Modal Expressions for Relative
Displacements Underlying Pseudo-velocity Shock-Response Spectra, for Idealized
Remote Shock Loadings: Derivation and Verification
Dr. R. David Hampton,
Abstract:
Recently, exact expressions were presented for the
time-domain response of a mass-spring-damper (MSD) system to a seismic input
comprising exponentially decaying sinusoids. Such an input could result
from a remote shock consisting of an ideal impulse, as filtered through the eigensystem comprising the linear model of a
structure. Using these results the analytical time responses were found,
of the (hypothetical) MSD system used for shock-response-spectrum (SRS)
determination, for remote shock inputs of three forms: (1) an ideal impulse,
(2) a rectangular pulse, and (3) a saw-tooth pulse. These responses
permit exact SRS determination without necessitating numerical evaluation of a
convolution integral. This paper first repeats in detail the earlier
derivations of the responses to these remote shocks, and then describes their
verification via a combination of algebraic-manipulation software, dimensional
analysis, numerical checks, and a 2DOF test case.
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