A Constrained Convex Approach to Modal Design Optimization of Vibrating Systems

Abstract

Abstract This paper introduces a general and flexible design method for the inverse modal optimization of undamped vibrating systems, i.e., for the computation of mass and stiffness linear modifications ensuring the desired system eigenstructure. The technique is suitable for the design of new systems or the optimization of the existing ones and can handle several design requirements and constraints. Paramount strengths of the method are its capability to modify an arbitrary number of parameters and assigned vibration modes, as well as the possibility of dealing with mass and stiffness matrices with arbitrary topologies. To this purpose, the modification problem is formulated as a constrained inverse eigenvalue problem and then solved within the frame of convex optimization. The effectiveness of the method is assessed by applying it to two different test cases. In particular, the second investigation deals with a meaningful mechanical design application: the optimization of a system recalling an industrial vibratory feeder. The results highlight the generality of the method and its capability to ensure the achievement of the prescribed eigenstructure.