Topological Optimization Technique for Free Vibration Problems

A topological optimization technique using the conception of OMD (Optimal Material Distribution) is presented for free vibration problems of a structure. A new objective function corresponding to multieigenvalue optimization is suggested for improving the solution of the eigenvalue optimization problem. An improved optimization algorithm is then applied to solve these problems, which is derived by the authors using a new convex generalized-linearization approach via a shift parameter which corresponds to the Lagrange multiplier and the use of the dual method. Finally, three example applications are given to substantiate the feasibility of the approaches presented in this paper.