Simultaneous optimization of multiple DVAs for multi-layered structure

Abstract

The design theory of dynamic absorbers is a classic research area in the vibration engineering. In contrast, there remain many problem settings where rigorous formulations are not widely known. This paper deals with a minimization of a maximum transmissibility when multiple dynamic absorbers are installed in a multi-layered structure. For the optimal solution, the author has found that the necessary conditions can be expressed in terms of equations via the submatrix of Jacobian, and optimization can be achieved using the Newton-Raphson method. This is suitable for the case that the numerical solution confirms that the heights of all resonance points coincide at the optimal solution. In this paper, it is shown that this formulation can be explained in the context of Lagrange's undetermined multiplier method.