Large amplitude flexural vibration of cross ply laminated composite plates

Large Amplitude Forced Vibrations of Elastic Structures

In a simple and straight forward manner the modal equations applicable for the large amplitude flexural vibrations of plates and shells are obtained by the Lagrange's method. These equations can easily be specialised to obtain the corresponding equations applicable for beams and rings. The basic nature of the modal equations for beams and plates on the one hand and rings and shells on the other hand are shown to exhibit hard and soft spring characteristics, respectively.

On the modal equations of large amplitude flexural vibration of beams, plates, rings and shells

Issued as Interim scientific reports no. [1-2], Annual reports no. [1-3], Final scientific report, and Reprints no. [1-2], Project no. E-16-629 (subproject is E-27-658)

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Linear & nonlinear effects in the vibration of elastic structures

Response of a Three-Layered Ring to an Axisymmetric Impulse

The general equations governing the large amplitude flexural vibration of any thin elastic shell using curvilinear orthogonal coordinates are derived and consist of two coupled, nonlinear, partial differential equations in the normal displacement w and the stress function F. From these equations, the governing equations for the case of shells of revolution or flat plates can be readily obtained as special cases. The material of the shell or plate is isotropic and homogeneous and Hooke's law for the two-dimensional case is valid. It is suggested that the difference between the hardening type of nonlinearity in the case of flat plates and straight beams and the softening type of nonlinearity in the case of shells and rings can, in general, be traced to the amount of curvature present in the underformed median surface of the structure concerned.

K. A. V. Pandalia

Papers

Large amplitude flexural vibration of thin elastic flat plates and shells