Analysis and active control of nonlinear vibration of composite lattice sandwich plates
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ORIGINAL PAPER
Analysis and active control of nonlinear vibration of composite lattice sandwich plates Yuyang Chai . Fengming Li . Zhiguang Song . Chuanzeng Zhang
Received: 15 April 2020 / Accepted: 26 October 2020 Ó Springer Nature B.V. 2020
Abstract This paper is devoted to investigate the nonlinear vibration characteristics and active control of composite lattice sandwich plates using piezoelectric actuator and sensor. Three types of the sandwich plates with pyramidal, tetrahedral and Kagome cores are considered. In the structural modeling, the von Ka´rma´n large deflection theory is applied to establish the strain–displacement relations. The nonlinear equations of motion of the structures are derived by Hamilton’s principle with the assumed mode method. The nonlinear free and forced vibration responses of the lattice sandwich plates are calculated. The velocity feedback control (VFC) and H? control methods are applied to design the controller. The nonlinear vibration responses of the sandwich plates with pyramidal, tetrahedral and Kagome cores are compared. The influences of the ply angle of the laminated face sheets, the thicknesses of the lattice core and face sheets and the excitation amplitude on the nonlinear vibration behaviors of the sandwich plates are investigated. The correctness of the H? control algorithm is verified by comparing with the experiment results reported in the literature. The controlled nonlinear Y. Chai F. Li (&) Z. Song College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China e-mail: [email protected] C. Zhang Department of Civil Engineering, University of Siegen, 57068 Siegen, Germany
vibration response of the sandwich plate is computed and compared with that of the uncontrolled structural system. Numerical results indicate that the VFC and H? control methods can effectively suppress the large amplitude vibration of the composite lattice sandwich plates. Keywords Composite lattice sandwich plates Nonlinear vibration properties Active vibration control Piezoelectric material Velocity feedback control (VFC) and H? control
1 Introduction Lightweight lattice sandwich structures, such as sandwich plates with pyramidal, tetrahedral and Kagome cores, are high-performance structures with high specific strength, high specific stiffness and multi-functional potential [1–4]. Moreover, they also have special properties such as vibration isolation [5, 6], sound absorption [7, 8] and heat dissipation [9]. Consequently, lattice sandwich structures have wide application prospects in the aerospace, high-speed trains and navigation industries, such as in the designs of fuselage, submarine bulkheads and sound barriers. In recent years, many scholars have conducted static experiments such as flat crush, shearing, lateral compression and bending on some novel lightweight lattice sandwich structures [10–13]. The failure modes
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and evaluation methods for the mechanical properti
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