A Reduced Model of a Thermo-Elastic Nonlinear Circular Plate

Abstract

Abstract. Nonlinear vibrations of a circular plate subjected to mechanical and thermal loadings are presented in the paper. A model of the plate is based on the extended Mindlin theory, taking into account nonlinear geometrical terms and acting heat uniformly distributed along the plate span. The dynamics of a coupled thermo-mechanical problem is reduced from a set of partial differential equations to ordinary differential equations. Considering oscillations around the first natural frequency just one mode reduction is proposed. The analysis shows that elevated temperature shifts the resonance curve and new post-buckling oscillations arise. Depending on initial conditions for the post-buckling state various scenarios of bifurcations take place and transient irregular oscillations may occur. The proposed one degree of freedom model shows a good agreement with response of the model based on three or five-modes reduction.

Buckling and free vibration characteristics of embedded inhomogeneous functionally graded elliptical plate in hygrothermal environment

“…Warminska et al. 34 analyzed the nonlinear vibrations of a circular plate subjected to mechanical and thermal loadings using the extended Mindlin plate theory. Employing the third-order shear deformation theory, Tebboune et al.…”

“…Chikh et al 33 studied the buckling of composite plate using the simplified higher order shear deformation theory. Warminska et al 34 analyzed the nonlinear vibrations of a circular plate subjected to mechanical and thermal loadings using the extended Mindlin plate theory. Employing the third-order shear deformation theory, Tebboune et al 35 analyzed the thermal buckling of FGP on elastic foundation.…”