Chapter 33 Modeling and Stochastic Dynamic Analysis of a Piezoelectric Shunted Rotating Beam Zhenguo Zhang, Ningyuan Duan, Jiajin Tian, and Hongxing Hua Abstract This work presents a variational based stochastic electromechanical coupling model for response analysis of a rotating cantilever beam with piezoelectric patches surface-mounted. The resonant shunt circuits are connected to the piezoelectric elements to reduce vibrations of some specific resonance frequencies. The deterministic equations of motion are derived by the generalised form of Hamilton’s principle for electromechanical systems and Rayleigh-Ritz modeling method based on the orthogonal polynomial bases, while the Penalty method is adopted to connect the beam and piezoelectric patches. The parameter uncertainties are taken into account in both the structural and electric components. The generalized polynomial chaos expansion (gPCE) is employed to represent propagation of parameter uncertainties and to estimate the statistical characteristics of the responses. Various results are presented and compared with the Monte Carlo simulation (MCS) in order to validate the efficiency of the proposed formulation. Uncertainty analyses are carried out to ascertain the effects of probabilistic parameters on the responses. The results reveal that both the structure and piezoelectric uncertainty can affect the vibration behaviors, and consideration of parameter uncertainties is needed in dynamic designs in order to minimise the vibration response at resonance frequencies. Keywords Rotating beam · Vibration · Stochastic dynamic · Electromechanical 33.1 Introduction Rotating beams provide basic components of many common engineering applications, such as turbine blades [1]. In the realistic applications, the turbine blades are subjected to high dynamic forces which can lead to high cycle fatigue failures. An effective vibration control of rotating beams is one of the most essential tasks for relevant designs of such systems. The shunted piezoelectric damping technique is a potentially applicable method to reduce the vibrations of turbine blades. In the applications of the piezoelectric damping to the turbine blades, most researches have been performed in the nonrotational frames and the rotational effects have been always neglected [2]. The main differences between the rotating and non-rotating beams are the additional Coriolis effects and centrifugal force due to the rotational motion, which will result in the considerable coupling of the vibration modes in different directions. When the aero-elasticity are involved, those effects may significantly influence the dynamic behaviors of rotating beam systems [3]. However, in most studies of rotating beams, only the bending and stretching deformations were considered, the Coriolis effects as well as the coupling among the elastic deformations of various directions, such as bending-stretching and bending-twist have been neglected. Moreover, in practice input parameters are always submitted to dispersions due to inherent uncertainties involving in manufacturing process and intrinsic properties of materials [4], so the response may also alter in the uncertain way. Thus, in order to accurately estimate the system performance, the consideration of effects of input uncertainties into the system modelling is necessary. However, little research exists regarding the rotating beams with uncertain parameters, and the effects of uncertainty propagation into uncertain responses remain misunderstood. Thus, the goal of this work is to (1) to develop multiphysics model of rotating beam with piezoelectric patches surfacemounted, and (2) allow a prediction of uncertain responses generated by uncertainties in both the structural and electric components based on a probabilistic framework. Z. Zhang ( ) · N. Duan · J. Tian · H. Hua Department of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China e-mail: zzgjtx@sjtu.edu.cn © Society for Experimental Mechanics, Inc. 2020 R. Barthorpe (ed.), Model Validation and Uncertainty Quantification, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-12075-7_33 281
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