’s dimensions. In this case, an enormous dis-

charging energy is required in order to achieve the

high acceleration levels of the pyroshock test speciﬁca-

tions. As also practiced in metal forming processes

which are based on considerably higher energy

amounts, the authors decided to include thermal cou-

pling in the model. Lorentz volume forces are strongly

dependend on the coil’s geometry which inﬂuences the

inductance and, consequently, the force distribution.

As it will be presented in the following section, the dis-

charge frequency depends on the total inductance, cap-

acity and active resistance which requires a study of the

discharge circuit.

3.1. Excitation circuit

Figure 5 represents the diagram of the excitation cir-

cuit. In the primary circuit C,Liand Ridenote for the

equivalent capacity of the capacitor banks charged by

the voltage U0, the total inner inductance and the resist-

ance of the high voltage discharge machine respectively.

L1and R1represent the self inductance and electrical

resistance of the coil. Accordingly, in the secondary

circuit L2and R2assume to be the active self induct-

ance and resistance of the carrying plate. Mrepresents

the mutual inductance between the coil and the testing

object varying strongly with the initial distance and

material between coil and carrying plate.

For a better understanding of the discharging process,

the excitation circuit (Figure 5) can be replaced by an

equivalent RLC resonator circuit, as presented in Figure 6.

With the assumption of both, negligible geometrical

and material nonlinearity in all three ﬁelds, the RLC res-

onator circuit can be considered having constant resistive,

inductive and capacitive elements, which, as described

e.g. in Winkler (1973), has the well known analytical solu-

tion for its resulting linear diﬀerential equation

dt LiþLa

ðÞI1tðÞþ RiþRa

ðÞI1tðÞþZt

CI1t0

ðÞdt0¼U0

ð1Þ

Figure 4. Laser Vibrometers and digital signal processing

devices utilized. Reproduced with kind permission from

Alexander Lacher (Lacher, 2011).

Figure 5. Scheme of excitation circuit.

4250 Journal of Vibration and Control 22(20)

with

La¼L1M



L2,Ra¼R1þM



R2ð2Þ

The resulting discharge currents for the primary and

secondary circuit can be written as follows

I1tðÞ¼U0!Cetsin !t,

I2tðÞ¼M

U0Cetþ!etsin !tþ’ðÞ



ð3Þ

in which

!¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

iþLa

ðÞ

p,¼R2

,¼1

RiþRa

LiþLa

’¼sin1R2

L2ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

iþLa

ðÞ

 ð4Þ

3.2. Numerical model

Figure 7 schematically shows the numerical simulation

procedure.The FE simulation considers the interactive

coupling of the magnetic, thermal and structural ﬁelds

sequently for each timestep which allows a realistic

approach of the system’s behaviour. In order to carry

out such a simulation four physics environments are

deﬁned.

The useful outputs of the ﬁrst electromagnetic ana-

lysis are the Joule heat generation rate [Watt] and the

Lorentz Forces. In the sequent thermal analysis the

heat generation rate of the pervious electromagnetic

analysis is interpolated onto the thermal domain in

order to calculate the temperature distribution.

Sequently, in the structural analysis the Lorentz

forces will interpolated from the previous electromag-

netic analysis utilizing the temperature distribution

from the previous thermal analysis. The primary

Figure 7. Schematic diagram.

Figure 6. Equivalent of excitation circuit.

Houshmand et al. 4251

output of the structural analysis are the displacements

of the test specimen and the coil, which may be large

enough to eﬀect the inductivities and resistivities. In

addition, the resulting themperature distribution from

the thermal analysis can also change the resistivities

and inductivities. To monitor this eﬀect the second elec-

tromagnetic analysis was implemented in each loop in

order to calculate the resistivities and the inductivities.

The displacements which were calculated in the previ-

ous structural analysis are used to update the geome-

tries of both the ﬁrst and second electromagnetic

analysis and also the thermal analysis (this geometry

update is called mesh morphing). Having this quick

introduction of the simulation loop (see Figure 7), it

is important to look into the theoretical background

of each physics environment in more detail.

The ﬁrst physics environment contains a magneto-

static analysis with static domain for air, conductor

domain for coil and eddy current domain for plate

elements to calculate the Lorentz forces on coil and

plate and the heat generation rate due to joule heating.

For a homogeneous, isotropic electroconductive

material, like most metals, the Lorentz forces can be

described as a cross product of the current density

vector jx,tðÞand the magnetic ﬂux vector Bx,tðÞby

means of

fx,tðÞ¼jx,tðÞ



Bx,tðÞN

Am



;ð5Þ

whereas the total excitation force FðtÞresults from inte-

gration over the volume V2of the carrying plate as

follows

FðtÞ¼ZV2

fx,tðÞdv:ð6Þ

The equation (5) serves as the basic magneto-struc-

tural coupling equation between the excitation circuit

and the carrying plate.

To calculate the magnetic ﬂux density vector Bx,tðÞ,

the magnetic ﬁeld intensity vector Hx,tðÞ, the electric

ﬂux density vector Dx,tðÞ, the electric ﬁeld intensity

vector Ex,tðÞand the electric current density jx,tðÞin

continua with the assumption that the electric ﬂux

density vector Dx,tðÞis constant in time, the quasi-

static Maxwell’s equations

rot Hx,tðÞ¼jx,tðÞ ð7Þ

Figure 8. Finite element model.

Table 1. Material properties.

Material properties Air Copper Aluminium

Relative permeability ½ 1 0.999 1.00002

Electrical resistivity ennm½ –17 28

Thermal conductivity kWnm1nK



– 400 237

Specific heat CJnkg1nK1



– 390 910

Mass density kgm3

 1 8900 2700

Young’s modulus E GPa½ – 115 70

Poisson’s ratio ½ – 0.34 0.35

Table 2. Circuit setups for parameter study.

Setup

kJ½U0kV½LaH½C½FRa½!½s1½nH1

1 0.4 1.825 2.183 240 0.0616 45.87 14116

2 0.8 2.582 2.183 240 0.0616 45.87 14116

3 1.3 3.291 2.183 240 0.0616 45.87 14116

4 0.8 1.825 2.063 480 0.0431 33.30 10453

5 1.3 1.972 1.03 700 0.0185 37.70 8980

4252 Journal of Vibration and Control 22(20)

are applicable. In order to study the excitation and the

system’s response by taking into account the consider-

ations shown in Figure 7, a 2D rotation-symmetric

ﬁnite element model was developed, using the Ansys

APDL (Ansys Parametric Design Language) software.

It is illustrated in Figure 8, in which the hemisphere on

top of the model, the circluar section on the bottom and

the small rectangulars denote for the air, the aluminium

plate and the copper coil’s rings respectively (for mater-

ial properties see Table 1).

In the present simulation of circular coil and plate

(diameter D¼1 m, thickness h¼0:04 m) the eddy cur-

rent density has tangential components only whereas

the magnetic ﬂux vector is directed in radial and axial

direction. Therefore the correlation between the

induced eddy current in the carrying plate j2x,tðÞand

it’s equivalent in excitation circuit from Figure 5 is

described as follows

I2tðÞ¼ZA2

jx,tðÞdnx,tðÞand dnx,tðÞ¼dAx,tðÞeFx,tðÞ

ð8Þ

with x¼r,F,zfgrepresenting the position of each

material point in cylindrical coordinates and the area

A2representing the cross section area of the test

object. According to equation (5) with equation (3)

and considering the correlation (equation (8)), the

mechanical excitation fx,tðÞtakes place at discharge

frequency !at a phase diﬀerence of ’with respect to

the discharge current in the coil. The phase diﬀerence

depends on the resistance R2of the carrying plate

varying with its thickness. For a thick testing object

the resistance is negligible and, consequently, there is

no phase diﬀerence between the discharge current in

the coil and the excitation, see also Winkler (1973)

and Xu et al. (2008). Additionally, it is important to

mention that, concerning the coil’s FE modeling, the

authors assume each of the 20 concentric copper rings

(small rectangulars in r.h.s. of Figure 8) to be one

separate coil with one separate winding, separate

dimensions and discharging circuit. In order to

approach one ﬂat coil in the simulation, all 20 rings

are linked to one single current I1.

A thermal transient analysis was applied as the

second physics environment for coil and plate elements

Figure 9. Excitation (discharge) currents I1according to Figure 5 from setups in Table 2.

Figure 10. Simulated force FðtÞon a circular plate resulting from Lorentz body forces according to (6) from setups in Table 2.

Houshmand et al. 4253

to calculate the temperature distribution due to Joule

heating. Consequently a structural transient analysis as

the third physics environment was used to calculate the

displacements considering the balance of momentum

after discretization

Mfgf

€

ugþ Dfg

ufgþKfgufg¼ f

 ð9Þ

in which Mfg,Dfgand Kfgare the global mass,

damping and stiﬀness matrixes. Vector ufg is the

global displacement vector and f

is the descretized

Lorenz forces vector. Finally, the last physics

environment contains a magnetostatic analysis with

static domain for all elements to calculate the active

inductance and resistance of the system in each

timestep.

At the end of each loop, the nodal coordinates of

each node were updated to the resulting displacement

to be used in the magnetostatic and thermal analysis. It

is important to point out the fact that the nodal coord-

inates for each node had to be reset to material coord-

inates before carrying out the structural analysis to

prevent the wrong calculation of the stresses. The phys-

ical properties of the materials are assumed to be con-

stant due to the very low changes in temperature. On

the ﬁrst sight, this assumption seems to be in contra-

diction to the discussion in the beginning of this section

Figure 12. Experimental setup; locations of measuring point and coil (top view).

Figure 11. Simulated SRS at point P from Figure 8, circular plate.

4254 Journal of Vibration and Control 22(20)

concerning the temperature dependence of the mater-

ial’s strength. However, concerning the system param-

eters considered in the present investigation, it ﬁnally

turned out that the maximum local temperature change

is approximately 30 K and can be neglected in terms of

the temperature dependence of material parameters.

After calculating the resistance and inductance it

turned out that these parameters can be assumed to

be constant due to small displacement of the carrying

plate relative to the gap between coil and plate which

validate the assumption of constant gap between coil

and carrying plate and consequently lineary behaving

discharge circuit. The displacement of the carrying

plate is, just at the discharge time, very small relative

to the gap between the coil and the plate.

4. Results

A parameter study of ﬁve diﬀerent setups has been

done by varying the discharging current’s parameters

from equation (3) according to Table 2. In setups 1, 2

and 3 diﬀerent capacitor charges Ecand, hence, diﬀer-

ent charging voltages U

are investigated based on one

unaltered circuit with values La,C,Raaccording to

Figure 6. Setups 4 and 5 additionally adress higher cap-

acitor banks and, therefore, diﬀerent circuit character-

istics. For each setup the SRS at point Pfrom Figure 8

is calculated in order to study the inﬂuence of param-

eter variation.

Figure 9 shows a comparison of the analytically

and experimentally determined currents I1according

to equation (3) in Figure 5. It can be distinguished

between setups 1, 2, 3 where, due to the constant

circuit characteristics, only the current’s amplitude

increases with increasing charging voltage U0

and setups 4, 5 additionally showing diﬀerent reson-

ance frequencies !. These tendencies can be recog-

nized in Figure 10 illustrating the resultant of the

repulsive Lorentz force simulated based on the FE-

model.

Figure 14. Outlook: producing high-power wavelet-type excitation by frequency modulation of discharge currents.

Figure 13. SRS from experiment, rectangular plate.

Houshmand et al. 4255

In Figure 11, the SRS graphs computed with respect

to the transversal acceleration data are shown in terms

of varying parameters from diﬀerent setups. Basically,

a shift of the SRS graph to higher amplitudes can be

observed. Only a negligible eﬀect on the SRS shape by

changing the circuit characteristics is resulting from the

parameter changes, at least in the range of the ﬁve

setups.

Additionally, experiments on a high voltage dis-

charge machine for high speed forming have been

performed incorporating a quadratic 1 m2aluminum

carrying plate at thickness h¼0:03 m, see Lacher

(2011c). The coil was located at one corner beneath

the plate, whereas the acceleration data during the

discharge process have been measured at the center

of the edge opposite to the excitation, as seen in

Figure 12.

The experimental SRS results obtained at the

measuring point (z-direction) are shown in Figure 13

where special attention has to be turned on the extreme

levels of maximum acceleration reaching up to 10,000 g

while, due to the distributional characteristics of the

volume forces, no evidence of damage or indentation

could be observed subsequently to the experiments

conducted.

Considering conventional pyroshock testing

techniques, comparable levels are only achieved by

the use of explosives which, however, show a wide

range of diﬀerent disadvantages such as poor control-

lability and repeatability as well as high damage

potential.

At this point the authors would like to point out the

fact that a comparison of SRS developments between

the analytical and experimental results in this paper has

not been in the focus of the investigation. Since the SRS

projects the dynamic response of the structure to a

sudden excitation and is highly aﬀected by the vibration

modes of the structure a rotational symmetric domain

has been selected for the analytical study, also for the

purpose of reducing CPU time. On the other hand, a

quadratic plate of the same dimension as the analytical

domain diameter has been chosen for handling reasons

in order to pursue the experimental part. Therefore the

SRS resulting from both analytical and experimental

works are not from the same basis and are not really

conform to comparison. However, the authors’ inten-

tion of pointing out the controllability and also the

predictability of both, the analytical and experimental

SRS tendencies has been successfully presented in this

study.

5. Conclusions and outlook

The present paper introduces a possible contactless

excitation method for pyroshock simulation showing

the potential of replacing existing techniques due to a

combination of their advantages. The method is based

on the discharging process of a simple RLC resonator

circuit, the coil of which is approached to a carrying

aluminum plate. During the discharging process, an

eddy current induces a transient locally distributed

repulsive Lorentz body force leading to remarkable

acceleration levels within a large bandwidth. The

authors present a sophisticated multiﬁeld model includ-

ing the exciting circuit as well as the coupling beween

the coil, and the plate by adressing magnetic, thermal

and structural coupling. Also, experiments with a high

voltage discharge machine and a common carrying

structure have been performed leading to very promis-

ing results in terms of the potential for practical pyr-

oshock test applications. Regarding the repeatability

and controllability as well as the broadband acceler-

ation levels and the nearly vanishing structural

damage of the testing equipment, the present mechan-

ism’s performance exceeds by far all existing test

facilities.

Considering the possibilities of inﬂuencing the SRS

graph in order to meet test speciﬁcations the presented

mechanism oﬀers several comfortable approaches

which, as an outlook, are proposed by the authors as

follows:

1. Wavelet-type excitation by frequency modulation of

discharge currents

As seen in Figure 14, the idea consists of charging a

number of RLC circuits with identical characteris-

tics. The discharge current of these circuits is then

frequency modulated by harmonically switching the

current with the help of power transistors.

The switching frequency can be tuned and, hence, serve

as system parameter in order to inﬂuence the accel-

eration signal at the specimen’s location. An amp-

lifying eﬀect of inﬂuencing the SRS can be procured

by adjusting the switching frequencies to the reson-

ance frequencies of the stucture carrying the speci-

men. Compared to common wavelet excitations by

piezoelectric actuators (see e.g. Bernaudin et al.

(2008) and Roggan (2012)) which are (due to limited

deﬂection capabilities) usually limited by low trans-

ferable signal bandwidth and/or power, the pro-

posed mechanism has a signiﬁcant advantage: the

high-power discharge current serves as a carrier of

the low-power frequency excitation signal. The large

acceleration amplitude coming from the high-power

discharging capacitor is frequency modulated by a

comparably low-power signal from the power

switches. This allows for both in parallel: high

power but controlled signal which is a novel com-

bination compared to existing pyroshock test excita-

tion methods. The method which has been

4256 Journal of Vibration and Control 22(20)

successfully performed in Roggan (2012) with the

help of piezo-actuators can be applied to the

method presented.The desired SRS from the test

speciﬁcations is used to serve as a reference signal

for a closed loop control circuit which would directly

lead to a preset SRS at a speciﬁc point on the spe-

cimen without the need of numerical simulation

2. Excitation by multiple coils

An alternative way of inﬂuencing the SRS can be found

in engaging a number of diﬀerent coils, each of them

having its proper characteristics and, hence, separate

discharge currents acting on the carrying plate in

terms of a combined and easily controllable

Lorentz body force. Both proposed mechanisms

show a promising way of inﬂuencing the character-

istics of SRS in a purely electrical and controllable

manner. Finally, an application to near ﬁeld pyr-

oshock tests is imaginable which could replace the

shock excitation by explosives.

Conflict of interest

The authors declare no conﬂict of interest.

Funding

This research received no speciﬁc grant from any funding

agency in the public, commercial or not-for-proﬁt sectors.

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