Vibration Of Triangular Plates Research Articles

Vibration of Triangular Plates: Point Supports, Mixed Edges and Partial Internal Curved Supports

A numerical method, which is a hybrid form of the Rayleigh-Ritz method and the Lagrangian multiplier method, is presented in this paper for the vibration analysis of general triangular plates with complicated supported conditions. These support conditions include internal clamped or simple point supports, mixed periphery boundary conditions and partial internal curved supports. Several plate examples are used to illustrate the method. Apart from the limiting cases of some of these triangular plates with point supports where existing results are available for comparison, the frequency parameters presented in this paper are new. They should be valuable to designers in some industrial applications.

Effects of large amplitude and transverse shear on vibrations of triangular plates

In this paper an analytical investigation of large amplitude free flexural vibrations of isotropic and orthotropic moderately thick triangular plates is carried out. The governing equations are expressed in terms of the lateral displacement, w, and the stress function, F, and are based on an improved non-linear vibration theory which accounts for the effects of transverse shear deformation and rotatory inertia. Solutions to the governing equations are obtained by using a single-mode approximation for w, Galerkin's method and a numerical integration procedure. Numerical results are presented in terms of variations of non-linear frequency ratios with amplitudes of vibrations. The effects of transverse shear, rotatory inertia, material properties, aspect ratios, and thickness parameters are studied and compared with available solutions wherever possible. Present results are in close agreement with those reported for thin plates. It is believed that all of the results reported here that are applicable for moderately thick plates are new and therefore, no comparison is possible.