Free Vibration and Electromechanical Response Analysis of Piezoelectric Beams using the Dynamic Stiffness Method and the Carrera Unified Formulation
Yu WANG, Alfonso PAGANI, Erasmo CARRERA, Xiang LIU
Abstract. This paper presents a Carrera Unified Formulation (CUF)-based dynamic stiffness method (DSM) for the free vibration and electromechanical response analysis of piezoelectric laminated beams. The displacement field and electric potential are described by Lagrange expansion (LE) over the beam cross-section, so that layer-wise material changes and local electromechanical coupling can be represented within a one-dimensional framework. The governing equations are derived from the principle of virtual displacements and the linear piezoelectric constitutive equations. Exact frequency-domain solutions are then used to build the dynamic stiffness matrix, and the Wittrick-Williams (WW) algorithm is employed to solve the resulting transcendental eigenvalue problem. Two cantilever configurations are studied: a classic bimorph PZT-5H/aluminum beam and a bimorph piezoelectric beam with a composite laminate substrate. For the benchmark bimorph configuration, the computed natural frequencies and mode shapes agree well with COMSOL finite element results. Load-resistance studies also show clear energy-harvesting behavior, with optimal resistances of 1.7783×104 Ω and 199.53 Ω for the two cases, giving maximum average powers of 4.6657×10-2 W and 1.495×10-2 W, respectively. The results demonstrate that the proposed CUF-DSM framework can provide accurate modal and electromechanical predictions with fewer degrees of freedom.
Keywords
Dynamic Stiffness Method, Carrera Unified Formulation, Piezoelectric Laminated Beams, Wittrick-Williams Algorithm, Electromechanical Coupling Response
Published online 11/8/2026, 6 pages
Copyright © 2026 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Yu WANG, Alfonso PAGANI, Erasmo CARRERA, Xiang LIU, Free Vibration and Electromechanical Response Analysis of Piezoelectric Beams using the Dynamic Stiffness Method and the Carrera Unified Formulation, Materials Research Proceedings, Vol. 73, pp 124-129, 2026
DOI: https://doi.org/10.21741/9781644904459-25
The article was published as article 25 of the book Mechanics of Advanced Materials and Structures
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
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