A coupled-field model of a rotating composite beam with an integrated nonlinear piezoelectric active element

Abstract

The dynamics of a system consisting of a rotating rigid hub and a thin-walled composite beam with embedded active element is presented. The beam comprises of a generally orthotropic host made of an arbitrary laminate and an additional layer of a transversely isotropic piezoceramic material. The higherorder constitutive relations for piezoelectric are used to properly model its electromechanical structural behaviour when operated in near resonance conditions or subjected to strong electric fields. In the mathematical formulation of the problem, the full two-way coupling piezoelectric effect is considered by adopting the assumption of a spanwise electric field variation. To enhance the generality of the formulation, the model considers also the hub mass moment of inertia and a non-constant rotating speed case. A general nonlinear system of mutually coupled partial differential equations is derived using the Hamilton principle, and the Galerkin method is applied to reduce these governing equations to the ordinary differential ones. A specific case of CAS lamination scheme that exhibits flapwise bending and twist mode elastic coupling is discussed in detail. Numerical results for system free vibrations are obtained to investigate the natural modeThe work is financially supported by Grant DEC-2012/07/B/ST8/03931 from the Polish National Science Centre.J. Latalski (B) Department of Applied Mechanics, Lublin University of Technology, ul. Nadbystrzycka 36, shapes and electrical field spatial distribution depending on the system rotation speed and laminae fibre orientation angle. Next, a forced vibration case is studied by applying to the hub a periodic driving torque with zero mean value. Nonlinear frequency response curves for the combined beam-hub system together with time series plots are prepared for different driving torque scenarios.

Nonlinear vibrations of a rotating thin-walled composite piezo-beam with circumferentially uniform stiffness (CUS)

“…Detailed derivation procedure of a six-DOF model of the beam with an arbitrary presetting angle θ and any circumferential lamination scheme has been presented in former authors papers [17] and [18]. These papers include also the list of adopted kinematic and structural assumptions to the mathematical model as well as the discussion on their significance.…”

“…It has been shown the electromechanical coupling in the structure comes from the shear deformation in flapwise bending plane. This model has been adopted in later research for the analysis of a rotating thin-walled composite beam with embedded piezoelectric layer [17]. In studies, a specific case of circumferentially asymmetric stiffness lamination scheme that exhibits flapwise bending and twist mode elastic coupling was considered.…”

A tale of two tails: developing an avian inspired morphing actuator for yaw control and stability

“…It is important to note that the piezoelectric coefficients reported here are specific to the Navy type II PZT used in the MFC, and do not represent the total piezoelectric coefficients of the MFC itself. Two models are tested here in ABAQUS: a specialized method which accounts for the MFC's modular structure [22], and a thermal analogy [23].…”

On the Existence of Time Delay for Rotating Beam with Proportional–Derivative Controller

“…They showed that the proposed model not only provided good numerical precision and efficiency, but also overcome the constraints expressed by Cartesian variables of a previous traditional nonlinear model. The dynamics of a structure consisting of a rotating rigid hub and a thin-walled composite beam with an embedded active part were introduced by Latalski [7].…”