The New Reciprocal Theorems And Its Application And One Application Of Eigenvalue Method

Energy principle in Elasticity includes deformation energy principals, variational principle, virtual work and virtual residual work principle and reciprocal theorem. Domestic and international scholars have contributed in researching both variational principle and the applications of its analytic and numerical value, and have obtained a lot of achievement. Similarly, there has been quite a lot development in the study of reciprocal theorem.In 1982, Prof. Fu Baolian put forward the modified proposition of reciprocal theorem, exploited the new function of reciprocal theorem, improved the new reciprocal theorem, founded reciprocal theorem method and formed new reciprocal theorem of solving the bending of thin rectangular plates with small deflections. In 2002, Prof. Fu Baolian also put forward reciprocal theorem of deformed bodies with finite displacements and the bending of thin rectangular plates with large deflections. Firstly, according to reciprocal theorems about bending of thin plates with large deflections, this paper researchs in the problem of rectangular plate's bending with large deflections. Secondly, according to reciprocal theorem of thick plates, this paper solves the problems of bending of thick rectangular plate under uniformly distributed load and linear distributed pressure. The deflection equations with different conditions are given in the paper, meanwhile the paper successfully exploits the corresponding software of approximate computation; at the same time, after every examples, this paper gives clear tables and graphs and analyzed the algorithms adopted .Sequentially systemic methods of applying reciprocal theorems in the problems of bending of thick or thin plates with large deflections are formed.It is very difficult to solve it because of the geometric nonlinearity of the bending of thin plates with large deflections. This paper first successfully solves the problems of the bending of thin plates with large deflections in six kinds of boundary conditions, the results of theirs are new .Compared with finite element method, the method have the property of simple, practical, advanced and are innovative to some degree.This paper successfully applies the exact corner static conditions of Prof. Fu Baolian to solve the problems of the thick plates'bending under uniformly distributed load and linear distributed pressure with impending corner, so has gained harvest that is superior to the former. It has got obvious innovations in both the processing of complex boundary conditions and the programming of computing.At last, this paper introduces the expression form of the signal in wireless communication, the basic knowledge of the array signal and MUSIC algorithm, while the paper also proposes MUSIC algorithm under the array structure of Model L, the estimating performance of the L array has been discussed.This paper exploits systematic programs in the process of calculation. These programs will have important effects in the farther research and engineering calculation.