Abstract
From the energy conservation principle, the contribution factor of an element to the natural frequency of the finite element discretized system of a membrane vibration problem is presented in this paper. Since the contribution factor of an element is derived from the general finite element formulation of structural eigenvalue problems, it can be used for solving the natural frequency optimization problem of any structure. Therefore, the method associated with it is called as a generalized evolutionary method. Using the contribution factor of an element, the relevant evolutionary criterion which bridges between the structural optimization and the conventional finite, element analysis can be easily established for the evolutionary natural frequency optimization of a structure. Physically, the contribution factor of an element implies the direct contribution of an element to the natural frequency of the structure. A square membrane with four sides fixed has been chosen as an example to show the usefulness and robustness of the generalized evolutionary method for natural frequency optimization of membrane vibration problems in the finite element analysis.
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