Domain Optimization Analysis in Frequency Response Problems Considering Proportional Viscous Damping

Abstract

The purpose of this paper is to present a numerical method for shape optimization problems related to frequency response problems of linear elastic continuum. Following the previous report in which no danaping was assumed, proportional viscous damping is considered in this paper. Minimization problems of strain energy, kinetic energy and absolute value of mean compliance are treated. A variational form of an equation of motion is obtained with complex number of displacement amplitude. Sensitivity function, that is called shape gradiant function, is derived using the Lagrange multiplier method. A technique using modal parameters for calculation of Lagrange multiplier function, that is called adjoint function, is shown. The traction method is applied for numerical analysis. Beamlike plate problems are analyzed to show the validity of this approach.