Shape optimization for strain energy minimization problem with damper element

Abstract

Dampers are often used for vibration suppression of a civil or mechanical structure. It is considered that vibration can be further suppressed by optimizing the shape of the structure after the installation of dampers. In this paper, we proposed a shape optimization method for minimizing strain energy for a structure with a viscous damper. The shape gradient function was derived using the Lagrange multiplier method. Both the frequency response and adjoint variable were solved using the modal analysis. It is expected that these calculations will be simplified. To obtain a smooth shape of the solution, H1 gradient method was used as the shape modification method. The numerical analysis was performed by combining the FEM software, HyperWorks, and a self-made program. A solid model excided by a load over a wide frequency range was used as a numerical example. From the analysis result, we confirmed the effectiveness of the shape optimization method considering the damper by H1 gradient method.