Natural frequencies of a non homogeneous isotropic elastic infinite plate of variable thickness resting on elastic foundation

Meccanica ◽  
1984 ◽  
Vol 19 (4) ◽  
pp. 320-324 ◽  
Author(s):  
J. S. Tomar ◽  
D. C. Gupta ◽  
Vinod Kumar
Keyword(s):  
Elastic Foundation ◽  
Variable Thickness ◽  
Natural Frequencies ◽  
Infinite Plate ◽  
Plate Of Variable Thickness

The normal modes of a heated elliptical plate of variable thickness

1983 ◽  
Vol 386 (1790) ◽  
pp. 35-54
Keyword(s):  
Temperature Distribution ◽  
Variable Thickness ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Middle Surface ◽  
Mode Shapes ◽  
Elliptical Plate ◽  
Exact Analysis ◽  
Plate Of Variable Thickness ◽  
Quadratic Temperature

An exact analysis is given of the natural frequencies and mode shapes of an unsupported elliptical plate whose thickness varies in a lenticular manner, vanishing at the boundary. Account is also taken of middle-surface stresses arising from a planar quadratic temperature distribution.

scholarly journals Natural frequencies of orthotropic circular plates of variable thickness.

AIAA Journal ◽  
1968 ◽  
Vol 6 (8) ◽  
pp. 1625-1626 ◽  
Author(s):  
ALAN P. SALZMAN ◽  
SHARAD A. PATEL
Keyword(s):  
Variable Thickness ◽  
Natural Frequencies ◽  
Circular Plates ◽  
Plates Of Variable Thickness

Some Results on Axisymmetric Vibration of Spherical Shells of Variable Thickness

1990 ◽  
Vol 112 (4) ◽  
pp. 432-437 ◽  
Author(s):  
A. V. Singh ◽  
S. Mirza
Keyword(s):  
Variable Thickness ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Spherical Shells ◽  
Varying Thickness ◽  
Wide Range

Natural frequencies and mode shapes are presented for the free axisymmetric vibration of spherical shells with linearly varying thickness along the meridian. Clamped and hinged edges corresponding to opening angles 30, 45, 60 and 90 deg have been considered in this technical brief to cover a wide range from shallow to deep spherical shells. Variations in thickness are seen to have very pronounced effects on the frequencies and mode shapes.

A Levy-Type Solution for a Rectangular Plate of Variable Thickness

1958 ◽  
Vol 25 (2) ◽  
pp. 297-298
Author(s):  
H. D. Conway
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Variable Thickness ◽  
Thickness Variation ◽  
Type Solution ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Arbitrary Boundary Conditions ◽  
Plate Of Variable Thickness

Abstract A solution is given for the bending of a uniformly loaded rectangular plate, simply supported on two opposite edges and having arbitrary boundary conditions on the others. The thickness variation is taken as exponential in order to make the solution tractable, and thus closely approximates to uniform taper if the latter is small.

scholarly journals Thermal Buckling and Free Vibration Analysis of Functionally Graded Plate Resting on an Elastic Foundation According to High Order Shear Deformation Theory Based on New Shape Function

2020 ◽  
Vol 10 (12) ◽  
pp. 4190
Author(s):  
Aleksandar Radaković ◽  
Dragan Čukanović ◽  
Gordana Bogdanović ◽  
Milan Blagojević ◽  
Blaža Stojanović ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shape Function ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
High Order ◽  
Functionally Graded Plate

Functionally graded square and rectangular plates of different thicknesses placed on the elastic foundation modeled according to the Winkler-Pasternak theory have been studied. The thermal and mechanical characteristics, apart from Poisson’s ratio, are considered to continuously differ through the thickness of the studied material as stated in a power-law distribution. A mathematical model of functionally graded plate which include interaction with elastic foundation is defined. The equilibrium and stability equations are derived using high order shear deformation theory that comprises various kinds of shape function and the von Karman nonlinearity. A new analytically integrable shape function has been introduced. Hamilton’s principle has been applied with the purpose of acquiring the equations of motion. An analytical method for identifying both natural frequencies and critical buckling temperature for cases of linear and nonlinear temperature change through the plate thickness has been established. In order to verify the derived theoretical results on numerical examples, an original program code has been implemented within software MATLAB. Critical buckling temperature and natural frequencies findings are shown below. Previous scientific research and papers confirms that presented both the theoretical formulation and the numerical results are accurate. The comparison has been made between newly established findings based on introduced shape function and the old findings that include 13 different shape functions available in previously published articles. The final part of the research provides analysis and conclusions related to the impact of the power-law index, foundation stiffness, and temperature gradient on critical buckling temperature and natural frequencies of the functionally graded plates.

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