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

Abstract

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 report 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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 2004
Accession Number
ADA428150

Entities

People

  • Nathan S. Wiedenman
  • R. D. Hampton
  • Ting H. Li

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Human Systems
  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Ammunition
  • Composite Materials
  • Convolution
  • Convolution Integrals
  • Engineering
  • Frequency
  • Integrals
  • Linear Systems
  • Materials
  • Mechanical Engineering
  • Military Research
  • Munitions
  • Projectiles
  • Resonant Frequency
  • Shock Response Spectra
  • Spectra
  • Weapons

Readers

  • Approximation Theory.
  • Combustion Dynamics and Shock Wave Physics.
  • Control Systems Engineering.