Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

Abstract

The free vibration analysis of the functionally graded (FG) double curved shallow shell structures with general boundary conditions is investigated by an improved Fourier series method (IFSM). The material properties of FG structures are assumed to vary continuously in the thickness direction, according to the four graded parameters of the volume distribution function. Under the current framework, the displacement and rotation functions are set to a spectral form, including a double Fourier cosine series and two supplementary functions. These supplements can effectively eliminate the discontinuity and jumping phenomena of the displacement function along the edges. The formulation is based on the first-order shear deformation theory (FSDT) and RayleighRitz technique. This method can be universally applied to the free vibration analysis of the shallow shell, because it only needs to change the relevant parameters instead of modifying the basic functions or adapting solution procedures. The proposed method shows excellent convergence and accuracy, which has been compared with the results of the existing literatures. Numerous new results for free vibration analysis of FG shallow shells with various boundary conditions, geometric parameter, material parameters, gradient parameters, and volume distribution functions are investigated, which may serve as the benchmark solution for future researches.

The Vibro-Acoustic Characteristics Analysis of the Coupled System between Composite Laminated Rotationally Stiffened Plate and Acoustic Cavities

“…pling system are established by using the modified Fourier series method [13,14]. S quently, energy functionals are formulated for both the structural and acoustic dom Leveraging the coupling characteristics between a composite laminated rotationally ened plate and acoustic cavities, a coupling potential energy of the plate-cavity cou system is defined.…”

“…This article aims to utilize the modified Fourier series method and first-order shear deformation theory to construct a unified analysis model of the vibro-acoustic characteristics of the coupling system between a composite laminated rotationally stiffened plate and acoustic cavities. Firstly, displacement and sound pressure functions of the coupling system are established by using the modified Fourier series method [13,14]. Subsequently, energy functionals are formulated for both the structural and acoustic domains.…”

Dynamic Analysis of Rectangular Plate Stiffened by Any Number of Beams with Different Lengths and Orientations

“…Displacement Function. In the present research, the admissible displacement functions of a plate and a beam are established by IFSM, which has been successfully applied to solve the vibration of beams [40,41], plates [42,43], and shells [44]. e improved Fourier series consists of main functions and auxiliary functions.…”

A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method

“…Brischetto et al [17] introduced the zig-zag function to overcome the discontinuity of displacement function; free vibration of curved plates was analyzed. Shi et al [18] analyzed free vibration of double-curved shallow shell structures by means of the improved Fourier series method (IFSM); the excellent convergence and accuracy of the presented method have been proved. Li et al [19][20][21][22] extended the modified Fourier-Ritz approach to evaluate the free vibration of rectangular plate, sector plate, and cylindrical, conical, and spherical panels and shells of revolution with general boundary conditions.…”