The pervasive shock response spectrum (SRS) and damage boundary methods for evaluating product fragility and designing external cushioning for shock protection are described in detail with references to the best available literature. Underlying assumptions are carefully reviewed and the central message of the SRS is highlighted, particularly as it relates to standardized drop testing. Shortcomings of these methods are discussed, and the results are extended to apply to more general systems. Finally some general packaging and shock-mounting strategies are discussed in the context of protecting a fragile disk drive in a notebook computer, although the conclusions apply to other products as well. For example, exterior only cushioning (with low restitution to reduce subsequent impacts) will provide a slenderer form factor than the next best strategy: interior cushioning with a &#x201c;dead&#x201d; hard outer shell.

Suresh Goyal

Jim M. Papadopoulos

Paul A. Sullivan

Shock Protection of Portable Electronic Products: Shock Response Spectrum, Damage Boundary Approach, and Beyond

By adjusting the analytic mass matrix or stiffness parameters, the correlation between measured and computed modal data can be improved. This article proposes a simple method for model optimization. Numerical examples will be included to illustrate the proposed approach.

B.P. Wang

F.H. Chu

Finite Element Model Optimization Using Diagonal Mass Matrix

This article focuses on the problem of guide-vane vibrations of reversible pump&#x2013;turbines, especially, in the pump mode. These vibrations are transmitted to the guide-vane shaft torque. The guide-vane vibrations are caused by the impeller exit flow, which has a turbulent and partly nondeterministic property. Experimentally determined flow velocities at the impeller exit are given. The mathematical models for theoretical torsional vibration prediction formulated using linear and nonlinear differential equations are presented. The results of theoretical calculations are compared with measurement results. The possibility of transferring the parameters from the model to the prototype is discussed.

Andrej Predin

Torsional Vibrations at Guide-Vane Shaft of Pump&#x2013;Turbine Model

This article addresses an application of the dynamic condensation in modal testing, which requires measurements of natural frequencies and a limited number of components of modal shapes only. The measured frequencies can be employed as the initial estimates in the iterated dynamic condensation to effectively find an exact solution for the original eigenvalue problem and determine the transformation matrix between the testing and nontesting coordinates. Complete modal shapes including the nontesting coordinates can then be estimated based on the limited measurements. Numerical results are presented to illustrate the feasibility and efficiency of the iterated dynamic condensation. A comparison with the experimental results of a multiple disk system is also provided.

Zhikun Hou

Shiyu Chen

Iterated Dynamic Condensation Technique and Its Applications in Modal Testing

A numerical method is presented to investigate the dynamic response of uniform orthotropic beams subjected to an impact of a mass. Higher order shear deformation and rotary inertia are included in the analysis of the beams. The impactor and laminated composite beam are treated as a system. The nonlinear differential governing equations of motion are then derived based on the Lagrange principle and modified nonlinear contact law, and solved numerically. The solution procedure is applicable to arbitrary boundary conditions. Numerical results are compared with those available in the literature to demonstrate the validity of the method, and very good agreement is achieved. The effects of boundary conditions on the contact force, contact duration, stress distributions, and beam deflection are discussed.

Lu Chun

K. Y. Lam

Behavior of Uniform Anisotropic Beams of Rectangular Section under Transverse Impact of a Mass

Statistical methodologies were employed for measuring and analyzing the explosively induced transient responses of a flat steel plate excited with shock. The application of design of experiment methodology was made to structure and test a Taguchi L9(32) full factorial experimental matrix (which uses nine tests to study two factors, with each factor examined at three levels) in which a helium-neon laser Doppler vibrometer and two piezocrystal accelerometers were used to monitor explosively induced vibrations ranging from 10 to 105 Hz on a 96 &#x000D7; 48 &#x000D7; 0.25 in. flat steel plate. Resulting conclusions were drawn indicating how these techniques aid in understanding the pyroshock phenomenon with respect to the effects and interrelationships of explosive-charge weight and location on the laser Doppler and contract accelerometer recording systems.

C. J. Litz

Laser Doppler Vibrometer: Application of DOE/Taguchi Methodologies to Pyroshock Response Spectra

The application of coupled Lagrangian&#x2014;Eulerian analysis to various types of underwater shock problems was investigated, with the verification and validation of this analysis approach in mind. Analyses were conducted for a simple TNT detonation problem and for the classical problems of an infinite cylindrical shell and a spherical shell loaded by a plane acoustic step wave. The advantages, disadvantages, and limitations of this approach are identified and discussed.

Young S. Shin

James E. Chisum

Modeling and Simulation of Underwater Shock Problems Using a Coupled Lagrangian&#x2014;Eulerian Analysis Approach

About this journal

Shock and Vibration publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience.&nbsp;

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Chief Editor&nbsp;Dr Tai Thai&nbsp;is based at the University of Melbourne and his current research focuses on high strength materials for sustainable construction of buildings, bridges and other infrastructure.

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Shock and Vibration - Table of contents 1997

title

Shock and Vibration publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience. 

Shock and Vibration