An analytical procedure for dynamic response determination of a viscoelastic beam with moderately large deflection using first-order shear deformation theory

In this article, the dynamic response of a viscoelastic beam with moderately large deflection subjected to transverse and axial loads is studied using the first-order shear deformation theory. The von-Karman strain displacement relations and Hooke's law are used for formulation. The solution of the equations, which are a system of nonlinear partial differential equations, are obtained analytically using the perturbation technique in conjunction with the eigenfunction expansion method. The results are compared with the finite elements method. Also, a sensitivity analysis is performed, and the effects of geometrical and material properties are investigated on the response.