Deflection and free vibration of symmetrically laminated quasi-isotropic thin rectangular plates for different boundary conditions

2013 ◽  
Vol 57 ◽  
pp. 197-222 ◽  
Author(s):  
Erkin Altunsaray ◽  
İsmail Bayer
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plates ◽  
Different Boundary Conditions

An exact solution for free vibration of thin functionally graded rectangular plates

2010 ◽  
Vol 225 (3) ◽  
pp. 526-536 ◽  
Author(s):  
A Hasani Baferani ◽  
A R Saidi ◽  
E Jomehzadeh
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Different Boundary Conditions

The aim of this article is to find an exact analytical solution for free vibration characteristics of thin functionally graded rectangular plates with different boundary conditions. The governing equations of motion are obtained based on the classical plate theory. Using an analytical method, three partial differential equations of motion are reformulated into two new decoupled equations. Based on the Navier solution, a closed-form solution is presented for natural frequencies of functionally graded simply supported rectangular plates. Then, considering Levy-type solution, natural frequencies of functionally graded plates are presented for various boundary conditions. Three mode shapes of a functionally graded rectangular plate are also presented for different boundary conditions. In addition, the effects of aspect ratio, thickness—length ratio, power law index, and boundary conditions on the vibration characteristics of functionally graded rectangular plates are discussed in details. Finally, it has been shown that the effects of in-plane displacements on natural frequencies of functionally graded plates under different boundary conditions have been studied.

Free vibration analysis of rectangular plates with arbitrary elastic boundary conditions

2021 ◽  
Vol 263 (5) ◽  
pp. 1891-1898
Author(s):  
Zhenshuai Wan
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Different Boundary Conditions ◽  
Elastic Boundary ◽  
Fourier Series Method ◽  
The Matrix ◽  
Elastic Boundary Conditions

boundary conditions are In this paper, an improved Fourier series method is presented for the free vibration analysis of rectangular plates with arbitrary elastic conditions. The stiffness value of the restraining springs is determined as required to simulate the arbitrary elastic boundary conditions. The exact solution of plates with arbitrary elastic boundary conditions is solved by the introduced supplementary func-tions. The matrix eigenvalue equation of plates is derived by using boundary conditions and the governing equations. Compared with exist methods, the presented method can be easily applied to most of plate vibration problems with different boundary conditions. To validate the accuracy of the presented method, numerical simulations with different boundary conditions are presented.presented.

A Novel and Accurate Ritz Formulation for Free Vibration of Rectangular and Skew Plates

2012 ◽  
Vol 79 (6) ◽  
Author(s):  
S. A. Eftekhari ◽  
A. A. Jafari
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Rectangular Plates ◽  
Natural Boundary ◽  
Boundary Points ◽  
Natural Boundary Conditions ◽  
Free Edges

One of the major limitations of the conventional Ritz method is its difficulty in implementation to the differential equations with natural boundary conditions at the boundary points/lines. Plates involving free edges/corners and irregularly shaped plates are two historical and classical examples which show that their solutions cannot be accurately approximated by the conventional Ritz method. To solve this difficulty, a simple, novel, and accurate Ritz formulation is introduced in this paper. It is revealed that the proposed methodology can produce much better accuracy than the conventional Ritz method for rectangular plates involving free edges/corners and skew plates.

A new simple shear deformation theory for free vibration analysis of isotropic and FG plates under different boundary conditions

2015 ◽  
Vol 11 (3) ◽  
pp. 437-470 ◽  
Author(s):  
Amale Mahi ◽  
El Abbas Adda Bedia ◽  
Abdelouahed Tounsi ◽  
Amina Benkhedda
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Temperature Rise ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Content Type ◽  
Different Boundary Conditions ◽  
Fg Plates ◽  
Shear Deformation Theories

Purpose – A new simple parametric shear deformation theory applicable to isotropic and functionally graded plates is developed. This new theory has five degrees of freedom, provides parabolic transverse shear strains across the thickness direction and hence, it does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the plate are satisfied rigorously. The paper aims to discuss these issues. Design/methodology/approach – Material properties are temperature-dependent and vary continuously through the thickness according to a power law distribution. The plate is assumed to be initially stressed by a temperature rise through the thickness. The energy functional of the system is obtained using Hamilton’s principle. Free vibration frequencies are then calculated using a set of characteristic orthogonal polynomials and by applying Ritz method for different boundary conditions. Findings – In the light of good performance of the present theory for all boundary conditions considered, it can be considered as an excellent alternative to some two-dimensional (2D) theories for approximating the tedious and time consuming three-dimensional plate problems. Originality/value – To the best of the authors’ knowledge and according to literature survey, almost all published higher order shear deformation theories have been limited to simply supported boundary conditions and without taking into account the thermal stresses effects. The existing 2D shear deformation theories of Reddy, Karama and Touratier can be easily recovered. Furthermore, this feature can be highly appreciated in an iterative design process where a large number of derived plate models can be tested by selecting only two parameters in a simple polynomial function which is computationally efficient. Finally, new results are presented to show the effect of material variation, and temperature rise on natural frequencies of the FG plate for different boundary conditions.

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