Optimization of Peak Power in Vibrating Structures via Semidefinite Programming

In this paper we consider the problem of designing a truss to minimize peak power input to the structure by a dynamic load. We first consider a model where known sinusoidal forces are applied to the truss, and our goal is to choose rod cross-sectional areas to minimize peak power subject to a constraint on the total mass of the structure. We then consider a second model where unknown forces are applied to the truss, and our goal is to choose rod cross-sectional areas to minimize the worst-case peak power over all unit magnitude forces. In both cases, we show that the optimization problems can be formulated as semidefinite programs. Numerical results are presented for both cases. I. Background This paper focuses on optimal design of truss structures for peak power minimization. Optimal design of truss structures has a long history, starting with the papers5 and.6 These problems are typically formulated in such a way that a ground structure, rod lengths, and material properties are specified, and the goal is to select rod cross-sectional areas to optimize some objective function. The majority of existing work on this topic involves optimization under static loads, with minimization of compliance subject to weight constraints being the most common formulation.