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Deep space exploration technology is an important development direction for scientific exploration. The penetrator method has been proposed as an inexpensive method of studying planetary bodies. The basic principle of this method is that the detection equipment carried by the high-speed penetrator hits a planetary body at a high speed and is buried up to several meters below the surface to carry out detection work. During the frictional collision process with the planets crust, the instantaneous acceleration peaks of the scientific payload (electronic instrumentation) are large. Shock protection of these payloads is necessary to improve their survival and mission success. In this paper, with the goal of improving the survival rate of scientific loads inside a penetrator, a penetrator with a multilayer energy-absorbing structure is developed, in which cushioning protection measures, such as an aluminum foam-filled corrugated tube(AFFT) structure, polyurethane rubber, and epoxy resin potting, are applied to the penetrator. Since the analysis of this process is a highly nonlinear problem, a numerical modeling method is the main approach in this paper. The LS-DYNA software platform was used to simulate the penetrators penetration process on a moon soil medium. The results obtained using empirical formulas and theoretical derivations were compared with the results of numerical analysis to ensure the accuracy of the penetration simulation model. The finite element model of the penetrator was then verified and modified by conducting shock response spectral experiments and shock simulations. The results showed that the spacer scheme had a positive effect on the impact isolation and energy absorption. In addition, this scheme provides an important reference for the design of the penetrator prototype to guarantee the success of subsequent ground rocket sled experiments.

A z-axis decoupled multi-frame vibration MEMS gyroscope (DMFVMG) is presented in this paper. Firstly, the decoupled principle is employed and the sense frame, Coriolis frame and drive frame are arranged through inner fame, intermediate frame and outer frame, and the movement characteristic analysis indicates that the structure is fully decoupled. The structure is simulated through mode analysis, harmonic response and drop shock response. The simulation results show that the resonant frequencies of the Sense Mode and Drive Mode are 10094Hz and 10162Hz, and the maximum deformation and stress with the shock analysis is 7.14 $\mu {\mathrm{ m}}$ and 235.19MPa (among three different directions). Then, the structure is fabricated through MEMS processing, and P-type single-crystalline silicon wafer and 7740 glass wafer are used. After that, the structure is packaged in a ceramic vacuum tube shell and the resonant frequencies and quality values of the sense and drive mode are 10354.21Hz and 5364, 10438.23Hz and 5219, the error between fabrication and simulation is 2.58% and 2.72%. And the monitoring system of DMFVMG prototype is established by analog circuit with drive closed-loop and sense open-loop. Then, the DMFVMG prototype is tested through turntable, and the range, scale factor and intercept are ±300°/s, −19.06mV/°/s and 95.43mV respectively. Finally, five repeated bias tests are arranged and the angular random walking values and bias stability are 0.2408°/ $\surd \text{h}$ , 0.2358°/ $\surd \text{h}$ , 0.2413°/ $\surd \text{h}$ , 0.2397°/ $\surd \text{h}$ and 0.2480°/ $\surd \text{h}$ , 2.858°/h, 3.159°/h, 3.428°/h, 1.891°/h and 3.467°/h respectively.

In this paper, a mode order optimized vibrating ring gyroscope (VRG) with high shock resistance is designed, and the improved optimization algorithm is proposed to optimize the structure design. The mode order of ${n}=2$ mode of the proposed VRG can be the first by structure design, which helps to enhance the anti-shock ability by increasing the translational mode frequency and avoid the excessive large ${n}=2$ mode frequency at the same time. The optimization method based on the differential evolution (DE) algorithm is developed to maximize the anti-shock ability of the VRG. At first, the shock response of VRG is analyzed. After representing the working principle and specific design of the designed VRG, the effect of the structural parameter of VRG on mode orders and frequencies of the ${n}=2$ mode and the translational mode as well as the shock response is simulated and analyzed. Finally, the structural design of VRG is transformed into a constrained optimization problem, and a modified DE algorithm integrated with the infeasible solution handling mechanism and the diversity enhancement strategy is applied to find feasible optimized structural parameters to maximize the shock resistance. The displacement and stress of optimized VRG structures under 10,000 g shock are small, which indicates the validity of the improved DE algorithm. Overall, the structure design and the optimization method in this paper can be a reference for other micromachined structure designs.

This article presents a novel electromagnetic variable stiffness isolator that achieves bidirectional stiffness regulation, which means that the isolator experiences a reduced stiffness when the applied current is positive and an increased stiffness when the opposite current is applied. In addition, the stiffness variations are equal for two currents with the same magnitude but opposite polarities. The proposed isolator can not only ensure the vibration isolation performance in working frequency zone that is relatively far from the natural frequency, but also can realize high-damping-like effect for shock response attenuation, without introducing any additional damping components that may complicate the system. The bidirectional stiffness regulation was realized by combining mechanical springs with hybrid magnets (permanent magnets and coil windings). Variation in the overall stiffness of the proposed isolator occurred when the current was continuously adjusted. A prototype of the isolator was designed, fabricated, and then tested with a round displacement step shock at the base. The theoretical analysis revealed that this device could be utilized as an active vibration isolator through certain control strategies. The experimental results proved the effectiveness of the proposed mechanism in shock isolation and revealed that it outperforms the conventional isolator in suppressing the residual vibration.

Pyrotechnic separation devices are widely used in space separation systems. However, these devices produce high-frequency, high-amplitude shock responses during operation, which endangers the safety of space systems. Hence, it is imperative to study the shock mechanism and characteristics during the unlocking process of a pyrotechnic separation device. This paper uses LS-DYNA finite element software and experiments to analyze the separation characteristics of the separation nut and predict its shock response, quantitatively decoupling the impact of preload and internal mechanism motion on separation shock. The results indicate that the shock response caused by the impact on the inner sleeve is the primary contributor to the total shock response of the separation nut (approximately 55% of the total response). The shock response caused by the release of the strain energy is very small, accounting for less than 5% of the total shock response. Adjusting the preload force without changing the charge and structure of the separation device did not have a clear impact on reducing the shock. This study shows that the shock of the separation device can be decreased by reducing the impact on the inner sleeve.

A novel shock absorber with the preload structure and global negative stiffness is proposed for the shock isolation of sensitive systems. The novel shock absorber is composed of a linear spring and permanent magnet sets. The preload force and negative stiffness region are related to the attractive force between permanent magnet sets. The aim of this paper is to investigate the shock isolation performance of the novel shock absorber. Firstly, a static analysis of the novel shock absorber is carried out. Secondly, the motion stability of the NSA is analyzed by the Jacobian Matrix and the shock response is calculated numerically compared with the conventional preload structures. Finally, the shock test of the novel shock absorber is completed to verify the above results. It is found that the novel shock absorber could be advantageous in improving shock isolation in terms of relative displacement and absolute acceleration compared with conventional preload structures.

The similarity between a shock response spectrum (SRS) and a target shock specification is essential in evaluating the success of a qualification test of a space component. Qualification testing facilities often utilize shock response databases for rapid testing. Traditionally, the comparison of two shocks (SRS) depends on visual evaluation, which is, at best, subjective. This paper compares five different quantitative methods for evaluating shock response similarity. This work aims to find the most suitable metric for retrieving an SRS from a pyroshock database. The five methods are the SRS difference, mean acceleration difference, average SRS ratio, dimensionless SRS coefficients, and mean square goodness-of-fit method. None of the similarity metrics account for the sign of the deviation between the target SRS and database SRS, making it challenging to satisfy the criteria for a good shock test. We propose a metric (the weighted distance) for retrieving the most similar SRS to a target SRS specification from a shock database in this work. The weighted distance outperforms the mean square goodness-of-fit and other metrics in database SRS retrieval for rapid qualification testing.

Using the molecular dynamics method based on the ReaxFF force field and combining it with the multi-scale shock technique, the physical and chemical change processes of CL-20/TNT co-crystals under shock loading were studied. Shock waves with velocities of 7, 8, 9 km s−1 were applied to CL-20/TNT co-crystals along the X, Y, and Z directions. The anisotropy brought by the co-crystal structure was analyzed. The results show that the temperature, stress, volume compressibility, decomposition rate, products, and the cluster of CL-20/TNT are strongly related to the direction of shock waves. With the same velocity, the shock wave along the Y direction can make the system more compressed, to obtain higher temperature and greater stress. When the velocities of shock waves are 7 km s−1 and 8 km s−1, systems with a higher degree of compression have a higher degree of chemical reaction, the reactants decompose faster, and richer products are generated. When the shock wave velocity is 9 km s−1, the chemical reactions are more intense, and the differences between reactants and products due to anisotropy are small. The amounts, compositions, sizes, and mass ratios of the cluster are strongly anisotropic due to the special layered structure of the energetic co-crystal, and the evolutionary processes are closely related to the chemical reaction process. The research in this paper can provide certain support for the understanding of the shock response process of energetic co-crystals.

Interpretation of field data from shock tests and subsequent assessment of product safety margins via laboratory testing are based on the shock response spectra (SRS). The SRS capture how a single degree of freedom (SDOF) structure responds to the shock at differing frequencies and, therefore, no longer contain the duration or other temporal parameters pertaining to the shock. A single duration can often be included in the technical specification or in the recreation of acceleration vs. time history from the specified SRS; however, there is little basis for that beyond technical judgment. The loss of such temporal information can result in the recreated SRS being the same while its effect on a system or component can be different. This paper attempts to quantify this deficiency as well as propose a simple method of capturing damping from shock waves that can allow the original waveform to be more accurately reconstructed from the SRS. In this study the decay rate associated with various frequencies that comprise the overall shock was varied. This variation in the decay rate leads to a variation in the acceleration vs. time history, which can be correlated to a “Damage Index” that captures the fatigue damage imparted to the object under shock. Several waveforms that have the same SRS but varying rates of decay for either high- or low-frequency components of the shock were investigated. The resulting variation in stress cycles and Damage Index is discussed in the context of the lognormal distribution of fatigue failure data. It is proposed that, along with the SRS, the decay rate is also captured to minimize the discrepancy between field data and representative laboratory tests.

Damage evolution in metals during laser-shock loading (spallation) is a complex phenomenon accompanied by extremely high temperatures, pressures, and strain rates that affect the void nucleation/growth mechanisms. The current modeling efforts at the atomic scales to investigate the evolution of microstructure undergoing the spall failure at the atomic scales are limited to a hybrid atomistic–continuum method that combines the two-temperature model (TTM) with the molecular dynamics (MD) simulations. This manuscript demonstrates this capability by investigating the mechanisms of nucleation/evolution of voids for a nanocrystalline Al system experiencing an ultrafast laser pulse. This capability, however, is unable to model the laser shock response of experimental systems (with grain sizes greater than 100 nm and thicknesses in the microns) as well as the post-spall behavior (damage growth or recompression behavior). This work combines the TTM with the quasi-coarse-grained dynamics (QCGD) method to extend MD-TTM simulations to the mesoscales. The hybrid QCGD-TTM approach retains the laser energy absorption, heat generation/transfer, and microstructure evolution (melting, defects, and damage) behavior predicted by MD-TTM simulations. The QCGD-TTM simulations allow the investigation of the wave propagation behavior, the evolution of microstructure (defects and damage), temperature, and pressure at the time and length scales of laser-shock experiments. The QCGD-TTM simulations reported here investigate the nucleation and post-spall damage evolution behavior during spall failure of sc-Al and 0.5 µm grain-sized pc-Al films with a thickness of up to 2 µm. The QCGD-TTM-predicted damage evolution behavior captures the post-spall behavior observed experimentally and retains the atomistic characteristics of void nucleation and void collapse.

Floating shock platform is generally used to test the antishock performance of large shipboard equipment. Shock acceleration signal will produce zero-shift phenomenon in the test measurement process, which will affect the subsequent shock response spectrum analysis. In this paper, a method of shock acceleration signal processing based on rigid body motion revision model is established. The rigid body motion revision model adopts the theory of ship’s seakeeping based on the hypothesis of KrylovFroude, in which the shock wave load of underwater explosion adopts the empirical formula. The bubble pulsation load adopts the GeersHunter spherical bubble model. The empirical mode decomposition method is used to eliminate the trend term of the low-frequency part of the acceleration signal, and the frequency filtering technology is used to eliminate the noise of the high frequency part. The response estimated by the rigid body motion model is used to modify the measured signal. The modified signal is analyzed by shock response spectrum to get the round design spectrum. The validity of the signal is determined by the Pauta criterion. Finally, the shock environment statistics of the whole platform is given. This method can eliminate the low-frequency trend term and high frequency noise and has good robustness. It can be applied to many kinds of signals. This method can provide technical support for antishock performance of shipboard equipment and also applied to other shock signal processing fields.

Failures of MEMS devices under shock are due to the overlap of the static and moving parts. The shock response of the microstructure under mechanical shock is investigated in this paper. This work presents modelling and simulation of the microstructures such as microcantilever, fixed–fixed flexure and serpentine structure and is further extended to optimize the response of high-g acceleration threshold switch under mechanical shock. The latching threshold for the high-g acceleration switch is estimated using the geometrical structure. The natural frequency of the serpentine spring-mass structure is selected to achieve the required displacement for latching. The dimensions of the switch are optimized in accordance with the natural frequency and to meet the requirement of latching for a given shock. The switch is fabricated on silicon on insulator wafer with a deep reactive ion etching process. The switch is tested on the static mechanical shock of 3500 g and shows a good agreement between analytical, numerical and experimental results.

Due to the recent development of the micro-launcher technology, soon nanosatellites are expected to be launched mainly as primary payloads and thus experience intense pyroshock events. This study proposes a novel CubeSat deployment system which alleviates such mechanical shock levels. The passive isolator Sorbothane thin films were integrated within the dynamic envelope of a testpod to evaluate the desired attenuation effects. A metal-to-metal mid-field shock testing (MFST) facility was manufactured to perform in-plane (IP) and out-of-plane (OOP) impacts. The MFST is capable of generating mechanical shock waves up to 10,000g for OOP direction and 5000g for IP excitations. The experiments illustrated that the Sorbothane isolators can attenuate shock levels by 3 dB and the flat adapter (mechanical joint) can attenuate shock levels by 4 dB. The measurements were successfully validated using the positive and the negative shock response spectrum (SRS) approach. In addition to that, the commercially available finite element analysis software ABAQUS was utilized to verify the experimental measurements and simulate the mechanical shock effects using explicit analysis.

The crystal oscillator is a widely used electronic component in a circuit, whose accuracy is strongly affected by the external mechanical environment. To depict the failure mechanism of the crystal oscillator, the damage boundary of this component under the shock environment is studied experimentally in this paper. Through subjecting “step-up” loads on different groups of crystal oscillators, two failure modes (frequency jumping and structural fracture) are monitored and validated. Experimental results prove that “frequency jumping” failure mode is governed by the value of the acceleration shock response spectrum (ASRS) in a certain frequency range, while the failure mode “structural fracture” is governed by the peak value of the ASRS. Through analyzing the shock response spectrum, damage boundaries are given for these two failure modes, which can provide a reference for component design and failure assessment.

This research proposes a new method for boat impact vibration attenuation using the exchange of momentum principle with a pre-straining spring mechanism. The boat dynamic is modeled using a hinged-supported beam structure. The wave excitation on the boat hull is expressed using one degree of freedom spring-mass system. The simulation study is performed to evaluate the impact damper performance in reducing the boat shock response. Two kinds of momentum exchange impact damper i.e., without and with pre-straining spring mechanism, are evaluated. The simulation results show that the impact damper with pre-straining spring mechanism (PSMEID) is better than the passive momentum exchange impact damper (PMEID) in reducing the boat shock vibration response

The shock response of a polymer-bonded copper powder was investigated by means of plate impact experiments in a gas gun (pressure range 1–8 GPa) and using in-contact explosive loading (pressures up to 37 GPa). Stress gauges were used to determine the material shock states in the planar impact, and the experimental data of shock and particle velocities (U, u) were fitted to a straight line giving a Hugoniot equation of state $${U=(0.85\pm 0.08)+(2.64\pm 0.05)\;u}$$. In the explosive loading experiments, the shock speed in the material was measured using optical methods, and impedance matching was performed to determine the shock state in the sample. Comparison between the two experiments shows that the states attained in the lower-pressure range (planar impact experiments) and higher-pressure range (explosive loading) follow the same Hugoniot curve, within 4% deviation.

The predictive modeling of the experimentally observed behavior of metallic materials under shock loading conditions (wave structures, spall strengths) is a critical challenge toward the design of next-generation structural materials. This challenge is due to the lack of computational methods that can predict microstructural evolution at the mesoscales under dynamic loading conditions. While classical molecular dynamics simulations have been able to provide atomic-scale insights in the defect and damage nucleation/evolution mechanisms, the capability to have a direct comparison with experimental data at the same time and length scales is still a challenge. The current computational approaches require that several approximations be made either for the loading conditions or for the micromechanisms related to defect evolution and interaction at the mesoscales. This viewpoint discusses the insights obtained from molecular dynamics simulations of shock deformation and spall failure of heterogeneous metallic microstructures. An example Al–Ni microstructure is used to identify the critical atomic-scale phenomena that need to be addressed by the mesoscale methods when considering shock deformation and failure (spallation) at the mesoscales.

A nonlinear dynamic model for describing shock response of half-sine programmer in shock test is constructed, in which many important factors in half-sine programmer such as size, hard nonlinearity, damping and initial impact velocity are considered, based on the damped Duffing equation, and the empirical static stiffness and shock stiffness calculation formulas of cylindrical rubber isolator. The shock pulse of half-sine programmer is measured and calculated by using shock test machine and Runge-Kutta method. Taking the minimum determination coefficient between the calculated and the measured shock pulse as the optimization objective, the parameters in the present model are determined by using quantum genetic algorithm (QGA), and meanwhile the extreme capacity in the present model for describing the dynamic behavior of half-sine programmer under shock excitations can also be verified. Experiments were implemented with drop shock test machine. The experimental results show that the present model is precise and efficient, and the prediction errors of pulse peaks and pulse widths were all below 5%, the waveform fitting errors between the calculated and the measured pulses are all less than 15%. The present results are helpful for designing the half-sine programmer.

An improved method based on the Hybrid Finite Element-Statistical Energy Analysis (FE-SEA) method and quasi-steady state theory is proposed to predict the response of spacecraft structure during the process of pyrotechnics separation. Firstly, the amplitude–frequency value of shock load is obtained by using time-frequency conversion technology. Then, according to the frequency response characteristics of each part of the spacecraft structure, a more accurate hybrid FE-SEA model is established. The piecewise loading method is used to predict the response of the hybrid model. Finally, the time domain response results are reconstructed, and the shock response spectrum (SRS) is calculated. Based on the test system of simulating pyroshock, the shock experiment of spacecraft structure is conducted. The high frequency and high velocity character of pyroshock could be effectively simulated, and an accurate shock force function could be obtained through the experiment. This indicates that the numerical results are in line with the ones of the experiment. The SRS obtained from experiments and calculations have similar trends and amplitudes. This conclusion verifies the rationality and sufficient accuracy of the novel method in this paper. The novel method presented in this paper greatly improves the computational efficiency. At the same time, it provides theoretical guidance for shock response prediction of spacecraft structure by steady-state methods.

All-atom molecular dynamics simulations were used to study shock wave loading in oriented single crystals of the highly anisotropic triclinic molecular crystal 1,3,5-triamino-2,4,6-trinitrobenzene (TATB). The crystal structure consists of planar hydrogen-bonded sheets of individually planar TATB molecules that stack into graphitic-like layers. Shocks were studied for seven systematically prepared crystal orientations with limiting cases that correspond to shock propagation exactly perpendicular and exactly parallel to the graphitic-like layers. The simulations were performed for initially defect-free crystals using a reverse-ballistic configuration that generates explicit, supported shocks. Final longitudinal stress components are between »8.5 GPa and »10.5 GPa for the 1.0 km s-1 impact speed studied. Orientation-dependent properties are reported including shock speeds, stresses, temperatures, compression ratios, and local material strain rates. Spatio-temporal maps of the temperature, stress tensor, material flow, and molecular orientations reveal complicated processes that arise for specific shock directions. The results indicate that TATB shock response is highly sensitive to crystal orientation, with significant qualitative differences for the time evolution of the stress tensor and temperature, elastic/inelastic compression response, defect formation and growth, critical von Mises stress, and strain rates during shock rise that span nearly an order of magnitude. A variety of inelastic deformation mechanisms are identified, ranging from crumpling of graphitic-like layers to dislocation-mediated plasticity to intense shear strain localization. To our knowledge, these are the first systematic MD simulations and analysis of explicit shock wave propagation along non-trivial crystal directions in a triclinic molecular crystal.

Technological advances in unmanned aerial vehicles (UAVs) have made it possible to employ drone deliveries for packaged products, but currently no standards of practice are available to qualify packaged products traveling through this distribution channel. This research proposes a methodology to collect field data from a UAV to develop simulation techniques for use with package testing equipment. This project utilized data recorders to measure the vibration, shock, and atmospheric field data on two models of the DJI drones. The root mean square G value (Grms), the power spectral density (PSD), maximum G-values and shock response spectrum, and atmospheric data were reported in this study. The study found that the general shape of the PSD profile of the drones differed from the PSD air profiles of the aircraft. The overall recorded Grms levels of the drones were also significantly higher than those of the published air profile of the aircraft. Moreover, the study found that the drone’s in-flight vibration intensities in the horizontal level were consistently higher than those in the vertical direction. The major sources of vibration and shock in both drones’ models originated from the two-propeller rotations. Shocks recorded during the flight reached 14 G, took place in the horizontal plane with the drone accelerating as opposed to the vertical plane where the drone is landing.

During the various stages of shock loading, many transient modes of deformation can activate and deactivate to affect the final state of a material. In order to fundamentally understand and optimize a shock response, researchers seek the ability to probe these modes in real-time and measure the microstructural evolutions with nanoscale resolution. Neither post-mortem analysis on recovered samples nor continuum-based methods during shock testing meet both requirements. High-speed diffraction offers a solution, but the interpretation of diffractograms suffers numerous debates and uncertainties. By atomistically simulating the shock, X-ray diffraction, and electron diffraction of three representative BCC and FCC metallic systems, we systematically isolated the characteristic fingerprints of salient deformation modes, such as dislocation slip (stacking faults), deformation twinning, and phase transformation as observed in experimental diffractograms. This study demonstrates how to use simulated diffractograms to connect the contributions from concurrent deformation modes to the evolutions of both 1D line profiles and 2D patterns for diffractograms from single crystals. Harnessing these fingerprints alongside information on local pressures and plasticity contributions facilitate the interpretation of shock experiments with cutting-edge resolution in both space and time.

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.

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.

The dynamic response of crystalline Cu-amorphous Cu63Zr37 nanolaminates under shock loading has been investigated in the present study by atomistic simulations to provide an insight of their overall deformation behavior with respect to different grain structure in the crystalline region. The dynamic characterization of the structural evolution of the nanolaminates during shock loading has been carried out based on various techniques including common neighbor analysis, dislocation analysis, Voronoi cluster analysis, pressure profile, and kinetic energy maps. Pressure profiles of single crystalline Cu Cu63Zr37 metallic glass (SC/MG) nanolaminate at relatively low shock velocity show the presence of an elastic precursor in the crystalline region owing to the plane-plane collision phenomenon. Increasing the shock velocities in the SC/MG specimen results in FCC to BCC phase transition in the crystalline region. In particular, the crystalline/amorphous interface causes the generation of reflected rarefaction wave back into the crystalline region which aids in the evolution and stabilization of the BCC phase. In the NC/MG specimen, the misalignment of planes across different grains reduces the intensity of elastic precursor at low shock velocity due to disruption in the plane-plane collision, whereas the grain boundaries act as nucleating region for the BCC phase during the high-velocity shock propagation. The coordination number of the Cu63Zr37 glass region has been found to increase during high-velocity shock loading which can be accounted by the formation of and indexed Voronoi polyhedra.

Shockwave propagation in polyethylene glycol diacrylate (PEGDA) hydrogels is simulated for the first time using nonequilibrium molecular dynamics simulations. PEGDA hydrogel models are built using the “perfect network” approach such that each crosslink junction is comprised of six chain connections. The influence of PEGDA concentration (20–70 wt%) on shock behavior is investigated for a range of particle velocities (200–1000 m/s). In agreement with reported experimental results in the literature on gels with similar densities, shock velocity and pressure in PEGDA hydrogels are found to increase with polymer concentration, within a range bounded by pure water and pure polymer behaviors. Nonlinear relationships are observed for shock pressure and shock front thickness as a function of concentration, and a logarithmic equation is proposed to describe this behavior. In addition, the relationship between pressure and shock front thickness is compared with hydrodynamic theory. Deviation from hydrodynamic predictions is observed at high particle velocities and this deviation is found to be related to viscosity changes. A power-law relationship between strain rate and pressure in PEGDA hydrogels is identified, similar to that of metals. However, a power-law exponent of 1.4 is computed for all gel concentrations, whereas an exponent of 4 is typically reported for metals.

The mechanical response of a copper-2 wt% beryllium alloy in either a solution treated or aged condition has been investigated within the shock loading regime. In terms of Hugoniot Elastic Limit, shear strength and spall (dynamic tensile) strength, the material in the aged condition has been observed to be significantly stronger than when in the solution treated state. Whilst these trends are the same as when tested under quasi-static conditions, the level of strengthening due to shock loading is less than during quasi-static loading. It is believed that the distribution of non-shearable particles within the microstructure (caused by aging) restrict the ability of the material to deform via dislocation motion and generation, which in turn reduces strain-rate sensitivity. Thus the relative differences in strength between aged and solution treated materials will be less under shock loading conditions compared to quasi-static conditions. In contrast, strong similarities between the shear strengths of the solution treated material and pure copper were noted. It has been suggested that twinning in the alloy may be responsible (due to the small contribution of twins to shock induced strengthening), although comparison of partial dislocation separation between the two materials suggest otherwise.

This paper focuses on the loading of small spacecraft induced by the triggering of separation systems. The article presents the experimental results for the shock loading level of small spacecraft manufactured by Lavochkin Association and analyses the causes of its observed increase. Recommendations are given for changing the testing techniques for the response to shock-impulse loading for similar objects.

The intensity of damage production during shock wave propagation in polycrystalline metallic systems is mostly dependent on the shock-defect interactions. Traditionally, different coincidence site lattice (CSL) grain boundaries (GBs) are introduced in the polycrystalline structure through various processing techniques to enhance the strength or plasticity. However, their dynamic response to the impulsive loading condition has not been elaborately explored to date, which necessitates a detailed study on the interaction between CSL GBs and shock wave. In this study, we have employed molecular dynamics simulations to investigate the response of both symmetric and asymmetric ∑5[1 0 0] tilt GBs of nickel bicrystal under the influence of shock-wave. We have also analysed the role of piston velocities and inclination angles of the GBs on the shock response and the consequent deformation behaviour. This investigation gives insight into the mechanical response and the underlying mechanisms which are inspected through atomic strain analysis, common neighbour analysis and pressure–time–distance mapping. The results show that the stacking faults formation takes place when specimens are subjected to lower shock velocities, whereas higher velocities facilitate phase transformation along with amorphization. There is a stark contrast between the specimens with symmetric and asymmetric tilt GBs in the manner of plastic deformation behaviour in response to shock-wave and GB failure at lower and higher piston velocities.

This article deals with the method of computer-aided studies of the results of tank container impact tests to confirm the ability of portable tanks and multi-element gas containers to withstand the impact in the longitudinal direction on a specially equipped test rig or using a railway flat car by impacting a flat car with a striking car, in compliance with the requirements of the UN Navigation Rules and Regulations. It is shown that the main assessed characteristic of the UN requirements is the spectrum of the shock response (accelerations) for the interval natural frequencies of the shock pulse. The calculation of the points of the shock response spectrum curve based on the test results is reproduced in four stages. A test configuration of the impact testing of the railway flat car with a tank container is presented, and the impact is performed in such a way that, under a single impact, the shock spectrum curve obtained during the tests for both fittings subjected to impact repeats or exceeds the minimum shock spectrum curve for all frequencies in the range of 2 Hz to 100 Hz. Formulas for determining the relative displacements and accelerations for the interval natural frequencies of the shock wave are given. The research results are presented in graphical form, indicating that the experimental values of the shock response spectrum exceed the minimum permissible values, the equation of the experimental curve of the shock response spectrum in the frequency range 0–100 Hz is described by power-law dependence. The coefficients of the equation were determined by the statistical method of maximum likelihood with the determination factor being 0.897, which is a satisfactory value, a comparative analysis showed that the experimental curve of the impact response spectrum in the frequency range 0–100 Hz exceeds the normalized curve, which confirms compliance with regulatory requirements. A new test configuration is proposed using a tank car with a bulk liquid, the processes in which upon impact differ significantly from other freight wagons under longitudinal impact loads of the tank container. The hydraulic impact resulting from the impact on the tank container and the platform creates an overturning moment that causes the rear fittings to be unloaded.

We leverage the phase segregated microstructure of polyurea to study its shock response using molecular dynamics (MD) simulation. The two phase segregated domains, the hard and the soft domains, are investigated separately. The shock response of the domains is studied using a multiscale shock-simulation approach that allows simulation of low pressure shocks. Both domains exhibit an unconventional behavior at low shock velocities that is typically associated with polymers. The shock response of the hard domain is marked by energy dissipation due to hydrogen bond breaking. Moreover, the radial distribution function suggests a severe distortion in the ring structure of aromatic moieties in the hard domain at high shock pressure. Finally, the shock Hugoniot of polyurea, obtained by combining the response of the two domains using a mixing rule, shows excellent match with experimental data.

In this paper the exact definition of shock response spectrum is given. The relation between Fourier spectrum of shock pulse and residual shock response spectrum is discussed with the following relationship: \(S\left(f \right)\, = \,2\pi f \, F(f)\). Finally, with paper introduces the programming of real-time analysing shock response spectrum with a mini-computer and a Fourier Analyser. Shock may be defined as suddenly transmission of a large amount of kinetic energy to a mechanical system which takes place in a relatively short time compared with the natural period of the mechanical system. It can produce very large force and acceleration and cause severe mechanical damage. In order to study the mechanical damage effect of shock and find an effective method of shock control, it is necessary to introduce the concept of shock response spectrum.

Shock response spectrum (SRS), calculated according to shock loading signal, is the primary metric for assessing the shock resistance ability of shipborne equipment. Nevertheless, the measured shock acceleration signal contains a trend term error that severely distorts the low frequency of the SRS. The accuracy of present correction methods cannot be assured due to a lack of reference. A discrete wavelet transform (DWT) and low-frequency oscillator combination method is proposed for correcting shock signals in this paper. The optimal wavelet parameters can be selected according to a low-frequency spectrum baseline fitted by the measured relative displacement to reject low-frequency trend term errors. Shock machine test results show that the average difference between the low-frequency spectrum baseline and uncorrected SRS is reduced from 89.8% to 3.2%, while the SRS slope rolled off to 5.8 dB/oct after imposing the proposed correction. The corrected SRS can faithfully show the actual shock loading characteristics of shipborne equipment in shock tests.

In order to study the transfer law of spacecraft pyrotechnic shock response, taking communication satellite as an example, the shock acceleration data of satellite deck with different distance from the pressing point and from decks to units are statistically analyzed during the process of satellite solar array electric unlocking. The shock response transfer law is summarized. This study is based on the real pyrotechnics shock test of telecommunication satellites. This article carries out data statistics and summarizes the transmission law of shock response, which can provide reference for the unit anti-shock design and layout, and effectively make up for the limitations of the finite element method in response prediction.

The application of gyroscopes in harsh environments has always been a hot topic. As a high-quality material for manufacturing gyroscopes, quartz crystals need to be designed and optimized to meet the normal operation of gyroscopes in harsh environments. The Micro Electronics Mechanical System(MEMS) quartz tuning forks resonant gyroscope is one of the quartz gyroscopes. The elastic structure (V-shaped beam) between the anchor support point and tuning forks plays a vital role in the MEMS quartz tuning forks resonant gyroscope. This structure determines the natural frequency of the gyroscope, and more importantly, determines the shock resistance of the gyroscope structure. In this article, the MEMS quartz tuning forks gyroscope with different V-shaped beam thicknesses are simulated and analyzed by finite element analysis simulation software. After the modal analysis and shock simulation (the half-cycle sine shock pulse with amplitude of 1500 g (g is the acceleration of gravity) and duration of 2 ms in the six shock directions), the results show that when the beam thickness is 80 &mu, m, the maximum stress is 94.721 MPa, which is less than the failure stress of quartz crystal. The gyroscope&rsquo, s shock resistance is verified through shock testing.

In order to achieve reasonably aero-engine landing shock data induction, first filter the shock data samples through ESD (Energy Spectrum Density) and SRS (Shock Response Spectrum), and then Actual SRS and Standard SRS were given on relevant standards and mathematical statistical methods. Casing shock of aeroengines were measured during landing, and Actual SRS and Standard SRS of two types of aero-engine installed in the same aircraft were obtained. The differences of shock characteristics on different directions in the same position were analyzed with the differences of shock characteristics of two types of aero-engine. The results show that the shock characteristics on different directions on the same position may vary greatly, and it is possible to reduce the risk of shock damage through changing installation direction of equipments or structures. Shock characteristics of two types of aero-engine may vary greatly, so that measured shock data of corresponding aero-engine should be selected as test condition on the shock test of airborne equipments or structures. The conclusions provide some guidance for shock absorption design of aero-engine and installation of airborne equipment.

An analytical model is developed to predict shockwave propagation and attenuation in hydrogels by combining the classical method of shock characteristics and a solution for the shock front structure. To guide the development of the model, molecular dynamics (MD) simulations are performed. Specifically, a one-dimensional shock pulse in poly(ethylene glycol) diacrylate (PEGDA) hydrogels is simulated with the nonequilibrium MD method. The role of polymer concentration on the shock response is evaluated by constructing hydrogels with 20, 35, and 50 wt% PEGDA concentrations in an idealized crosslinked network. Steady-state pressure-density and shock-particle velocity relationships are established using the Murnaghan equation of state. Shock front structure is characterized by a power-law equation that relates the shock front thickness with shock pressure. These results are used as critical input for the shock propagation and attenuation model. The model is then evaluated via comparison with the classical method of characteristics. It shows significant improvement in accuracy and successfully captures salient features of shockwave attenuation, including the shock pressure amplitude, the velocities of the shock and release waves, and the attenuation timeline. Hydrogels with higher polymer concentrations exhibit a shorter attenuation time at all particle velocities studied. This behavior is attributed to differences in bulk properties and shock front structure in hydrogels with different polymer/water concentrations.

Random vibration and shock testing are used to identify weaknesses in products or to verify if products can survive particular mechanical environment. The procedure of developing shock and vibration test specification for vibrating components on intelligent guidance robots using response spectra is presented in this paper. Fatigue Damage Spectrum (FDS) is used to show the potential error introduced by directly calculating the Power Spectral Density (PSD) of the field measured non-Gaussian signal, and to derive a damage equivalent Gaussian signal with Mile’s equation. Shock Response Spectrum (SRS) is calculated for field measured shock signal and an equivalent transient signal is synthesized using mixed sine waves. Envelope is applied to compensate for the dispersion of multiple test results. A case study is given to demonstrate the procedure.

The response of single crystalline tantalum to one-dimensional shock loading has been investigated as a function of crystalline orientation to the loading axis. Results show that this has a significant effect, particularly on the Hugoniot elastic limit (HEL). [100] and [111] HELs are near identical with the [110] HEL having the lowest strength. This is contrary to predictions obtained by applying the Schmid factor analysis, where the ordering was expected to be (highest strength first) [111], [110], with the [100] orientation being the softest. Adopting a more appropriate model based on uniaxial strain conditions, as was previously done successfully for FCC aluminum and copper, did not rationalize our observations. We show that a non-Schmid effective stress model, incorporating twinning/anti-twinning asymmetry, has much greater success in reproducing the experimental relative HELs magnitudes. Using this model, we make a quantitative estimation of the magnitude of non-Schmid effects and compare these to equivalent low temperature, quasi-static estimates from the literature.

Large-scale nonequilibrium molecular dynamics (MD) simulations of shock waves in nanocrystalline iron show evidence of plasticity before the polymorphic transformation takes place. The atomistic structure in the shock direction shows an elastic precursor, plastic deformation, and shock-induced phase transformation from bcc to hcp iron. In this Rapid Communication, large-scale MD models show that the shock response of iron is highly related to the ramp time of the applied shocks. For long ramp times we observe significant plastic relaxation and formation of microstructure defects. Pressure-induced phase transformations in iron are accompanied by stress relaxation achieving almost fully relaxed three-dimensional hydrostatic final states. The evolution of the stress relaxation is in agreement with theory and experiments. Analysis of the x-ray diffraction patterns calculated from the atomistic structure using the Debye equation revealed pronounced anisotropy of the line broadening that is caused by stacking faults in hcp Fe and by dislocations in bcc Fe.

This study proposes a method to apply dual criteria for the assessment of product damage based on the deceleration signal in a crash-stop incident. To evaluate the shock effects, a procedure is proposed to decompose the original crash signal into two components, i.e. an equivalent crash signal and a residual shock signal. The characteristics of crash signals are analysed in both time and frequency domains. It is found that the equivalent crash signal can represent the original crash signal if the dominant frequency (fn) of the product structure is relatively lower than the effective frequency (fs) of the crash signal, i.e. f n f s ≤ 1 5 . Otherwise, the original crash signal should be used in the assessment of product damage if f n f s > 1 5 . The dual damage criteria method is proposed by combing the maximum-acceleration vs. velocity-change (Amax-ΔV) diagram and shock response spectrum (SRS), i.e. the former can offer a lower bound of damage boundary on Amax-ΔV diagram while the latter can define an upper bound of damage boundary on SRS graph. The method of dual damage criteria is illustrated numerically using two types of cantilever beams, as an example. The proposed method can be applied with the critical SRS (Sc) method recommended in ASTM D3332-99 for the packaging design and test, and may also be considered in the design and test of other impact energy and shock absorbers in a crash-stop incident.

A lamb wave is a guided wave that propagates along a plate-like structures in various systems. Particularly, in space structures where weight saving is very important, various vibrations are often transmitted as Lamb waves; therefore, control and mitigation of Lamb waves are important issue. Since the high frequency components included in the pyroshock can be fatal to electronic devices, many engineers have studied shock isolators for mounting and protecting such electronic devices. Lamb waves, as with light, are refracted with a certain angle due to the difference in wave speed between the two media. Using the refraction of the lamb waves, shock response for selected region can be reduced by changing direction of the wave. Theoretically, this effect can be achieved by simply attaching a thin elastic material on the host plate to change flexural stiffness. Thus, it would be a very efficient solution to reduce shock response in a specific area behind the patch on the wavefront path by attaching one elastic patch on the path of the Lamb wave. In this study, we proposed elastic patches of various shapes for shock reduction, and the shock reduction characteristics of several patches were numerically and experimentally confirmed. The plane Lamb waves generated from the array of piezoelectric disk attached to the thin metal plate were refracted when passing through the elastic patch; as a result, the shock response was decreased in the area behind the patch.

The shock initiation of heterogeneous solid explosives, such as binderized PETN-based explosives, is governed by mesoscopic processes. However, there is a scarcity of direct measurements probing these phenomenon so we employ modeling to improve our understanding of them. Here we perform grain-scale simulations in the multi-physics code, ALE3D, to investigate the shock response of explicitly resolved energetic grains and pores following planar impact. Non-reactive simulations are used to calculate an unreacted equation of state (EOS) for the heterogeneous explosive and constituent ingredients. These calculated EOSs are compared to historic models. The effects of pore size and distribution on the non-uniform temperature and pressure fields within the shocked material is investigated. These studies are important because they provide insight on mesoscopic processes and form the basis for new morphology aware explosive models.

The phase transition of crystalline and amorphous silica materials to a stishovite-like high-pressure phase has received considerable interest. While most work has focused on pure SiO2 glass (fused silica), studies identifying a similar high-pressure phase transformation in soda-lime glass have not been performed. Marked differences in the network structure and compressibility of soda-lime glass as compared to fused silica raise questions as to how a stishovite transition might manifest in these glasses. In this work, new plate impact experiments on soda-lime glass have been performed to ∼110 GPa to measure the Hugoniot response in the high-pressure regime. Results of these tests were unable to find evidence of a transition to a high-pressure polymorph under shock loading. A glass constitutive model is proposed to capture this newly measured high-pressure response. Good agreement between time resolved measurements and simulation results from the CTH hydrocode with this model implemented are shown, along with additional insights into the apparent glass behavior.

A 40 mm bore gas gun was used to investigate the shock response of three viscoelastic polymer materials: Dragonshield BCTM, Versathane P650, and a blend of Versathane P250 and P1000. Sabots carrying Al or Cu metal disks were launched into target assemblies containing the polymer material. The target consisted of a thin metal disk on the impact side, a 6.5-mm-thick polymer disk, and a thick metal backup disk. Fifty ohm manganin gauges were epoxied between the metal/polymer and polymer/metal interfaces to measure the interface stresses and shock transit time. Measured longitudinal stresses ranged from 3 to 47 kbar. The interface particle velocity, shock velocity, mean stress, and uniaxial strain were calculated for each experiment. This article describes the experimental technique, analysis methodology, and results.

We present computational studies of experiments that measure the impact shock response in energetic materials on nanosecond-micrometer scales using a multi-material, arbitrary Lagrangian-Eulerian code, ALE3D. In the experiments, a laser launches an aluminum flyer-plate that impacts the energetic material. After impacting the energetic material, the output shock is detected by the motion imparted to a glass window. Experiments are also performed without energetic materials to focus on the flyer-plate drive conditions. Numerical results demonstrate agreement with experimental data for the laser-driven acceleration of the aluminum flyer and the first ∼5 ns after the flyer impacts the glass window. Our simulations indicate that we have to account for back-surface curvature in the flyer produced during the launch to give agreement with the experiment. Preliminary results are presented with an energetic liquid, nitromethane, using an equation-of-state and chemical kinetics model generated from the thermo-chemical code, Cheetah.

We have investigated the shock response of detonation nano-diamonds under dynamic conditions using the Dynamic Compression Sector of the Advance Photon Source for the purposes of understanding the potential fracture mechanism of nano-diamonds and to identify potential avenues for structural energy release. Commercial detonation nano-diamonds exhibit a compressed core, expanded shell that has been proposed to be a potential source for structural bond energy release under a fracture condition. Dynamic diffraction images from two-stage light gas gun experiments to 5.3 km/s were collected on compressed samples of nano-diamonds and Viton fluoropolymer binder mixture in various shock states. Powder diffraction data is refined to extract out core/shell changes with shock loading and show a bimodal response where the shell signal decreases with shock loading while the core signal shows a non-fractured response. These points to a partial fracturing of the nano-diamond particle without accompanying energy release from the core.