The effects of shear deformation and rotary inertia on the electrical analogs of beams and plates for multimodal piezoelectric damping

Analogous electrical networks were previously derived from the Euler–Bernoulli and Kirchhoff–Love theories to represent beams and plates, respectively, for use in multimodal structural vibration damping. However, these networks do not account for shear deformations or rotary inertia, which can resul...

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Bibliographic Details
Published in:International journal of circuit theory and applications 2024-06, Vol.52 (6), p.2985-2998
Main Authors: Luo, Alan, Lossouarn, Boris, Erturk, Alper
Format: Article
Language:English
Subjects:
Analogs
Beam theory (structures)
Circuit design
Deformation effects
Electrical networks
electromechanical analogy
Energy harvesting
Mechanics
Mindlin plates
multimodal damping
Physics
piezoelectric coupling
Piezoelectricity
Plate theory
Rotary inertia
Shear deformation
Structural vibration
Topology
vibration control
Vibration damping
Vibrations
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Summary:Analogous electrical networks were previously derived from the Euler–Bernoulli and Kirchhoff–Love theories to represent beams and plates, respectively, for use in multimodal structural vibration damping. However, these networks do not account for shear deformations or rotary inertia, which can result in suboptimal vibration damping performance when used on moderately thick beams and plates. In this paper, we investigate the incorporation of shear deformation and rotary inertia using Timoshenko–Ehrenfest beam theory and Mindlin–Reissner plate theory to develop improved electrical networks that can more accurately represent thick beams and plates. Our findings suggest that the inclusion of shear deformation and rotary inertia can significantly improve the frequency coherence of the electrical networks and multimodal vibration damping for thicker structures. The electrical analogs presented here are of use for various applications, especially to conveniently design complex circuit topologies in fields spanning from vibration attenuation to energy harvesting. The electrical analogs of moderately thick cross‐section beams and plates have been developed by considering shear stiffness and rotary inertia from higher order structural theories. The electrical analogs can be used in piezoelectric vibration damping.
ISSN:0098-9886
1097-007X
DOI:10.1002/cta.3899