720 Thermally Induced Vibration of Inhomogeneous Beams and Rectangular Plates Due to Cyclic Variation of Heat Supply and Transverse Load

Abstract The thermally induced vibrations of rectangular plates and beams under some typical heat applications are studied. The basic parameter of the problem, B, is found to depend on the natural frequency of the structure and on a characteristic thermal time. Curves are presented of the variation with B of the ratio of the deflections calculated including and neglecting the effect of inertia. The role of inertia is found to be important for rapidly applied heat inputs and for thin plates. An approximate formula for its rapid estimation is also presented.

Download Full-text

Large Deflection of Unsymmetric Cross-Ply and Angle-Ply Plates

Journal of Mechanical Engineering Science ◽

10.1243/jmes_jour_1976_018_031_02 ◽

1976 ◽

Vol 18 (4) ◽

pp. 179-183 ◽

Cited By ~ 23

Author(s):

C. Y. Chia ◽

M. K. Prabhakara

Keyword(s):

Boundary Conditions ◽

Large Deflection ◽

Perturbation Technique ◽

Transverse Load ◽

Load Force ◽

Rectangular Plates ◽

Linear Partial Differential Equations ◽

Transverse Deflection ◽

Anisotropic Rectangular Plates ◽

Good Agreement

An approximate solution to the von Karman-type large-deflection equations of unsymmetrically laminated, anisotropic, rectangular plates under uniform transverse load is formulated by the perturbation technique. The membrane boundary conditions are the zero normal and shear boundary forces. By expressing the load, force function and transverse deflection in the form of series, the governing equations and boundary conditions are reduced to a series of linear partial differential equations and boundary conditions. In each approximation a solution is assumed in the form of polynomials which satisfy the associated boundary conditions and physical requirements for deflection and and three membrane forces in unsymmetric cross-ply and angle-ply plates. Taking the first three terms in the truncated series, numerical results are graphically presented for the load-deflection relations, bending moments and membrane forces in unsymmetric cross-ply and angle-ply plates with various values of aspect ratio and total number of layers. The present third approximation is in good agreement with the existing solutions for large deflections of isotropic and unsymmetric angle-ply plates having the ratio of central deflection to thickness up to the value of 2.

Download Full-text

Buckling Analysis of Inhomogeneous Rectangular Plates Subjected to Non-uniform Heat Supply

The proceedings of the JSME annual meeting ◽

10.1299/jsmemecjo.2003.1.0_181 ◽

2003 ◽

Vol 2003.1 (0) ◽

pp. 181-182

Author(s):

Takuya MORIMOTO ◽

Yoshinobu TANIGAWA

Keyword(s):

Heat Supply ◽

Buckling Analysis ◽

Rectangular Plates ◽

Uniform Heat

Download Full-text

Thermally Induced Vibration of Inhomogeneous Material Rectangular Plate Due to Cyclic Variation of Thermal and Mechanical Loads

10.1063/1.2896865 ◽

2008 ◽

Cited By ~ 2

Author(s):

Ryuusuke Kawamura ◽

Yoshinobu Tanigawa ◽

Naoki Matsumoto ◽

Glaucio H. Paulino ◽

Marek-Jerzy Pindera ◽

...

Keyword(s):

Rectangular Plate ◽

Inhomogeneous Material ◽

Cyclic Variation ◽

Mechanical Loads ◽

Thermally Induced

Download Full-text

Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions

European Journal of Engineering and Technology Research ◽

10.24018/ej-eng.2021.6.7.2690 ◽

2021 ◽

Vol 6 (7) ◽

pp. 144-152

Author(s):

Onodagu P. Dinwoke ◽

Aginam C. Henry ◽

Uzodinma C. Franklin

Keyword(s):

Shear Deformation ◽

Deformation Theory ◽

Ritz Method ◽

Shear Deformation Theory ◽

Transverse Load ◽

Rectangular Plates ◽

External Work ◽

Deformation Function ◽

Depth Ratio ◽

Out Of Plane

This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-plane displacement coefficients. Numerical results for the present study were obtained for the thick isotropic SSSS rectangular plates and comparison of the results of this research and previous work done in literature showed good convergence. However, It was also observed that the result obtained in this present study are significantly upper bound as compared with the results of other researchers who employed the higher order shear deformation theory (HSDT), first order shear deformation theory (FSDT) and classical plate theory (CPT) theories for the in – plane and out of plane displacements at span – depth ratio of 4. Also, at a span - depth ratio of and above, there was approximately no difference in the values obtained for the out of plane displacements and in-plane displacements between the CPT and the theory used in this study.

Download Full-text

Solution of Some Problems in Bending of Thin Clamped Plates by Means of the Method of Muskhelishvili

Journal of Applied Mechanics ◽

10.1115/1.4011512 ◽

1957 ◽

Vol 24 (2) ◽

pp. 295-298

Author(s):

L. I. Deverall

Keyword(s):

Conformal Mapping ◽

Mapping Function ◽

Elliptic Functions ◽

Transverse Load ◽

Rectangular Plates ◽

Convergence Properties ◽

Clamped Plate ◽

Central Maximum ◽

Method Of Solution ◽

Square Plate

Abstract In this paper, the complex variable method of N. I. Muskhelishvili is applied to the problem of bending for small deflections of a thin, isotropic, homogeneous, clamped plate with transverse load. The functional equation involved in Muskhelishvili’s method is solved by means of series expansions. The necessary conformal mapping functions are found from the Schwarz-Christoffel formula or expansion of elliptic functions. For uniformly loaded square and rectangular plates, the central (maximum) deflection obtained by the method of Muskhelishvili is compared to the corresponding deflections obtained by other methods. Deflections for the square plate are given for three and five terms, respectively, of the series expansion of the conformal mapping function in order to estimate convergence properties of the method of solution. The solution for a uniformly loaded clamped plate of equilateral triangular planform is also discussed. Central deflection for this case is given.

Download Full-text