Elastodynamic Analysis of a Completely Elastic System

The completely elastic system considered for this vibration analysis consists of an offset slider-crank mechanism having (a) elastic supports and mountings of the mechanism permitting translational vibrations of the shafts and supports, (b) elastic shafts permitting torsional vibrations, (c) elastic links of the mechanism which deform due to external or internal body forces and allow flexural and axial vibrations. Both the effect of the deformations caused by the inertia forces in the mechanism links, shafts, and supports and the effect of change in the inertia forces due to these deformations are taken into account in constructing a general mathematical model for conducting elastodynamic analysis. The rigid displacements (finite and infinitesimal) of the mechanism links due to deformations in the support are evaluated using a truncated Taylor series approximation. Deformation in the links caused by the inertia forces is approximated by a finite number of terms in a Fourier series using the Raleigh-Ritz method. The Lagrange equations of motion are used to obtain coupled time varying linear ordinary differential equations of motion for the vibration analysis of the slider-crank mechanism. The method in general may be applied to any planar or spatial system consisting of elastic links, elastic shafts, and elastic supports. Numerical examples are presented for illustration.