A Lumped Parameter Approach to Vibration and Stress Analysis of Elastic Linkages

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Abstract
A method of kineto-elastodynamic analysis is developed employing lumped parameter models for simulating moving mechanism components considered as simply-supported beams subject to in-plane bending. Application of finite difference approximations to Euler’s beam theory leads to a system of nonlinear, ordinary differential equations of motion, and numerical solution of these equations is illustrated for specific examples. Variable as well as uniform cross-section members are analyzed for elastic vibration and stresses. By means of a general optimization procedure presented, nonuniform beam contours are obtained which provide a substantial stress reduction relative to the uniform case, without a corresponding increase in total mass.

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