THE LUMPED PARAMETER METHOD FOR ELASTIC IMPACT PROBLEMS
Abstract
A fundamental study of the mechanical impact between two elastic bodies is undertaken. The objective of the study is to develop an analytical method to predict the impact force for subsequent application to vibration and noise problems. The basis of the method evolved consists of replacing the continuous elastic bodies by a finite assembly of spring-mass-damper elements which collectively duplicate the contact point mobilities of the original bodies. The contact interface is provided by a Hertzian contact law model; and the mobilities by either modal expansion methods or by experiment. Several classical impact problems involving simple beams and plates are solved to illustrate the method and to assess its accuracy. Two mechanical systems, consisting of a free rigid mass transversely impacting a free-free beam and a freely suspended plate are given as illustration of complex body shapes where the contact mobilities were obtained by measurement. The advantages of this lumped parameter method in solving impact problem are its simplicity of mathematical formulation and ease of implementation for complex body shapes. As a bonus, it provides a better understanding of the coupling effect of the excited modes on the occurrence of multiple impacts.
Degree
Ph.D.
Subject Area
Mechanical engineering
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