Finite element evaluation of free vibration characteristics of magneto-electro-elastic rectangular plates in hygrothermal environment using higher-order shear deformation theory

2018 ◽  
Vol 202 ◽  
pp. 1339-1352 ◽  
Author(s):  
M Vinyas ◽  
S.C. Kattimani
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Vibration Characteristics ◽  
Rectangular Plates ◽  
Hygrothermal Environment

A finite element–based assessment of free vibration behaviour of circular and annular magneto-electro-elastic plates using higher order shear deformation theory

2019 ◽  
Vol 30 (16) ◽  
pp. 2478-2501 ◽  
Author(s):  
M Vinyas ◽  
AS Sandeep ◽  
T Nguyen-Thoi ◽  
F Ebrahimi ◽  
DN Duc
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Elastic Plates ◽  
Benchmark Solutions

In this article, the free vibration behaviour of circular and annular magneto-electro-elastic plates has been investigated under the framework of higher order shear deformation theory. The three-dimensional finite element formulation has been derived with the aid of Hamilton’s principle by taking into account the coupling between elastic, electric and magnetic properties. The equations of motion are solved using condensation technique. Furthermore, the credibility of proposed finite element formulation has been validated using COMSOL software and also by comparing the results with previously published articles. Special attention has also been paid to assess the influence of parameters such as coupling effect, stacking sequences and inner-to-outer diameter ratio. The numerical results reveal that the coupled natural frequencies of the annular magneto-electro-elastic plates vary significantly with the circular hole dimensions incorporated. The circular and annular plates are considered as one of the prominent structural components in various engineering and industrial application. Therefore, the proposed finite element formulation and the results presented in this article can serve as benchmark solutions for the design and analysis of smart sensors and actuators.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

scholarly journals A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Fuzhen Pang ◽  
Cong Gao ◽  
Jie Cui ◽  
Yi Ren ◽  
Haichao Li ◽  
...  
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Numerical Verification ◽  
First Order

This paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. The analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. The displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. The boundary restraints of FG spherical shell can be easily simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method. To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. The results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). The impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are also presented.

Sign in / Sign up

Export Citation Format

Share Document