Large amplitude free vibration analysis of circular arches with variable thickness

Abstract

This study aims to investigate the large amplitude nonlinear vibration of variable thickness arches with different cross-sectional shapes under different boundary conditions. The governing equations of the arches are derived using Hamilton's principle by considering their geometric nonlinearities. Then, the differential quadrature method (DQM) is employed for the discretization to obtain the ordinary differential equations of motion for the circular arches with variable thickness. The theoretical model is validated by comparing the linear and nonlinear natural frequencies of arches. The nonlinear vibration characteristics of arches are solved using the direct iteration scheme. The effects of the slenderness ratio, modified slenderness ratio of the arch, and variable thickness parameters under different cross-sectional shapes on the nonlinear to linear frequency ratios of the arches with clamped and pin-ended boundary conditions are investigated. The results indicate that appropriate variable thickness parameters can improve the linear frequency and the nonlinear to linear frequency ratio of arches, which offers some suggestions for the design of variable thickness arches.