Abstract
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.
Highlights
Excessive structural vibration can lead to noise and mechanical failure, and further result in comfort and safety problems
Inspired by the quasi-linear behaviour of Synchronized switch damping (SSD), we propose in the paper a new modelling method for the structure with SSD based on linearisation
We use a lumped parameter model with SSDNC and a beam finite element model with synchronized switch damping on short circuit (SSDS) containing few DOFs to numerically verify the algorithm, respectively (Section III-C); to compare the results given by linearisation with published experimental data, a FE model of cantilever beam with a large number of DOFs is investigated (Section IV); the applicability to complex structures in industry and the high efficiency of the proposed method are further discussed by a blisk FE model with SSDNC (Section V)
Summary
Excessive structural vibration can lead to noise and mechanical failure, and further result in comfort and safety problems. Lefeuvre et al [13] proposed SSDV (SSD based on voltage source) by adding a pair of constant voltage sources with opposite polarity to the circuit This increases the voltage on the piezoelectric patch and enhance the damping. We use a lumped parameter model with SSDNC and a beam finite element model with SSDS containing few DOFs to numerically verify the algorithm, respectively (Section III-C); to compare the results given by linearisation with published experimental data, a FE model of cantilever beam with a large number of DOFs is investigated (Section IV); the applicability to complex structures in industry and the high efficiency of the proposed method are further discussed by a blisk FE model with SSDNC (Section V).
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