Abstract
The effects of initial geometric imperfection and pre- and post-buckling deformations on vibration of isotropic rectangular plates under uniaxial compressive in-plane load have been studied. The differential equations of plate motions, using the Mindlin theory and Von-Karman stress-strain relations for large deformations, were extracted. The solution of nonlinear differential equations was assumed as the summation of dynamic and static solutions. Due to a large static plate deflection as compared with its vibration amplitude, the differential equations were solved in two steps. First, the static equations were solved using the differential quadrature method and the arc-length strategy. Next, considering small vibration amplitude about the deformed shape and eliminating nonlinear terms, the natural frequencies were extracted using the differential quadrature method. The results for different initial geometric imperfection and different boundary conditions reflect the impact of the mentioned factors on the natural frequencies of plates.
Highlights
Because of the high strength-to-weight ratio, plates have been widely used in various industrial applications
The natural frequencies of a supported square plate for different initial imperfection amplitudes are calculated without any external compressive load
The figure shows that an increase in the initial imperfection amplitude results in an increase of plate stiffness, and causes an increase in the natural frequencies
Summary
Because of the high strength-to-weight ratio, plates have been widely used in various industrial applications. NG and White [4] developed the Rayleigh-Ritz and finite element methods to study the effects of pre- and post-buckling deformations on natural frequencies of uniaxial isotropic rectangular plates. They concluded that by increasing the load, the fundamental frequency of plate decreases in the pre-buckling state and increases in the postbuckling state. To the best of authors’ knowledge, the dynamic behavior of geometrically imperfect plates considering shear deformations and different boundary conditions using the differential quadrature method has not been yet investigated. This study considers effects of initial imperfection and pre- and post-buckling deformations on natural frequencies and modal shapes of uniaxially loaded rectangular isotropic plates. The natural frequencies and mode shapes of the buckled plate could be determined by solving the resulting eigenvalue problem
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