Size-dependent bending and vibration analysis of piezoelectric nanobeam based on fractional-order kinematic relations

• Published in: Applied mathematics and mechanics Vol. 46; no. 7; pp. 1261 - 1272
• Main Authors: Fan, Zhiwen, Qing, Hai
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2025; Springer Nature B.V
• Edition: English ed.
• Subjects: Applications of Mathematics; Bending; Boundary conditions; Boundary value problems; Cantilever beams; Classical Mechanics; Differential equations; Euler-Bernoulli beams; Finite element method; Fluid- and Aerodynamics; Fractional calculus; Free vibration; Kinematics; Kinetic energy; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Partial Differential Equations; Strain energy; Variational principles; Vibration analysis; Vibration response; scale effect; Riesz-Caputo fractional-order derivative; Euler-Bernoulli piezoelectric beam; fractional-order finite element method (FEM); O342; 26A33

In this paper, a fractional-order kinematic model is utilized to capture the size-dependent static bending and free vibration responses of piezoelectric nanobeams. The general nonlocal strains in the Euler-Bernoulli piezoelectric beam are defined by a frame-invariant and dimensionally consistent Rie...