A linearised analysis for structures with synchronized switch damping

Synchronized Switch Damping (SSD) is a semi-active damping technology based on piezoelectric materials. It has advantages such as broadband and no need to tune. Despite the nonlinear governing equations, structures with SSD exhibit quasi-linear behaviour such as the resonant frequencies hardly vary with respect to energy level of excitation. Inspired by these phenomena, in this paper we propose a linearisation method for SSD, where the nonlinear force is equivalent to frequency-dependent viscous damping and linear stiffness coefficients. Closed-form expressions of these linearised parameters are given, making the method applicable both for lumped parameter models and finite element (FE) models. In the derivation a general force equation is used, so the linearised method is applicable for several typical variants of SSD, such as SSDS (S for 'on short-circuited'), SSDI (I for 'on inductance'), SSDV (V for 'on voltage') and SSDNC (NC for 'on negative capacitance'). The method is first validated against nonlinear simulations with harmonic and random vibration respectively, then further compared with experimental data in a published paper. Good agreements are found. We show that the proposed method can dramatically accelerate the computational efficiency, which is especially suitable for predicting the dynamic performance of complex structures with SSD. Eventually, a dummy integrally bladed disk with SSD is analysed to illustrate a potential application direction. There are more than 120k DOFs in the FE model, making full nonlinear simulation very time-consuming. However the simulation is finished within seconds by the proposed method and the typical damping characteristics of SSD are well captured.