A unified Fourier series solution for vibration analysis of FG-CNTRC cylindrical, conical shells and annular plates with arbitrary boundary conditions

2020 ◽  
Vol 232 ◽  
pp. 111549 ◽  
Author(s):  
Bin Qin ◽  
Rui Zhong ◽  
Tiantian Wang ◽  
Qingshan Wang ◽  
Yongge Xu ◽  
...  
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Series Solution ◽  
Arbitrary Boundary ◽  
Conical Shells ◽  
Arbitrary Boundary Conditions ◽  
Annular Plates

scholarly journals In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xianjie Shi ◽  
Dongyan Shi ◽  
Zhengrong Qin ◽  
Qingshan Wang
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Wide Spectrum ◽  
Arbitrary Boundary ◽  
Different Boundary Conditions ◽  
Plane Vibration ◽  
Arbitrary Boundary Conditions ◽  
Annular Plates ◽  
Generalized Fourier Series

In comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular plates with arbitrary boundary conditions along each of its edges. Regardless of the boundary conditions, the in-plane displacement fields are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of in-plane vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current solution for predicting the in-plane vibration characteristics of annular plates subjected to different boundary conditions.

A Modified Fourier Solution for Free Damped Vibration Analysis of Sandwich Viscoelastic-Core Conical Shells and Annular Plates with Arbitrary Restraints

2016 ◽  
Vol 08 (08) ◽  
pp. 1650094 ◽  
Author(s):  
Chuanmeng Yang ◽  
Guoyong Jin ◽  
Weijian Xu ◽  
Zhigang Liu
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Current Method ◽  
Fourier Series Expansion ◽  
Algebraic Equations ◽  
Arbitrary Boundary ◽  
Conical Shells ◽  
Annular Plates ◽  
Damping Characteristics ◽  
Loss Factors

In this paper, arbitrary boundary conditions including classical and elastic ones are considered in analyzing the vibration and damping characteristics of the sandwich conical shells and annular plates using a simple and efficient modified Fourier solution. The displacement field is expressed as the linear combination of a standard Fourier series and several supplementary terms. The addition of these terms make the Fourier series expansion applicable to any boundary conditions, and the Fourier series expansions improved drastically regarding its accuracy and convergence. Instead of adopting conventional differentiation procedure, a Rayleigh–Ritz technique based on the energy function is conducted which leads to a set of algebraic equations. Then natural frequencies and loss factors can be obtained by solving the algebraic equations. Accuracy and reliability of the current method are checked by comparing the present results with the existing solutions. Influences of some vital parameters on the free vibration and damping performance of sandwich shells and plates are discussed. The detailed effect of restraints from different directions on the frequencies and loss factors is investigated. So, the method can provide a guide to design sandwich structures with desired vibration characteristic and well damping performance by reasonably adjusting the boundary condition. Some new numerical results are presented for future validation of various approximate/numerical methods.

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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