Optimum design of a plate based on the minimization of the vibration energy.

An optimization method is proposed to reduce the vibration of structures, where the total vibration energy is adopted as the objective function to be minimized. The theory of modal analysis is introduced in the optimization, and the sensitivity of the vibration energy with respect to the change of design variable is represented as a function of the sensitivities of both natural frequencies and natural modes. The proposed method is applied to the optimum design problem of a rectangular plate with clamped edges, which is loaded by a central exciting force. The finite element method is used for the computation, and the thickness of elements is adopted as the design variable. The solution of the problem demonstrates not only the excellence of the method for the reduction of vibration but also the ability to control the shift of resonance frequency.