Free and Forced Vibration Analysis of Uniform and Stepped Conical Shell Based on Jacobi–Ritz Time Domain Semi-Analytical Method

Abstract

Under arbitrary boundary conditions, a Jacobi–Ritz time domain semi-analytical method is proposed to study the vibration behaviors of uniform and stepped conical shells. Based on the idea of the differential element method and the first-order shear deformation theory (FSDT), the vibration analysis models of uniform and stepped conical shell structures are established. The axial and circumferential displacement tolerance functions are expressed by the Jacobi polynomial and the Fourier series. The complex boundary conditions are simulated by using artificial spring technology. In light of the Ritz method and the Newmark-[Formula: see text] integral method, the free and forced vibration results of the structure can be figured out in the time domain. The numerical results demonstrate that the proposed method has excellent accuracy and remarkable dependability when compared to the finite element method (FEM). Numerical examples are used to examine the forced and free vibration behaviors under various boundary conditions, semi-vertex angles, thicknesses, and load characteristics.