Modelling of a Rotating Active Thin-Walled Composite Beam System Subjected to High Electric Fields

Latalski, Jarosław

doi:10.1007/978-981-10-0959-4_24

Cited by 5 publications

(13 citation statements)

References 24 publications

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“…For the specific case of an active material subjected to electric field in poling direction x 3 (thicknesswise) and limiting the analysis to linear strains and cubic nonlinearities in the electric field as well as plane stress condition, a set of reduced constitutive equations for the converse effect is [26] …”

Section: Electromechanical Governing Equationsmentioning

confidence: 99%

“…Since the active material is poled through its thickness with traditional surface electrodes normal to axis 3, one can retain electric displacement term D 3 only. The direct piezoelectric effect equation is as follows [26] In the above expressions ξ 33 is material permittivity coefficient, χ 33 andχ i , i = 1, 2, 3 are members of the third-and the fourth-order electric susceptibility tensors, respectively [16,27].…”

Section: Electromechanical Governing Equationsmentioning

confidence: 99%

“…(1) with respect to six mechanical degrees of freedom (u 0 , v 0 , w 0 , ϑ y , ϑ z , ϕ) and electrical one (E 3 ) yields seven electromechanical differential equations of motion and the associated boundary conditions. These are as follows [26]:…”

Section: Electromechanical Governing Equationsmentioning

confidence: 99%

“…(26). The dynamic response of the structure is examined around the first resonance of the combined beam-hub structure and considering different magnitudes of driving torque amplitude ρ.…”

Section: Forced Vibrationsmentioning

confidence: 99%

“…Also the electrically nonlinear piezoelectric constitutive relation has not been taken into account when studying the discussed structures. To bridge this gap, the present paper is given as an extension of recent author's research [26], where the derivation of an analytical model for these types of hybrid systems was presented. In the proposed formulation the non-classical effects like material anisotropy, rotary inertia, first-order transverse shear deformation and warping restraint are incorporated.…”

Section: Introductionmentioning

confidence: 99%

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

Latalski

2017

Nonlinear Dyn

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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.

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Section: Electromechanical Governing Equationsmentioning

confidence: 99%

Section: Electromechanical Governing Equationsmentioning

confidence: 99%

Section: Electromechanical Governing Equationsmentioning

confidence: 99%

“…(26). The dynamic response of the structure is examined around the first resonance of the combined beam-hub structure and considering different magnitudes of driving torque amplitude ρ.…”

Section: Forced Vibrationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Latalski

2017

Nonlinear Dyn

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Dynamics and Saturation Control of Rotating Composite Beam with Embedded Nonlinear Piezoelectric Actuator

Latalski

Warmiński

2017

Springer Proceedings in Physics

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

Latalski

Warmiński

2019

Nonlinear Dyn

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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 setup 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

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Modelling of a Rotating Active Thin-Walled Composite Beam System Subjected to High Electric Fields

Cited by 5 publications

References 24 publications

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

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

Dynamics and Saturation Control of Rotating Composite Beam with Embedded Nonlinear Piezoelectric Actuator

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

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