Minimizing the vibrational response of a lightweight building by topology and volume optimization of a base plate for excitatory machinery

Abstract

This paper deals with the problem of minimizing the vibration amplitude response of a lightweight building from rotating machinery by extended topology optimization of a flexible, single material base plate for the machinery. A modular lightweight building is modeled and used for the analysis of the vibrational response. The excitation frequency is assumed to be given, and the design objective is chosen as minimization of the product of the frequency response of the building transmitted from the machinery base plate, and the volume of solid material used in the design of the base plate. The design and performance of optimized machinery base plates are illustrated and discussed by means of numerical example problems with different excitation frequencies, different levels of Rayleigh damping, and different installation positions of the base plate with the machinery in the building. Finally, the satisfaction of the KKT (Karush-Kuhn-Tucker) necessary condition for optimality is investigated for one of the numerically optimized designs.