The Analysis, Based On The Mode Shape Orthogonality Elastic Plate Power

Elastic thin plate is widely used in all kinds of engineering fields. It is of high theoretical significance and high practical valve to researsh a dynamic analysis method for elastic thin plate. In different kinds of solution , besides approximate methods of calculus of differences , energy approach, finite-element method, lumped mass method, all sorts of theory solution have definite limitation. Some dissatisfy the vibration differential equation, some dissatisfy boundary conditions , or others have both shortcomings. Even if forementioned conditions are satisf iable , the mode of vibration don't possess character of orthogonality . The mode of vibration is orthogonal .which is the most basic and important theory in vibration theory. Based on orthogonality of mode of vibration ,we put forward arrangement method on the main mode direction.Its basic way is to elect a main vibration direction at two vibration direction. In this text , we adopt this method to analyse the rectangular plate of one side freedom and one point.For guaranteeing orthogonality of mode , the waveform number is only. But the same time for guaranteeing mode curve satisfy the whole boundary condition , at other vibration direction the waveform number isn' t only. The vibration curve shape we adopt should fit the homologous boundary condition shape. Based on this mode function expression could satisfy the whole boundary condition of vibration differential equation and possess orthogonality of mode. By plate's boundary condition we can found the homologous homogeneous linear system of equations. Guaranteeing main mode to have nonzero solution, the homologous coefficient are not zero all. So we can get the vibration frequency equation, and ascertain plate' s vibration frequency and homologous vibration .The plate of one side simply supported and one angular point supported not only possess simply supported edge , clamped edge, free elevator angle point , but also have angular point of post supported. During the plate vibrationcourse , angular point generate the homologize periodic change counterforce .At the same time the angular point displacement is zero , owing to boundary condition complexity, the plate ' s dynamical analysis have some hardness. In this text we take arrangement method on the main mode direction's dynamical analysis to successfully solve the question and acquire content result.The arrangement method on the main mode direction possess universal applicability. It not only work out classic boundary constituent rectangular plate' s vibrate, but also dispose prsent plate of post supported angular point . In the text we take this method to have dynamical analysis for plate of one side simple supported and one post supported angular point , and procure the content outcome.