DYNAMICS OF ORTHOTROPIC PLATES USING CHARACTERISTIC ORTHOGONAL POLYNOMIAL- GALERKIN’S METHOD

DYNAMICS OF ORTHOTROPIC PLATES USING CHARACTERISTIC ORTHOGONAL POLYNOMIAL- GALERKIN’S METHOD

ABSTRACT

The assumed deflection shapes used in the approximate method such as in the Galerkin method were normally formulated by inspection and sometimes by trial and error , until recently, when a systematic method of constructing such a function in the form of Characteristic Orthogonal Polynomials (COPs) was developed in 1985. However, vibrational analysis of plates with different support and boundary conditions are much more complicated. This project used Characteristic Orthogonal Polynomial to obtain satisfactory approximate shape functions of plate of different support and boundary conditions. The functions were applied to Galerkin indirect variational method. To this end, new sets of stress- strain relations for orthotropic plate were derived. The principle of force of inertia was introduced, yielding the corresponding dynamic governing equation of orthotropic plate. This results obtained show an improvement to previous work done in this regard. The result were reasonable when compared with somewhat obtained in the previous work. The study have contributed in addressing problem of dearth of literature orthotropic plate vibration problems.