Nonlinear free vibration of heated orthotropic rectangular plates (Q1067854)
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scientific article; zbMATH DE number 3930486
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonlinear free vibration of heated orthotropic rectangular plates |
scientific article; zbMATH DE number 3930486 |
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Nonlinear free vibration of heated orthotropic rectangular plates (English)
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1986
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An analytical analysis of free vibrations of a heated orthotropic rectangular thin plate under various boundary conditions is presented. The nonlinear governing equations are derived from von Kármán plate theory and Berger's analysis separately; from them the Duffing-type nonlinear ordinary equations are then obtained by employing Galerkin's method using one-term approximation. The methods of successive approximation and complete elliptic cosine are applied to solve the nonlinear equations. The influence of temperature changes and large amplitudes on the period of free vibrations are established; also the buckling temperature is obtained. The analytical solutions are compared with numerical results from Runge-Kutta method. Two different approaches to linearize thermoelastic plate equations are considered and compared.
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uncoupled case
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von Kármán nonlinear plate theory
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three coupled governing equations
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Berger's analysis
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uncoupled quasi-linear equations
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direct linearization
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coupled linear solutions
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uncoupling of linearized equations
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single linear equation for plate flexural vibration
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analytical analysis
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heated orthotropic rectangular thin plate
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various boundary conditions
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nonlinear governing equations
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Duffing-type nonlinear ordinary equations
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Galerkin's method
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one-term approximation
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successive approximation
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complete elliptic cosine
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temperature changes
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large amplitudes
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period of free vibrations
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buckling temperature
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compared with numerical results from Runge-Kutta method
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Two different approaches to linearize thermoelastic plate equations
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