Vibrations of piezoelectric nanobeams considering flexoelectricity influence: a numerical approach based on strain-driven nonlocal differential/integral models

In this work, a numerical study is presented for the free vibration behavior of piezoelectric Bernoulli–Euler nanoscale beams considering flexoelectric and nonlocal effects. Strain-driven nonlocal formulations of Eringen’s theory in both differential and integral forms are used to capture nonlocal i...

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Bibliographic Details
Published inJournal of the Brazilian Society of Mechanical Sciences and Engineering Vol. 44; no. 2
Main Authors Ansari, R., Faraji Oskouie, M., Nesarhosseini, S., Rouhi, H.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2022
Springer Nature B.V
Subjects
Boundary conditions
Differential equations
Engineering
Equations of motion
Finite difference method
Free vibration
Integral equations
Mathematical analysis
Mechanical Engineering
Operators (mathematics)
Piezoelectricity
Quadratures
Slenderness ratio
Technical Paper
Flexoelectric effect
Arbitrary boundary conditions
Numerical method
Eringen’s nonlocal theory
Piezoelectric nanobeam
Free vibration
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ISSN1678-5878
1806-3691
DOI10.1007/s40430-021-03325-6

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Summary:In this work, a numerical study is presented for the free vibration behavior of piezoelectric Bernoulli–Euler nanoscale beams considering flexoelectric and nonlocal effects. Strain-driven nonlocal formulations of Eringen’s theory in both differential and integral forms are used to capture nonlocal influences. By Hamilton’s principle, the equation of motion and boundary conditions are obtained which are numerically solved. In the solution method, the finite difference and generalized differential quadrature (GDQ) methods are applied for discretizing the differential and integral equations, respectively. Also, matrix differential and integral operators are proposed. After investigating the convergence and validation of the approach, the influences of nonlocality, flexoelectric coefficient and slenderness ratio on the linear free vibrations of nanobeams subject to different end conditions are studied in the numerical results. It is revealed that the paradox related to the results of differential formulation for nanocantilevers is resolved by the proposed integral formulation.
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ISSN:1678-5878
1806-3691
DOI:10.1007/s40430-021-03325-6