Analysis of plares using differntial quadrature method

Plates with various boundary conditions are common components in many fields of engineering, especially in civil and mechanical engineering. Vibtaion of plate is an important research area that has been studied by many researchers. Structural health monitoring is one of the most important keys in maintaining safety and integrity of structures and a voiding loss of human life and/or monetary loss due to the catastrophic failure of structures. Among many structural health-monitoring techniques, the dynamic response-based damage detection method attracts most attention due to its simplicity for implementation. This technique makes use of the dynamic response of structures, which offers unique information on the defects contained with these structures. Changes in the physical properties of the structures due to damage can alter the dynamic response, such as the natural frequency and mode shape. These physical parameter changes can be extracted to predict damage information, such as the presence, location and severity of damage in a structure. As a basis of dynamics-based structural health monitoring technique, free vibration of beams with cracks has been under extensive examination in the last three decades.Most engineering problems are governed by a set of partial differential equations with proper boundary conditions. In general, it is very difficult to obtain the closed-form solution of these equations. On the other hand, the