Shock Response Spectrum Research Articles

Wave-based analysis of dual acoustic black holes for anechoic termination of shock testing devices

Shock testing is an important issue for the survivability of an equipment under shock environment in aerospace and military industries. One of the problems faced in conventional shock testing devices is the need for redesigning of the geometry whenever the responses to different shock environments are tested. To circumvent the redesigning processes, a structure with two ‘acoustic black holes (ABHs)’ on both ends, referred to as the beam with dual ABHs, is proposed as a shock testing device. The beam with dual ABHs is capable of simulating diverse shock environments by controlling the applied force because it can be regarded as an infinite beam at high frequency range with the aid of the anechoic terminations by the ABHs. To systematically investigate the beam with dual ABHs, we develop a wave-based method that uses the reflection matrix of an ABH to perform free and forced vibration analyses. From the analyses on frequency response function and shock response spectrum of the beam with dual ABH, it is suggested that the beam with dual ABHs is feasible as a semi-permanent shock testing device.

Dynamic analysis of laser shock response: Experimental and numerical studies

Abstract Laser is an excellent shock source with the advantages of non-contact, high controllability and broadband frequency, which has great potential to replace traditional mechanical impact and simulate pyroshock. In this paper, the dynamic response induced by laser shock is studied both experimentally and numerically. Firstly, laser shock tests are conducted. The general characteristics of laser shock response are experimentally investigated, where the effects of transparent overlays and absorbent coatings are evaluated in terms of shock response spectrum. Furthermore, a finite element (FE) model is developed and validated by comparing simulation and experimental results. Based on FE model, the effects of power density, pulse duration, and spot size of laser on the dynamic response are evaluated. The results demonstrate that laser shock response has fantastic high-frequency and broadband-frequency characteristics and shock response spectrum amplitude of laser shock can be obviously improved by adding transparent overlays and absorbent coatings. The amplitude of shock response spectrum is in quadratic correlation with laser power density. Laser pulse duration significantly influences the slope of shock response spectrum, but power density and spot size of laser have little effect on the slope.

Simulator of pyroshock environment and effect rules of its adjustable parameters

During the launching of spacecraft, the on-board devices will undergo a series of pyroshock environments. In order to verify the reliability of these devices under these pyroshock environments, all of them are needed to take the shock test before launching. This paper has carried out an in-depth research on the simulation method of the pyroshock based on the true explosive excitation. In this study, a simulator containing multiple adjustment parameters is presented and the safety is considered by the design of the protective cover. And the working process of this setup is simulated with the explicit dynamic codes LS-DYNA. What’s more, the effects of the adjustment parameters on the three factors of shock Response Spectrum (SRS) of the resonant board are explored carefully. The rules achieved in this paper are verified by a typical example. The results indicate that the improved simulator can avoid the danger of explosive and make full use of the advantage of actual explosive excitation. And the test condition can be quickly realized at the simulator according to the effect rules of the three adjustable parameters.

Stochastic response analysis of elastic and inelastic systems with uncertain parameters under random impulse loading

Response analysis of structural systems under impulse loading is extremely important for appropriate design against accidental loads such as blast. Herein, the response of elastic and inelastic single degree of freedom (SDOF) systems with uncertain parameters under random impulse loadings is investigated. Four different types of impulse loading profiles (rectangular-, half-sine wave-, and two triangular-shaped), having same duration and impulse, are applied to the SDOF systems with varying fundamental periods of vibration. Non-sampling stochastic simulation procedure based on the generalized polynomial chaos (gPC) expansion technique is used to model the dynamic response of the SDOF systems duly considering the uncertainties. Effects of uncertainty levels in the input parameters on the peak response and sensitivity of the peak response to the uncertain input parameters are investigated in detail. It is concluded that the propagation of uncertainties from the inputs to the response quantities is more prominent in stiffer systems. Amongst the impulse profiles considered, those pulses with sudden rise in force lead to higher deviations in response of the systems for a given uncertainty scenario. Further, it is observed that the shock response spectra of all the impulse loads are more sensitive to the uncertainties when time periods are less than or close to the loading duration. Furthermore, the gPC expansion-based simulation technique is observed to be an efficient alternative to computationally demanding conventional Monte Carlo (MC) simulation for quantifying the uncertainties.

Analytic Approach to the Shock Response Spectrum of Friction Joints

Because of dry friction in the contact surface of bolted, riveted, and clamped band joints, they are potentially suitable for mitigating vibration in structures. This capability is activated if excitation vector has a component on the contact surface, and this depends on the joint geometry. A fundamental study on the shock response spectrum (SRS) of a single-degree-of-freedom model of joint containing Jenkins element as a bilinear hysteresis for dry friction modeling is considered here. The equation of motion is analytically solved for extracting the SRS to rectangular base acceleration pulse. The effect of various physical parameters, influenced by joint geometry and fastener pretension, on the acceleration transmissibility is investigated. The highest level of SRS is studied when physical parameters vary and optimum values of these parameters are determined for minimizing the SRS. The consequence of this fundamental study can be useful for designing joints as a dissipation mechanism in structures. In the solution process before extracting the SRS, some phenomenological studies are carried out on stick/slip phenomenon in the joint.

On the analysis of nonlinear dynamic behavior of an isolation system with irrational restoring force and fractional damping

An archetypal isolation system with rational restoring force and fractional damping is proposed and investigated based on the nonlinear mechanism of geometric kinematics. The equations of motion of this nonlinear isolator subject to nonlinear damping and external excitation are derived based on the Lagrange equation. For the free vibration system, the nonlinear irrational restoring force, nonlinear stiffness behaviors, and fractional damping are investigated to show the complex transitions of multi-stability. For the forced vibration system, the analytical expressions of force transmissibility of the nonlinear isolator with single-well potential under the perturbation of viscous damping and harmonic forcing are formulated by applying the harmonic balance method. The shock response spectra of the perturbed system subject to half-sine input are evaluated by the maximum responses. The Melnikov analysis and empirical method are employed to determine the analytical criteria of chaotic thresholds for the homoclinic orbit of the perturbed system with symmetric double-well characteristics. The numerical simulations are carried out to demonstrate periodic solutions, periodic doubling bifurcation, and chaotic solutions. The maximum displacements have been obtained to show the isolation characteristics in the case of chaotic vibration.

Shock response prediction of the typical structure in spacecraft based on the hybrid modeling techniques

In order to solve the failure of traditional methods in the response prediction for the complex spacecraft under the wide frequency shock load, this paper provides the FE-SEA (Finite Element-Statistical Energy Analysis) hybrid modeling technique to improve the virtual mode synthesis and simulation (VMSS). Taking the L-shape typical structure as an example, the research is developed through the numerical analysis and experiment verification. In the FE-SEA hybrid model of the typical structure, the two honeycomb boards which have a higher modal density are built as the SEA model, while the connection beam that has a larger stiffness is established as FE model. And then the hybrid model is computed with the VMSS code, giving the transient response results. A shock experiment for the typical structure is carried out to verify the correctness of the methodology above. The results indicate that the numerical results have the similar trend and magnitudes with the ones of the experiment in time domain, and the shock response spectrum (SRS) of the numerical results can realize the ±6 dB tolerance limit compared with the experiment results. This paper finds that the FE-SEA hybrid modeling techniques for the typical structure can effectively overcome the problem of the dynamic differences between the substructures under the excitation of shock load, and the combination of FE-SEA and VMSS has the ability to predict the shock responses of the typical structure accurately. The research methods and conclusions achieved in this paper are expected to further extend to the shock response calculation of the complex spacecraft structures.

Calculation of the shock response spectrum of the prestressed steel cable

The abrupt fracture of prestressed steel strand will form a great unloading impact force, which will influence the displacement and internal force of the remaining structure. Shock response spectrum method can reduce the computation and ensure the accuracy. In order to obtain the shock response spectrum of the steel strand at the moment of failure, this paper proposes to solve the dynamic response of a single degree of freedom structure after cable break through programming under the premise of knowing the failure time of the strand and the corresponding cable tensioning. We select several unloading curves that are the closest to the test, and solve the response spectrum of the broken cable under different failure time and damping, finally, the response spectrum method is compared with the finite element method by numerical simulation. It can be found that the dynamic coefficient will show different trends due to the change of unloading methods. In the same unloading method, the failure time has little impact on the shock response spectrum, but the impact of damping on the shock response spectrum is very obvious.

Visualization of pyroshock wave reduction by insulator using a laser shock based simulation method

Various pyro-devices are used in space structures because of their high power-to-weight ratio, high reliability, and compact size. However, when a pyro-device fires, it generates a strong, high-frequency shock wave called a pyroshock wave, which causes high-frequency-sensitive electronic equipment to malfunction. Therefore, it is important to analyze and minimize pyroshock waves near electronic equipment to prevent damage. In this paper, we propose a shock wave scanning method by a Q-switched laser to analyze shock reduction and visualize shock wave propagation in a real-world complex structure. This technique was applied to evaluate and visualize the shock reduction by rubber insulators mounted in a configuration such that a pyroshock wave is transferred and propagated via a butyl rubber mount to an electronic component mounting panel. An average of 20% in the mean acceleration differences in shock response spectra between an actual pyroshock wave and a laser-simulated pyroshock wave was achieved. The use of the butyl rubber mount reduced the shock wave by 75%, and the reduced pyroshock propagation was quantitatively visualized.

Intelligent Time‐Domain Parameters Matching for Shock Response Spectrum and Its Experimental Validation in Active Vibration Control Systems

Shock response spectrum (SRS) test is a kind of vibration test that uses the principle of equivalent damage to simulate complex shock and vibration environment for evaluating product fragility. However, for a certain SRS, neither an analytical nor a unique inverse time‐domain shock waveform (TSW) exists, making the SRS test a very challenging problem. Synthesis of a TSW using a group of wavelets with different frequencies, amplitudes, and phases is considered to be a very promising method. However, it is challenging to find an optimal group of wavelets since there are hundreds of optimization variables and objective functions. In this paper, a novel intelligent parameter matching method for TSW synthesis is proposed for the SRS test. A variable‐weight method has been introduced to combine the effects of hundreds objective functions so that the optimization problem can be solved by using the genetic algorithm. The frequency response function of the shaking system has been taken into consideration in the calculation of the objective function, so the synthesized TSW can be applied directly to the SRS test. In the optimization process, normalized control factors have been formulated for the optimization variables so that they can be tuned in a reasonable small range to avoid irrationality and accelerating convergence in searching process. The effectiveness of the proposed method has been verified experimentally in two active vibration control systems, in which one contains a 500 N minishaker and the other contains a 1‐ton shaking table. It can be seen from the experimental results that the proposed method can accurately synthesize the input TSW for the shaking system, where the output TSW and SRS can accurately meet the time‐ and frequency‐domain specification.

A Correction Method for the Underwater Shock Signals of Floating Shock Platforms Based on a Combination of FFT and Low‐Frequency Oscillator

Accurate shock loading is required for evaluating and analyzing the shock resistance of warship equipment. However, measured shock acceleration signals contain trend term errors, which cause serious low‐frequency distortion of the shock response spectrum (SRS). We propose a combination method of fast Fourier transform (FFT) and low‐frequency oscillator for correcting the underwater shock signals. Based on the equal displacement line fitted by the measured displacement response data, the Fourier transform spectrum of the shock acceleration signal is corrected for eliminating low‐frequency errors. The results of underwater explosion tests on a floating platform indicate that the average difference between the equal displacement line and SRS in the low‐frequency band (4∼20 Hz) can be reduced from 14.7% to 3.5%, and the mid‐high‐frequency band without the trend term is nearly unaffected. The corrected SRS can faithfully reflect the actual shock environment of the warship equipment at a specific installation location of the floating shock platform.

Hybrid Method of Modal Analysis and Laser Shock Scanning to Visualize the Pyroshock Propagation in a Tension Joint

The use of pyrodevices in the aerospace industry has been increasing because of their ability to implement separation missions with a small weight, for example, space launchers, spacecrafts, and missiles. During operation, pyrodevices generate pyroshock, which causes failures of electronic devices. Recently, a pyroshock simulation method using laser shock has been developed to evaluate the risk of pyroshock before flight mission. However, depending on the structure, the laser shock showed some difficulty simulating pyroshock in the low‐frequency regime accompanying vibration. Therefore, in this study, we developed a hybrid method of numerical modal analysis and laser shock‐based experimental simulation to visualize the pyroshock propagation in all the relevant frequency regimes. For the proof of concept of the proposed method, we performed experiments of explosive bolt‐induced shock and pyrolock‐induced shock in the open‐box‐type tension joint and compared the hybrid simulation results with actual pyroshock. From the results, we obtained the simulated time‐domain signal with an averaged peak‐to‐peak acceleration difference (PAD) of 11.2% and the shock response spectrum (SRS) with an averaged mean acceleration difference (MAD) of 28.5%. In addition, we were able to visualize the simulation results in the temporal and spectral domains to compare the pyroshock induced by each pyrodevice. A comparison of the simulations showed that the pyrolock had an impulse level of 1/12 compared to the explosion bolt. In particular, it was confirmed that the pyrolock‐induced shock at the near field can cause damage to the electronic equipment despite a smaller impulse than that of the explosive bolt‐induced shock. The hybrid method developed in this paper demonstrates that it is possible to simulate pyroshock for all the frequency regimes in complex specimens and to evaluate the risk in the time and frequency domain.

An Improved Adaptive Genetic Algorithm for Optimizing Pyroshock Acceleration Synthesis

The shock response spectrum (SRS) applied to pyroshock designs and tests for space systems does not include input acceleration time history; therefore, it cannot be used directly in structural nonlinear dynamic analysis before acceleration time history is synthesized. Existing synthesis methods typically rely on certain experimental data. In this study, a combined method for pyroshock acceleration synthesis is presented using a series of wavelets at low frequencies and damped sines at medium-high frequencies in the absence of experimental data. To improve the quality of the synthesized SRS, we develop an improved adaptive genetic algorithm (IAGA) with nonlinear adaptive adjustments of crossover and mutation probabilities. Numerical tests show that combined with the developed IAGA, the new method achieves higher accuracy and practicability in the synthesis of pyroshock acceleration compared with traditional methods. This work is expected to improve the calculation accuracy of spacecraft structure response under pyroshock loads.

Prediction method of shock response spectrum in spacecraft component shock test

Prediction method of shock response spectrum in spacecraft component shock test

Experimental and numerical investigation on the shock characteristics of U-notched ZL205A specimens under dynamic mixed-mode loading

Abstract Shock environment assessment and improvement during stage separation is an important issue of concern in aerospace engineering. This paper focuses on shock response caused by dynamic fracture of aluminum alloy separation plate, which usually undergoes mixed mode loading during separation. Based on Split Hopkinson Tensile Bar (SHTB) apparatus, five groups of U-notched ZL205A specimens with different loading angles (0°, 30°, 45°, 60°, and 90°) are designed to simulate mixed mode loading for shock characteristics testing. There piezoelectric accelerometers are used to measure the acceleration time histories, and the maximum shock response spectrum (SRS) are applied for shock data analysis. Meanwhile, the ANSYS/LS-DYNA finite element software is implemented for numerical analysis. The actual fracture angles measured from the recovered specimens are used to describe the actual fracture modes. The numerical and experimental results are in good agreement, showing that the shock response along the specimen’s length and thickness directions increases with the fracture angle, while there is a slight distinction in the specimen’s width direction with different fracture angles. On average, the shock response is more remarkable in pure tensile fracture mode, which is 2.6 times the pure shear fracture mode. As a result, increasing the study of shear fracture component is meaningful for the shock reduction through the structural design of separation plate.

Space-qualified fast steering mirror for an image stabilization system of space astronomical telescopes.

A space-qualified fast steering mirror (SQ-FSM) was designed, built, and tested at the National Astronomical Observatories of the Chinese Academy of Sciences for an image stabilization system of space astronomical telescopes, which is used for the tip-tilt correction of small jitter of the satellite platform; this achieved image stability in a closed-loop manner. Its design primarily faces four challenges involving (1)sustaining the specified sine and random vibration without launch lock, as well as shock response spectrum experiments; (2)surface form error of a clear aperture of ϕ120 mm less than 1/50λ root mean square (RMS, λ=632.8 nm) with a relatively rigid mirror support; (3)resonance frequency of at least 800Hz and as high as possible; (4)minimum reaction force and torque in order to decrease its unfavorable influence on the satellite platform. To achieve these goals, the global optimizations and compromises have to be made throughout the design process. The study reviews the detailed design of the SQ-FSM with respect to the four challenges, mainly by keeping the mirror and its support lightweight, mirror bonding and solidification, actuator and its stiffness, flexure support of the mirror and its holder, material optimization for weight, stiffness, and coefficient of thermal expansion, as well as finite element analysis on statics and dynamics. The performances are also measured and expatiated, including the surface form, resonant frequency, tip-tilt stroke, vibration and shock response spectrum experiments, etc., which validate the performances of the SQ-FSM.

Low-pass-filter-based shock response spectrum and the evaluation method of transmissibility between equipment and sensitive components interfaces

According to the features of the sources of pyroshock and ballistic shock, this study considers the pyroshock and ballistic shock generated by their respective impulsive sources as damped harmonic waves with different frequencies. According to the linear superposition assumption of damped harmonic waves in a linear elastic structure, a shock analysis method based on low-pass-filtered shock signals and their corresponding shock response spectrum (SRS), termed as low-pass-filter-based shock response spectrum (LPSRS), is proposed. LPSRS contains rich information of the frequency distribution of the shock excitation signal. A method to calculate shock transmissibility is proposed based on LPSRS and basic modal information of the equipment structure. LPSRS and SRS curves can be predicted at any given position of the equipment structure. The prediction method is validated by finite element method (FEM) simulation.

Selected methods of accelerated durability tests of systems and subsystems of high mobility vehicles

The analysis of selected methods useful in accelerated testing of systems and subsystems of high mobility vehicles has been presented. The paper contains information about a few methods applied in calculating the load signal in time and frequency domians: Constant Amplitude Loading – CAL, Peak Valley Extraction – PVE, Block Load Sequence – BLS, Statistical Exceedance Method – SEM, Increasing Load Frequency – ILF, Multiaxial Peak Valley Extraction – MPVE, Time Correlated Fatigue Analysis – TCFA, Simple PSD Scaling, Shock Response Spectrum – SRS, Extreme Response Spectrum – ERS, Fatigue Damage Spectrum – FDS. Parameters such as pseudo – damage, equivalent loads and equivalent mileage have been presented as well. Those parameters are useful when the influence of road conditions on durability of the vehicle is compared. An initial assessment has been presented on the example of a tested vehicle of high mobility. The high mobility wheeled vehicle was tested in various on- and off-road conditions at the proving ground test center. After tests the signal of load acting on a chosen element of the vehicle frame was inspected, corrected and analyzed. The goal of testing was to find the method to calculate the remaining useful life of the main part of the vehicle. The results obtained have proved the validity of the adopted accelerated testing procedure for this type of vehicles.

Numerical study on separation shock characteristics of pyrotechnic separation nuts

This paper establishes a finite element model of pyrotechnic separation nuts and simulates the whole separation process based on the explicit dynamic codes LS-dyna with Arbitrary Lagrange-Euler (ALE) algorithm. The separation shock generated in the unlocking process is analyzed in detail and the results reveal that the pyrotechnic explosion shock and strain energy shock are two sources for the whole separation shock. Besides that, the influence of prestress on the separation shock and its two shock sources is also researched. The results show that the prestress could strengthen all three shocks, especially the strain energy release shock. This paper also compares the shock response spectrum (SRS) of the three shocks and finds that the SRS of separation shock is equal to the envelope of the SRS of pyrotechnic explosion shock and strain energy release shock. In the model of this paper, the pyrotechnic explosion shock plays a dominant role in the frequency range of 100 Hz to 10 KHz. The conclusions got in this work are helpful to insight the mechanism of separation shock and can provide a reference for the design of separation nuts.

Damage boundary of structural components under shock environment

This paper studies the damage of structural components (solid structures and electronics) under severe shock environment introduced by intensive impulsive loads. Two types of critical states of shock response spectrum (SRS) are identified, i.e. the critical SRS state governed by the maximum relative displacement and absolute acceleration, and the critical SRS state governed by the maximum pseudo velocity. The damage boundary of a given component under shock environment is determined analytically in a wide range of frequency domain, which shows good agreement with experimental and numerical results. The proposed method can be used to guide the shock environment adaptability design of aerospace and other structural components.