Research On Determination Of Dynamic Load Distributions Applied To Kirchhoff Plates And Mindlin Plates

It is well-known that identification of load distributions has always been a worthy problem in science and engineering which catches researchers' much attention. Researches on loading capacity of structures are very important in the fields of aviation, spaceflight, watercraft, automobile, building and bridges et al. So it is significant for improving and optimizing structures and its materials to make clear exactly of load distributions applied to the structures. However, not any kind of load applied to any structure can be measured through some special instruments according to actual experiences. In the circumstances we hope to identify load distributions through correlative quantities like strains and displacements etc that can be measured conveniently. And the key point is how to set up the relationship between the measured information and the unknown load distributions. The former researches on this problem mostly focused on identification of impact forces applied to structures, while the problem of identification of dynamic load distributions has been studied singularly as far as know. The problem of identification of dynamic load distributions applied to Kirchhoff plate and Mindlin plate by inverse analysis is studied in this paper. Kirchhoff plate is also called classic thin plate and Mindlin plate is one basic kind of thick plate, and it is representative and universal to select the two typical kinds of plates as research objects. How to select and obtain suitable additional information is very important to a common inverse problem. The strains on the surface of plate, which are easily measured by strain-gauges during experiments, are selected as additional information for load identification in this study. Yet the additional information data used in the paper are obtained through calculation rather than direct measuring, which means necessary to solve a forced vibration problem of plate (direct problem) before load identification. Rayleigh-Ritz method is a very popular and efficient approximate approach for vibration problems. In the procedure of solving the vibration problems of Kirchhoff rectangular plate and Mindlin rectangular plate by means of Rayleigh- Ritz method, the orthogonal Bernouilli-Euler beam functions and Timoshenko beam functions are employed as the base functions to expand the unknown variables. Moreover another advantage of applying Rayleigh-Ritz method to the direct problem is that we could get the exact analysis expressions of strains, which is no doubt much convenient. The control vibration system of Kirchhoff plate is a four-order partial differential equation about one independent variable in space, while that of Mindlin plate is a two-order system of partial differential equations about three independent variables in space. For identifying the load distributions in right hand, it is necessary to discretize such differential systems in space. The finite element method and pseudospectral method are applied respectively to discretize the continuous differential control systems of Kirchhoff plate and Mindlin plate into a simple algebraic system. According to the relationship between displacement-strain in plate theories, we obtain the transform function connecting the unknown load vector...