Structural topology optimization for forced vibration problem using level set method

For the purpose of structure vibration reduction, a structural topology optimization for forced vibration problem is proposed based on the level set method. The objective of present study is to minimize the frequency response at the specified points or surfaces on the structure with an excitation frequency or a frequency range, subject to the given amount of the material over the admissible design domain. The sensitivity analysis with respect to the structural boundaries is carried out, while the X-FEM is employed for solving the state equation and the adjoint equation. The optimal structure with smooth boundaries is obtained by the level set evolution with advection velocity, derived from the sensitivity analysis and the optimization algorithm. A number of two-dimensional numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed approach.