Dynamic Analysis Of Non-uniform Plate With Time Dependent Boundary Conditions

• Main Authors: Shyi-Hwang Chen, 陳錫煌
• Other Authors: Sen-Yung Lee
• Format: Others
• Language: zh-TW
• Published: 1995
• Online Access: http://ndltd.ncl.edu.tw/handle/84488766195470627742

碩士 === 國立成功大學 === 機械工程研究所 === 83 === In the present study, the analysis of dynamic response for plate structures is presented. The first, the governing equations and the associated boundary conditions for an nonuniform plate, resting on a Winkler elastic foundation, with time dependent boundary conditions, and general transverse forces, are derived via the Hamilton's principle. The non- homegeneous boundary conditions are transformed into homogeneous ones through the procedure of change of dependent variable. By utilizing the Laplace transform and inverse transform, the dynamic response of the nonuniform plate is obtained. Because it is assumpted that the transverse force per unit area p(x,y,z) ,the exciting functions (i.e. the slope of the base, the displacement of the base , the external monent the shear force excitations,the translational spring constants, and the rotational spring constants at the left end and the right end of the plate) are odd functions, it is only apply for the case where the transverse force per unit length p(x,y,z) the exciting functions are odd functions. The shifting functions in terms of the fundamental solutions of nonuniform plate are presented and the pysical meaning of these shifting functions are explored.the shifting functions takes the physic meanings as the non-dimensional static deflection of a generally elastically restranined plate subjected to a unit non- dimensional monment and a unit non-dimensional slope of the base at the left end ,a unit non-dimensional shear force and a unit non-dimensional displacemint of the base at the left end, a unit non-dimensional monment and a unit non-dimensional slope of the base at the right end ,a unit force and a unit non- dimensional displacemint of the base at the right end of plate. This shifting functions can be applied to calculate the closed- form stiffness matrix of nonuniform plate elements. In this paper, the coefficients of the shifting function in the general case and the limiting five cases are presented.