Abstract
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 modified 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 first order derivatives of certain eigenvalues with respect to design variables are used to determine whether or not a specific 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 confined range of design variables which contains the extreme value can be obtained. Numerical examples are presented to illustrate the feasibility and efficiency of the proposed method.
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