Analytical Determination of Shock Response Spectra for an Impulse-Loaded Proportionally Damped System

Volume 1 ◽  
2004 ◽  
Author(s):  
R. David Hampton ◽  
Nathan S. Wiedenman ◽  
Ting H. Li
Keyword(s):  
Transient Response ◽  
Shock Loading ◽  
Response Spectrum ◽  
Response Spectra ◽  
Analytical Determination ◽  
System Response ◽  
Mechanical Shock ◽  
Shock Response ◽  
Mass Spring ◽  
The Impact

Many military systems must be capable of sustained operation in the face of mechanical shocks due to projectile or other impacts. The most widely used method of quantifying a system’s vibratory transient response to shock loading is called the shock response spectrum (SRS). The system response for which the SRS is to be determined can be due, physically, either to a collocated or to a noncollocated shock loading. Taking into account both possibilities, one can define the SRS as follows: the SRS presents graphically the maximum transient response (output) of an imaginary ideal mass-spring-damper system at one point on a flexible structure, to a particular mechanical shock (input) applied to an arbitrary (perhaps noncollocated) point on the structure, as a function of the natural frequency of the imaginary mass-spring-damper system. For a response point sufficiently distant from the impact area, many Army platforms (such as vehicles) can be accurately treated as linear systems with proportional damping. In such cases the output due to an impulsive mechanical-shock input can be decomposed into exponentially decaying sinusoidal components, using normal-mode orthogonalization. Given a shock-induced loading comprising such components, this paper provides analytical expressions for the various common SRS forms. The analytical approach to SRS-determination can serve as a verification of, or an alternative to, the numerical approaches in current use for such systems. No numerical convolution is required, because the convolution integrals have already been accomplished analytically (and exactly), with the results incorporated into the algebraic expressions for the respective SRS forms.

scholarly journals Aspects of Strength Testing of Tank Containers in Compliance with the Requirements of the UN Navigation Rules and Regulations

2021 ◽  
Vol 9 (3) ◽  
pp. 349
Author(s):  
Andrii Sulym ◽  
Pavlo Khozia ◽  
Eduard Tretiak ◽  
Václav Píštěk ◽  
Oleksij Fomin ◽  
...  
Keyword(s):  
Natural Frequencies ◽  
Response Spectrum ◽  
Experimental Curve ◽  
Bulk Liquid ◽  
Frequency Range ◽  
Test Configuration ◽  
Shock Response ◽  
Shock Response Spectrum ◽  
Spectrum Curve ◽  
The Impact

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.

scholarly journals Vibro-Acoustical Sensitivities of Stiffened Aircraft Structures Due to Attached Mass-Spring-Dampers with Uncertain Parameters

Aerospace ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 174
Author(s):  
Johannes Seidel ◽  
Stephan Lippert ◽  
Otto von Estorff
Keyword(s):  
System Response ◽  
Fuzzy Arithmetic ◽  
Parameter Uncertainties ◽  
Excitation Spectra ◽  
Radiated Noise ◽  
Linking Elements ◽  
Manufacturing Tolerances ◽  
Suitable Framework ◽  
Mass Spring ◽  
The Impact

The slightest manufacturing tolerances and variances of material properties can indeed have a significant impact on structural modes. An unintentional shift of eigenfrequencies towards dominant excitation frequencies may lead to increased vibration amplitudes of the structure resulting in radiated noise, e.g., reducing passenger comfort inside an aircraft’s cabin. This paper focuses on so-called non-structural masses of an aircraft, also known as the secondary structure that are attached to the primary structure via clips, brackets, and shock mounts and constitute a significant part of the overall mass of an aircraft’s structure. Using the example of a simplified fuselage panel, the vibro-acoustical consequences of parameter uncertainties in linking elements are studied. Here, the fuzzy arithmetic provides a suitable framework to describe uncertainties, create combination matrices, and evaluate the simulation results regarding target quantities and the impact of each parameter on the overall system response. To assess the vibrations of the fuzzy structure and by taking into account the excitation spectra of engine noise, modal and frequency response analyses are conducted.

Critical Shock Response Spectrum of a Beam Under Shock Loading

2016 ◽  
Author(s):  
Bingwei Li ◽  
Qingming Li ◽  
Bo Liu ◽  
Zhiling Niu ◽  
Zijun Nangong ◽  
...  
Keyword(s):  
Shock Loading ◽  
Response Spectrum ◽  
Offshore Structures ◽  
Shock Response ◽  
Shock Response Spectrum ◽  
Shock Environment ◽  
Severe Shock ◽  
Structural Failures ◽  
Structural Engineers ◽  
The Relationship

The offshore structures experience severe shock environment caused by storms, episodic waves, icebergs or supply ships. The aerospace equipment may also encounter severe shock loadings due to pyrotechnic shock. The intensive shock causes structural failures, or even results in fatal consequences on the related facilities and persons. Therefore it is important to study the response and the damage behavior of structures under shock loading. The damage boundary of a beam under shock is studied, based on the structural dynamics and the shock response spectrum analysis. The relationship between the critical real velocity and the critical pseudo velocity is investigated, and the concept of loading factor is proposed. A simple and practical rule of estimating structure fragility is developed based on the pseudo velocity shock response spectrum and the loading factor. The explicit numerical simulation of a beam under shock loading is carried out using LS-DYNA. The critical shock response spectrums as well as the loading factor of the beam is obtained. This paper has an important significance of helping structural engineers to design the offshore and aerospace equipment under shock environment.

Behaviour of Multi-Layered Corrugated Paperboard Cushioning Systems under Impact Loads

2006 ◽  
Vol 3-4 ◽  
pp. 383-390 ◽  
Author(s):  
Michael A. Sek ◽  
Vincent Rouillard
Keyword(s):  
Extreme Events ◽  
High Speed ◽  
Shock Loading ◽  
Response Spectrum ◽  
Field Measurements ◽  
Mechanical Shocks ◽  
Impulsive Loads ◽  
Shock Response ◽  
Original Field ◽  
Shock Response Spectrum

This paper presents some of the latest results of a research project aimed at using composite corrugated paperboard structures for protection of products against mechanical shocks and vibration during transportation and handling. Specifically, the behaviour of multi-layered corrugated paperboard (MCPB) under shock loading is investigated. Conventionally, packaging cushion design requires the determination of the maximum expected shock levels or equivalent drop which are usually determined from statistical analysis of original field measurements. With this approach, it is generally acknowledged that the cushioning element is engineered to provide adequate protection for statistically likely events but not for extreme events with low statistical likelihood. It is reluctantly accepted that, should it occur, the latter will result in damage to the product. MCPB can be formed with a broad range of compressive characteristics and with various proportions of elastic and plastic behaviour. The objective of this experimental investigation was to determine the optimum elastic/plastic proportion to extend the protective range to include large shock levels. The experimental results obtained include the effects of compression history on the stress-strain properties of MCPB as well as the behaviour of the material in both virgin and pre-compressed form under impulsive loads. The mechanism of deformation of the corrugations (flutes) was studied using high-speed video equipment. The complex acceleration signals produced during deformation of the composite corrugated paperboard cushions under shock loading were analysed by means of the shock response spectrum. Experiments have shown that inserting a sacrificial crumple element of virgin corrugated paperboard at the optimum contact area ratio dramatically lowers the overall level of the resulting shock response spectrum. This has the effect of increasing the allowable drop height for a limited number of extreme events. The main conclusion of the research is that MCPB in both virgin and pre-compressed forms can be combined to provide significantly enhanced protection to products against mechanical hazards during distribution.

Transient Response of Submerged Plates Subject to Underwater Shock Loading: An Analytical Perspective

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
Zhanke Liu ◽  
Yin L. Young
Keyword(s):  
Structural Dynamics ◽  
Transient Response ◽  
Shock Loading ◽  
Structural Response ◽  
Small Range ◽  
Pressure Loading ◽  
Structure Interaction ◽  
Shock Response ◽  
Analytical Perspective ◽  
Underwater Shock

In this paper, Taylor’s floating air-backed plate (ABP) model is extended to the case of a submerged water-backed plate (WBP) within the acoustic range. The solution of the WBP is cast into the same format as that of the ABP with a modified fluid-structure interaction (FSI) parameter, which allows a unified analysis of the ABP and WBP using the same set of formulas. The influence of back conditions on fluid and structural dynamics, including fluid cavitation, is systematically investigated. Asymptotic limits are mathematically identified and physically interpolated. Results show that the WBP experiences lower equivalent pressure loading, reduced structural response, and hence lower peak momentum gaining. The time to reach peak momentum is shorter for the WBP than for the ABP. Cavitation is found to be almost inevitable for the ABP, while relevant to the WBP only for a small range of the FSI parameter. Implications to shock response of submerged structures are briefly discussed.

A Proposed Method to Standardize Shock Response Spectrum (SRS) Analysis: To Provide Agreement Between Tests Performed at Different Facilities

1996 ◽  
Vol 39 (3) ◽  
pp. 19-24
Author(s):  
Strether Smith ◽  
Bill Hollowell
Keyword(s):  
Analytical Procedure ◽  
Response Spectrum ◽  
Critical Parameters ◽  
Software Systems ◽  
Data Sets ◽  
Mechanical Shock ◽  
Analysis Algorithm ◽  
Shock Testing ◽  
Shock Response ◽  
Shock Response Spectrum

Discussions among practitioners of the shock-testing art and a series of round robins have shown that the results obtained from mechanical shock experiments performed in different laboratories very widely. To emphasize the problem, it has been found that different generations of hardware/software systems from one of the major system vendors produce results that disagree by up to 30 percent. A 1995 paper described a study that examined some of the critical parameters that affect shock response spectrum (SRS) results and reported on their use by some of the practitioners in the field.1 The paper showed that parameters such as anti-alias filter characteristics, ac-coupling strategies, and analysis algorithm/strategy can strongly affect the results and that they are not uniformly applied by system suppliers or users. This paper discusses the problem further and presents an analytical procedure that may be applied to achieve agreement between the data sets acquired and analyzed by different laboratories.

scholarly journals A Computationally Efficient Ground-Motion Selection Algorithm for Matching a Target Response Spectrum Mean and Variance

2011 ◽  
Vol 27 (3) ◽  
pp. 797-815 ◽  
Author(s):  
Nirmal Jayaram ◽  
Ting Lin ◽  
Jack W. Baker
Keyword(s):  
Ground Motion ◽  
Response Spectrum ◽  
Ground Motions ◽  
Structural Response ◽  
Response Spectra ◽  
Selection Algorithm ◽  
Target Response ◽  
Computationally Efficient ◽  
Mean And Variance ◽  
The Impact

Dynamic structural analysis often requires the selection of input ground motions with a target mean response spectrum. The variance of the target response spectrum is usually ignored or accounted for in an ad hoc manner, which can bias the structural response estimates. This manuscript proposes a computationally efficient and theoretically consistent algorithm to select ground motions that match the target response spectrum mean and variance. The selection algorithm probabilistically generates multiple response spectra from a target distribution, and then selects recorded ground motions whose response spectra individually match the simulated response spectra. A greedy optimization technique further improves the match between the target and the sample means and variances. The proposed algorithm is used to select ground motions for the analysis of sample structures in order to assess the impact of considering ground-motion variance on the structural response estimates. The implications for code-based design and performance-based earthquake engineering are discussed.

scholarly journals Shock Response Spectra Reconstruction of Pointwise Explosive-Induced Pyroshock Based on Signal Processing of Laser Shocks

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
S. Y. Chong ◽  
J. R. Lee ◽  
C. W. Kong
Keyword(s):  
Signal Processing ◽  
Response Spectrum ◽  
Arbitrary Point ◽  
Response Spectra ◽  
Industrial Applications ◽  
Reconstruction Method ◽  
Laser Shock ◽  
Signal Processing Algorithm ◽  
Magnetic Components ◽  
Shock Response

Pyroshock has been an issue of great concern for aerospace and defense industrial applications. When pyroshock devices are detonated, they can easily cause failures in electronic, optical, relay, and magnetic components generally in mid- and far-fields which is not avoidable at the design level. Thus, many numerical and experimental pyroshock simulations have been widely studied to predict explosive-induced pyroshock effect quantitatively, especially the shock response spectrum (SRS). In this study, a laser shock-based pyroshock reconstruction method is proposed to simulate a pointwise explosive-induced pyroshock signal. The signal processing algorithm for the laser shock-based pyroshock reconstruction is developed in a LabVIEW platform and consists of subbands decomposition, SRS matching in decomposed bands, and wave synthesizing. Then, two experimental setups are configured to obtain pyroshock signals and laser shock signals at four points in an aluminum plate. The reconstructed pyroshock signals synthesized according to the signal processing of the laser shocks demonstrate high similarity to the real pyroshock signals, where the similarity is evaluated by the mean acceleration difference between the SRS curves. The optimized settings of the subband decomposition were obtained and can be in the future used in a pyroshock simulator based on laser shock for pyroshock simulation at any arbitrary point.

Methodology for Assessing Shock Effect due to Aircraft Impact Considering the Nonlinear of Impact Zone and Soil-Structure Interaction

2017 ◽  
Author(s):  
Yugang Sun ◽  
Shujian Cheng ◽  
Honghui Ge ◽  
Xiaowen Wang ◽  
Fang Yuan ◽  
...  
Keyword(s):  
Linear Model ◽  
Soil Structure ◽  
Response Spectra ◽  
Material Nonlinearity ◽  
Soil Structure Interaction ◽  
Impact Zone ◽  
Structure Interaction ◽  
Shock Response ◽  
Two Factors ◽  
The Impact

Based on the shock damage propagation distances and the median fragility limit of the equipments, the NEI 07–13 employs the shock damage rules for determining the potential for affecting safe shutdown and fuel cooling equipments. However, the NEI 07–13 does not provide more detailed guidance for performing the shock damage assessments, because both the shock damage distances and the methodology for developing the median fragility limit are not provided in NEI 07–13. This paper discussed methodology developed for performing simplified assessments for shock effects considering the material nonlinearity of the impact zone and the soil-structure interaction. Three different models (i.e., linear model, nonlinear mode, and SSI model) were developed to calculate the in-structure shock response. The results of the linear model show the shock response due to aircraft impact would completely propagate from the center of initial impact zone and then along a structure pathway (e.g. wall, floor, basemat) to the in-structure without any energy dissipation. As a result, the in-structure shock response spectra are considerably higher than the spectra associated with the design-basis earthquake in the high frequency range. In order to reduce the shock effects on the in-structure safety-related systems and equipments, the material nonlinearity of the impact zone and the soil-structure interaction were incorporated in the dynamic analysis. The numerical results show that both the material nonlinearity and the soil-structure interaction would obviously absorb the energy of the shock waves, so the in-structure shock response spectra were reduced due to these two factors. Finally, the representative shock response spectra were compared with those used in the seismic margin assessment in order to assess specific equipment survival.

Sign in / Sign up

Export Citation Format

Share Document