Stochastic Vibration Responses of Functionally Graded Three-Stage Conical–Cylindrical Combined Shell Structure Subjected to Various Stationary Stochastic Excitations

Abstract

This paper proposed a theoretical model for analyzing the stochastic vibration responses of functionally graded three-stage conical–cylindrical combined shell structure (FG-TSCCCSS) subjected to various stationary stochastic excitations. The theoretical model is established by employing the differential quadrature method in conjunction with pseudo excitation method (PEM) in the framework of FSDT. The material property parameters of FG-TSCCCSS along the thickness direction are ascertained based on four-parameter power–law distributions in terms of volume fractions of constituents of FGMs. The FG-TSCCCSS mainly consists of three conical shell segments with different tapers and one cylindrical shell segment. The coupling between adjacent shell segments is achieved by means of common nodes. The various boundary conditions of FG-TSCCCSS are simulated by applying the penalty function method. Based on the above model, the convergence analysis of the established model for determining the value of the penalty factor and the number of differential quadrature nodes first. Then, the precision and reliability of the proposed numerical model are verified by comparing the present solutions with the results of literature works and finite element software. Finally, the stochastic vibration response analysis of FG-TSCCCSS is carried out by investigating the influences of power–law distribution, power–law exponent, boundary condition, stochastic excitation type and taper angle on the natural frequency and PSD acceleration response of FG-TSCCCSS. The paper can provide the theoretical reference and numerical tool for the random vibration response evaluation of combined shell structures of various engineering application fields.