The Research On The Static And Dynamic Characteristics Of Moderately Thick Plates Subjected To Complex Boundary Conditions

As a basic structure part, the moderately thick plates are widely used in the modern engineering fields, such as aerospace, navigation and construction. Therefore, the research on the static and dynamic mechanical characteristics of the plate is very important. Based on Improved Fourier Series Method (IFSM) with Hamilton Principle and Rayleigh-Ritz method,this research investigates the static and dynamic characteristics of rectangular plate with any boundary conditions. Besides the general classical boundary conditions, the vibration characteristics of rectangular plates with the elastic boundary conditions are also taken into consideration.Firstly, the static characteristics analysis model of rectangular Mindlin plates with variable thickness and general boundary condition is constructed based on the improved method of two-dimensional Fourier series. Rectangular Mindlin plate's displacement function is represented as the superposition of standard cosine and sine series, in which the sine term is introduced to overcome the problem that derivative of displacement and rotation functions is discontinuous at the boundary edge.Secondly, the dynamic analysis model of uniform thickness rectangular plates and orthotropic rectangular plates with general boundary condition is established using the improved methods of two-dimensional Fourier series and Hamilton principle with the first-order Mindlin clipboard theory. The coefficients of displacement series expansion are taken as the generalized coordinates, and determined with the Ratleigh-Ritz method. Thus the vibration charcateristics of rectangular plate can be obtained by solving the standard eigenvalue problem. Then the problems of free vibration and forced vibration of rectangular plates with the classical boundary and complex boundary conditions are detailed investigated.And then the influence of boundary conditions and structural parameters on the free vibration characteristics is examined. The impact on the forced vibration of boundary conditions, loss factor and the loading position of external excitation force is also discussed.Finally, based on the three-dimensional elasticity theory, the vibration analysis model of thick rectangular plates with general boundary conditions is built with the improved method of three-dimensional Fourier series. Analysis of free vibration of moderately thick rectangular plates with classical and elastic boundary conditions is carried out and the results are checked with the literature data under the same conditions based on Mindlin plate theory. On the basis of free vibration analysis, the research investigates the effect of boundary conditions, aspect ratio and the ratio of the span and thickness on the modal characteristics for rectangular plates,as well as the effects on harmonic response of boundary conditions, loss factor and the loading position of external excitation force. Contrast to the relevant literature data and finite element data, the method of correctness and reliability is verified.Through numerical examples, the accuracy and versatility of the current method are extensively demonstrated. Unlike most existing solution framework, all the classical homogeneous boundary conditions the current approach can be universally treated as the special cases when the stiffness for each of restraining springs is equal to either zero or infinity. Then the vibration analysis of plate subjected to general boundary conditions are carried out. Some vasic rules are summarized, and can provide some theory technical support for engineering design.