Solution existence of the optimization problem of truss structures with frequency constraints

A basic theory is presented for determining the solution existence of frequency optimization problems for truss structures. This theory says that the natural frequencies remain unchanged when a truss is modi®ed uniformly and that the natural frequency constraint is usually the key constraint in determining the solution existence of a truss dynamic optimization problem. Based on this theory, a practical method is presented, in which only the ®rst order derivatives of certain eigenvalues with respect to design variables are used to determine whether or not a speci®c natural frequency constraint is achievable. If there is a solution for a given frequency constraint, a solution existence result can be obtained very quickly using the method. Otherwise, the extreme value of the corresponding natural frequency or a small con®ned range of design variables which contains the extreme value can be obtained. Numerical examples are presented to illustrate the feasibility and eciency of the proposed method