Vibration analysis of beams using the generalized differential quadrature rule and domain decomposition

Abstract

This study dealt with domain decomposition in the recently proposed generalized differential quadrature rule. In detail, the authors concentrated on the free vibration of multispan and stepped Euler beams, and beams carrying an intermediate or end concentrated mass. Since compatibility conditions should be implemented in a strong form at the junction of the subdomains concerned, the FEM techniques used for internal moments and shear forces must not be used. Compatibility conditions and their differential quadrature expressions were explicitly formulated. A peculiar phenomenon was found in differential quadrature applications that equal-length subdomains gave more accurate results than unequal-length ones using the same number of subdomain grids. Various examples were presented and very accurate results have been obtained.