Free and forced vibration of variable stiffness composite annular thin plates with elastically restrained edges

2016 ◽  
Vol 149 ◽  
pp. 398-407 ◽  
Author(s):  
Ping Tan ◽  
G.J. Nie
Keyword(s):  
Forced Vibration ◽  
Variable Stiffness ◽  
Thin Plates ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

scholarly journals Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
María Virginia Quintana ◽  
Ricardo Oscar Grossi
Keyword(s):  
Plate Theory ◽  
Ritz Method ◽  
Free Vibrations ◽  
Rectangular Domain ◽  
Internal Line ◽  
Thin Plates ◽  
Mode Shapes ◽  
Approximate Analytical Solutions ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

This paper deals with a general variational formulation for the determination of natural frequencies and mode shapes of free vibrations of laminated thin plates of trapezoidal shape with an internal line hinge restrained against rotation. The analysis was carried out by using the kinematics corresponding to the classical laminated plate theory (CLPT). The eigenvalue problem is obtained by employing a combination of the Ritz method and the Lagrange multipliers method. The domain of the plate is transformed into a rectangular domain in the computational space by using nonorthogonal triangular coordinates and the transverse displacements are approximated with a set of simple polynomials automatically generated and expressed in the triangular coordinates. The developed algorithm allows obtaining approximate analytical solutions for mentioned plate with different geometries, aspect ratio, position of the line hinge, and boundary conditions including translational and rotational elastically restrained edges. It allows studying the influence of the mentioned line on the vibration frequencies and respective mode shapes. The algorithm can easily be programmed and it is numerically stable. Additionally, as a particular case, the results of triangular plates can be easily generated.

scholarly journals An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Xue Kai ◽  
Wang Jiufa ◽  
Li Qiuhong ◽  
Wang Weiyuan ◽  
Wang Ping
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
Cross Sectional ◽  
Fourier Cosine ◽  
Cosine Series ◽  
The Matrix ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

An analysis method is proposed for the vibration analysis of the Mindlin rectangular plates with general elastically restrained edges, in which the vibration displacements and the cross-sectional rotations of the mid-plane are expressed as the linear combination of a double Fourier cosine series and four one-dimensional Fourier series. The use of these supplementary functions is to solve the possible discontinuities with first derivatives at each edge. So this method can be applied to get the exact solution for vibration of plates with general elastic boundary conditions. The matrix eigenvalue equation which is equivalent to governing differential equations of the plate can be derived through using the boundary conditions and the governing equations based on Mindlin plate theory. The natural frequencies can be got through solving the matrix equation. Finally the numerical results are presented to validate the accuracy of the method.

An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges

2013 ◽  
Vol 572 ◽  
pp. 489-493 ◽  
Author(s):  
Kai Xue ◽  
Jiu Fa Wang ◽  
Qiu Hong Li ◽  
Wei Yuan Wang ◽  
Ping Wang
Keyword(s):  
Series Solution ◽  
Rectangular Plates ◽  
Analysis Method ◽  
Original Function ◽  
Cross Sectional ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Fourier Cosine Series ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

An analysis method has been proposed for the vibration analysis of the Mindlin rectangular plates with general elastically boundary supports, in which the vibration displacements and the cross-sectional rotations of the mid-plane are sought as the linear combination of a double Fourier cosine series and auxiliary series functions. The use of these supplementary functions is to solve the potential discontinuity associated with the x-derivative and y-derivative of the original function along the four edges, so this method can be applied to get the exact solution. Finally the numerical results are presented to validate the correct of the method.

Transverse Vibration of Plate Structures With Elastically Restrained Edges by the Spline/Finite Strip Method

1993 ◽  
Vol 115 (3) ◽  
pp. 295-302 ◽  
Author(s):  
Abdul Hamid Sheikh ◽  
Madhujit Mukhopadhyay
Keyword(s):  
Natural Frequencies ◽  
Stiffened Plates ◽  
Plate Structures ◽  
Finite Strip ◽  
Strip Method ◽  
Finite Strip Method ◽  
Spline Finite Strip ◽  
Elastically Restrained Edges ◽  
Elastically Restrained ◽  
Comparison Of The Results

The newly developed spline finite strip method has been applied to determine the natural frequencies of plates and stiffened plates with edged elastically restrained against translation and rotation. The stiffener has been modelled so that it can be situated anywhere within the plate strip. The formulation has been generalized in such a manner that it can handle general shaped plates and stiffeners having arbitrary orientation and eccentricity. A consistent formulation has been adopted to incorporate the contribution of the edge restraints in the structural stiffness matrix. Numerical examples as available in the literature are solved and the comparison of the results indicates good accuracy of the method. New results in the form of natural frequencies corresponding to the higher modes particularly for plates/stiffened plates with nonclassical boundaries are presented.

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