An analytic method for free and forced vibration analysis of stepped conical shells with arbitrary boundary conditions

2017 ◽  
Vol 111 ◽  
pp. 126-137 ◽  
Author(s):  
Kun Xie ◽  
Meixia Chen ◽  
Zuhui Li
Keyword(s):  
Boundary Conditions ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Analytic Method ◽  
Arbitrary Boundary ◽  
Conical Shells ◽  
Arbitrary Boundary Conditions ◽  
Forced Vibration Analysis

scholarly journals A Semianalytic Method for Vibration Analysis of a Sandwich FGP Doubly Curved Shell with Arbitrary Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Zhongyu Zhang ◽  
Jiayang Gu ◽  
Jianjun Ding ◽  
Yanwu Tao
Keyword(s):  
Boundary Conditions ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Arbitrary Boundary ◽  
Forced Vibration Analysis ◽  
Doubly Curved ◽  
Curved Structure

Due to the excellent mechanical properties of doubly curved structure and functionally graded porous (FGP) material, the study of their vibration characteristics has attracted wide attention. The main aim of this research is to establish a formulation for free and forced vibration analysis of a new Sandwich FGP doubly curved structure. Four models of Sandwich materials are considered. The potential energy and kinetic energy functions are obtained on the foundation of the first-order shear deformation theory (FSDT). The idea of domain energy decomposition is applied to the theoretical modeling, where the structure is segmented along the generatrix direction. The continuity conditions for the interfaces between adjacent segments are balanced by the weighted parameters. For each segment, the displacement functions are selected as the Jacobi orthogonal polynomials and trigonometric series. The boundary conditions of the structure are obtained by the boundary spring simulation technique. The solution is obtained by the variational operation of the structural functional. The convergence performance and correctness of the theoretical model are examined by several numerical examples. Finally, some novel results are given, where free and forced vibration characteristics of Sandwich FGP doubly curved structures are examined in detail.

scholarly journals A Unified Spectro-Geometric-Ritz Method for Vibration Analysis of Open and Closed Shells with Arbitrary Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-30 ◽  
Author(s):  
Dongyan Shi ◽  
Yunke Zhao ◽  
Qingshan Wang ◽  
Xiaoyan Teng ◽  
Fuzhen Pang
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Analysis Model ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Auxiliary Functions ◽  
Arbitrary Boundary Conditions ◽  
Closed Shells

This paper presents free vibration analysis of open and closed shells with arbitrary boundary conditions using a spectro-geometric-Ritz method. In this method, regardless of the boundary conditions, each of the displacement components of open and closed shells is represented simultaneously as a standard Fourier cosine series and several auxiliary functions. The auxiliary functions are introduced to accelerate the convergence of the series expansion and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries. The boundary conditions are modeled using the spring stiffness technique. All the expansion coefficients are treated equally and independently as the generalized coordinates and determined using Rayleigh-Ritz method. By using this method, a unified vibration analysis model for the open and closed shells with arbitrary boundary conditions can be established without the need of changing either the equations of motion or the expression of the displacement components. The reliability and accuracy of the proposed method are validated with the FEM results and those from the literature.

scholarly journals A Modified Fourier–Ritz Formulation for Vibration Analysis of Arbitrarily Restrained Rectangular Plate with Cutouts

2018 ◽  
Vol 2018 ◽  
pp. 1-22
Author(s):  
Yiming Liu ◽  
Zhuang Lin ◽  
Hu Ding ◽  
Guoyong Jin ◽  
Sensen Yan
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Flexural Vibration ◽  
Vibration Characteristics ◽  
Geometric Parameters ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Stiffness Constant ◽  
Proper Values

A modified Fourier–Ritz method is developed for the flexural and in-plane vibration analysis of plates with two rectangular cutouts with arbitrary boundary conditions, aiming to provide a unified solving process for cases that the plate has various locations or sizes of cutout, and different kinds of boundary conditions. Under the current framework, modifying the position of the cutout or the boundary conditions of the plate is just as changing the geometric parameters of the plate, and there is no need to change the solution procedures. The arbitrary boundary conditions can be obtained by setting the stiffness constant of the boundary springs which are fixed uniformly along the edges of the plate at proper values. The strain and kinetic energy functions of a plate with rectangular cutout are derived in detail. The convergence and accuracy of the present method are demonstrated by comparing the present results with those obtained from the FEM software. In this paper, free in-plane and flexural vibration characteristics of the plate with rectangular cutout under general boundary conditions are studied. From the results, it can be found that the geometric parameters and positions of the cutout and the boundary conditions of the plate will obviously influence the natural vibration characteristics of the structures.

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