Independent Coordinate Coupling Method for Free Vibration Analysis of a Plate With Holes

A rectangular plate with a rectangular or a circular hole has been widely used as a substructure for ship, airplane, and plant. Uniform circular and annular plates have been also widely used as structural components for various industrial applications and their dynamic behaviors can be described by exact solutions. However, the vibration characteristics of a circular plate with an eccentric circular hole cannot be analyzed easily. The vibration characteristics of a rectangular plate with a hole can be solved by either the Rayleigh-Ritz method or the finite element method. The Rayleigh-Ritz method is an effective method when the rectangular plate has a rectangular hole. However, it cannot be easily applied to the case of a rectangular plate with a circular hole since the admissible functions for the rectangular hole domain do not permit closed-form integrals. The finite element method is a versatile tool for structural vibration analysis and therefore, can be applied to any of the cases mentioned above. But it does not permit qualitative analysis and requires enormous computational time. Tremendous amount of research has been carried out on the free vibration of various problems involving various shape and method. Monahan et al.(1970) applied the finite element method to a clamped rectangular plate with a rectangular hole and verified the numerical results by experiments. Paramasivam(1973) used the finite difference method for a simply-supported and clamped rectangular plate with a rectangular hole. There are many research works concerning plate with a single hole but a few work on plate with multiple holes. Aksu and Ali(1976) also used the finite difference method to analyze a rectangular plate with more than two holes. Rajamani and Prabhakaran(1977) assumed that the effect of a hole is equivalent to an externally applied loading and carried out a numerical analysis based on this assumption for a composite plate. Rajamani and Prabhakaran(1977) investigated the effect of a hole on the natural vibration characteristics of isotropic and orthotropic plates with simply-supported and clamped boundary conditions. Ali and Atwal(1980) applied the Rayleigh-Ritz method to a simply-supported rectangular plate with a rectangular hole, using the static deflection curves for a uniform loading as admissible functions. Lam et al.(1989) divided the rectangular plate with a hole into several sub areas and applied the modified Rayleigh-Ritz method. Lam and Hung(1990) applied the same method to a stiffened plate. The admissible functions used in (Lam et al. 1989, Lam and Hung 1990) are the orthogonal polynomial functions proposed by Bhat(1985, 1990). Laura et al.(1997) calculated the natural vibration characteristics of a simply-supported rectangular