On the exact reduction and eigensolution for the Galerkin element method

The Galerkin element method (GEM) is an improved type of finite element ana lysis which is particularly suited to vibration problems. When determining natural frequencies, a special eigenproblem is to be solved by an iteration method, but it is found that the iteration procedure does not converge to every mode, so some modes will be missed. Also, during every iteration cycl e it is necessary to invert a dynamic: stiffness matrix Corresponding to sl ave coordinates and this is quite time consuming. In this paper, an explana tion is given as to why certain modes are missed and an effective algorithm is presented for overcoming the problem of missed modes. The numerical ana lysis shows that the proposed algorithm is very successful, exhibiting both fast and steady convergence. (C) 1999 Elsevier Science Ltd. All rights res erved.