Optimization of mid-frequency vibration for complex built-up systems using the hybrid finite element–statistical energy analysis method

This article deals with the sensitivity analysis of dynamic response and optimal size design of complex built-up systems in the mid-frequency range. A complex built-up system may be fabricated from many components which often differ greatly in materials and sizes. It may be subjected to many different wavelength structural deformations and may typically exhibit mixed mid-frequency behaviour which is very sensitive to uncertainties at higher frequencies. To perform optimization on the mid-frequency vibration of complex built-up systems, the hybrid finite element (FE)–statistical energy analysis (SEA) method, in which the deterministic and statistical subsystem are respectively modelled using FE and SEA, is implemented in this work. In this context, an efficient direct differentiation method for sensitivity analysis is derived. Two numerical examples illustrate the efficiency and effectiveness of the proposed optimization model.