Abstract
A rotating system comprising a hub and a thin-walled laminate cantilever beam with embedded nonlinear piezoelectric layers is analysed in the paper. The reinforcing fibres set-up in composite material conforms to circumferentially uniform stiffness lamination scheme. This configuration exhibits the mutual bending couplings in two orthogonal planes. Nonlinear analytical model of a piezoelectric material embedded onto the beam walls is postulated by considering the higher-order constitutive relations with respect to electric field variable. Moreover, to properly model electromechanical structural behaviour, the full two-way coupling piezoelectric effect is considered. To this aim, the assumption of a spanwise electric field variation is postulated in the mathematical model of the structure. Based on previous authors’ research, the system of mutually coupled nonlinear equations of motion is formulated. In the numerical analysis the forced response of the system under zero and nonzero mean value harmonic torque excitation is considered. In particular, the influence of hub inertia, excitation amplitude and mean rotating speed on system dynamics is investigated. The results are presented in the form of appropriate frequency response plots and bifurcation diagrams.
Highlights
The continuous development of composite materials offers a great potential for modern structural systems that can take advantage of unique composite material properties as well as material tailoring technology
Mixed theories adopting the geometrically linear Bernoulli–Euler hypothesis for the mechanical components and a first-order theory for the electrical variable can be found in the recent literature [15,35]. Conclusions summarizing these papers indicate that the Euler–Bernoulli beam model severely over-predicts the structural behaviour of tested functional structures, especially at low frequencies and low length-towidth aspect ratios. This over-prediction is of particular importance in case of composite materials that exhibit relatively low shear stiffness when compared to classical isotropic materials
We investigate dynamics of the system imposing periodic torque μ to the hub
Summary
The continuous development of composite materials offers a great potential for modern structural systems that can take advantage of unique composite material properties as well as material tailoring technology. This over-prediction is of particular importance in case of composite materials that exhibit relatively low shear stiffness when compared to classical isotropic materials Another important aspect in proper modelling the piezoelectric functional structures is mutual interaction of mechanical and electrical domains of the system. With respect to former research a new governing equation was formulated representing the electric field distribution within the piezoceramic domain 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]. Regarding the referenced papers and to the best of authors knowledge, these aspects of CUS laminated multifunctional beams with nonlinear piezoelectrics have not been studied in detail yet
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