Numerical Ezamples of Eigenvalue Problem on Elastic Beam with Non-Uniform Section
Eigenvalue analysis procedures of a elastic beam with non-uniform section are proposed by each method using Boundary Element Method (BEM) and Finite Element Method (FEM). For the eigenvalue problem of elastic beam with uniform section, mathematical solutions are known under typical boundary conditions. However, it is extremely difficult for the eigenvalue problem of nonlinear equation to obtain the mathematical solution, since the governing equation of elastic beam with non-uniform section is formulated as nonlinear equation. Thus the characteristics equation to calculate the eigenvalue of elastic beam with non-uniform section are proposed and formulated under the continuity and boundary conditions based on internal force and deformations for the divided each uniform section as shown in figure 1.In such a formulation, the characteristic equations based on FEM can be constructed as general eigenvalue problem. On the other hand, the one based on BEM cant be constructed as general eigenvalue problem on various boundary conditions. So, the eigenvalue equations based on BEM are solved by Determinant Search Procedure. In this study, to discuss the effectiveness of proposed procedure, numerical results are shown through comparison of BEM and FEM solutions.
K.Morihira R.Uchino R.Endo N.Tosaka
Graduate student of Polytechnic University,Kanagawa,Japan Department of Architectural System Engineering,Polytechnic University,Kanagawa,Japan Department of Architecture,Tokyo Denki University,Tokyo,Japan
国际会议
南京
英文
1
2009-10-18（万方平台首次上网日期，不代表论文的发表时间）