Free and Forced Vibration Analysis of Airtight Cylindrical Vessels with Doubly Curved Shells of Revolution by Using Jacobi-Ritz Method

Jing

et al. 2018

Materials

Self Cite

The paper introduces a semi-analytical approach to analyze free vibration characteristics of stepped functionally graded (FG) paraboloidal shell with general edge conditions. The analytical model is established based on multi-segment partitioning strategy and first-order shear deformation theory. The displacement components along axial direction are represented by Jacobi polynomials, and the Fourier series are utilized to express displacement components in circumferential direction. Based on penalty method about spring stiffness technique, the general edge conditions of doubly curved paraboloidal shell can be easily simulated. The solutions about doubly curved paraboloidal shell were solved by approach of Rayleigh–Ritz. Convergence study about boundary parameters, Jacobi parameters et al. are carried out, respectively. The comparison with published literatures, FEM and experiment results show that the present method has good convergence ability and excellent accuracy.

Section: Fundamental Theorymentioning

confidence: 99%

Application of First-Order Shear Deformation Theory on Vibration Analysis of Stepped Functionally Graded Paraboloidal Shell with General Edge Constraints

Jing

et al. 2018

Materials

Self Cite

“…In addition, the coordinate system ( , , ) is also shown in Figure 1, which will be used in the analysis. The arbitrary boundary technique [43][44][45][46][47] is introduced to implement the general boundary condition in which one group of liner spring ( = 0, , 0, and denote the location of the spring; i.e., 0 represents the location of the edge = 0) and two groups of rotation springs and are introduced to simulate the related boundary forces in each boundary of a plate, as shown in Figure 1. The general boundary condition is easily obtained by assigning the stiffness of the boundary springs with various values.…”

Section: Theoretical and Numerical Formulationsmentioning

confidence: 99%

An Accurate Solution Method for the Static and Vibration Analysis of Functionally Graded Reissner‐Mindlin Rectangular Plate with General Boundary Conditions

Liu

et al. 2018

Shock and Vibration

Self Cite

This paper presents an accurate solution method for the static and vibration analysis of functionally graded Reissner-Mindlin plate with general boundary conditions on the basis of the improved Fourier series method. In the theoretical formulations, the governing equations and the general elastic boundary equations are obtained by using Hamilton’s principle. The components of admissible displacement functions are expanded as an improved Fourier series form which contains a 2D Fourier cosine series and auxiliary function in the form of 1D series. The major role of the auxiliary function is to remove the potential discontinuities of the displacement function and its derivatives at the edges and ensure and accelerate the convergence of the series representation. The characteristic equations are easily obtained via substituting admissible displacement functions into governing equations and the general elastic boundary equations. Several examples are made to show the excellent accuracy and convergence of the current solutions. The results of this paper may serve as benchmark data for future research in related field.

“…Mindlin plate with arbitrary elastic point edge supports is shown in Figure 1. The boundary conditions are presented by three kinds of restraining springs [29][30][31][32][33][34], namely, translational, rotational, and torsional springs. Springs are evenly arranged on each edge of Mindlin plate.…”

Section: Point-supported Edge Conditions the Rectangularmentioning

confidence: 99%

A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges

et al. 2018

Shock and Vibration

Self Cite

A series solution for the transverse vibration of Mindlin rectangular plates with elastic point supports around the edges is studied. The series solution for the problem is obtained using improved Fourier series method, in which the vibration displacements and the cross-sectional rotations of the midplane are represented by a double Fourier cosine series and four supplementary functions. The supplementary functions are expressed as the combination of trigonometric functions and a single cosine series expansion and are introduced to remove the potential discontinuities associated with the original admissible functions along the edges when they are viewed as periodic functions defined over the entire x-y plane. This series solution is approximately accurate in the sense that it explicitly satisfies, to any specified accuracy, both the governing equations and the boundary conditions. The convergence, accuracy, stability, and efficiency of the proposed method have been examined through a series of numerical examples. Some numerical examples about the nondimensional frequency and mode shapes of Mindlin rectangular plates with different point-supported edge conditions are given.