Size-dependent vibration of laminated functionally graded curved beams covered with piezoelectric layers

Abstract

The nonlocal piezoelectric theory and first-order shear deformation theory are combined to study the nano-scale effect on the free vibration of a laminated functionally graded curved nano-beam covered with piezoelectric layers. The first-order shear deformation theory is introduced to consider the shear deformation and rotary inertia effects resulting from the torsional and flexural deformations. The effective elastic properties of the elastic nano-layers are estimated by using the Cox model. The governing equations are derived by employing Hamilton’s principle, and the efficient differential quadrature method is used to solve the discretized equations. Through numerical examples, it is found that the effects of beam thickness, volume fraction of fibers, curve parameter and boundary conditions on the natural frequencies are quite related to the nonlocal coefficient of curved beam. The vibration characters of curved nano-beam are discussed in detail.

Keywords:

• Laminated functionally graded curved beams
• piezoelectric layers
• size-dependent vibration
• nonlocal piezoelectric theory
• fundamental frequency

Additional information

Funding

This work is supported by the projects of Error! Hyperlink reference not valid. (No. 12172236), Education Department Foundation for Young Researcher in Hebei Province of China (No. QN2021132).