Nonlinear vibration and stability analysis of double-walled piezoelectric nanoresonator with nonlinear van der Waals and electrostatic excitation

Abstract

In this work, nonlinear vibration and frequency response analysis of a double-walled piezoelectric nanoresonator based on a cylindrical nanoshell is performed using the Gurtin–Murdoch surface/interface theory. The piezoelectric nanoresonator is simultaneously subjected to the visco-Pasternak medium and nonlinear van der Waals and electrostatic forces. It is found that the electrostatic and piezoelectric voltages, length to radius ratio, nanoresonator gap width, linear and nonlinear van der Waals coefficients and other parameters can effectively change the flexural rigidity of the system, which in turn affects the nonlinear frequency response. Also, increasing or decreasing of some parameters leads to increase or decrease in the resonance amplitude, resonant frequency, instability of the system, nonlinear behavior and bandwidth.

Vibration analysis and pull-in instability behavior in multi walled piezoelectric nano-sensor with fluid flow conveyance: influences of surface/interface energy

“…The geometrical parameters of the cylindrical shell are the length , the mid-surface radius with nanoshell thickness 2ℎ and coated by two piezoelectric layers with total thickness 2ℎ for the outer walled and also the mid-surface radius +1 and nanoshell thickness 2ℎ ( +1) for the other inner walled layers. All of the physical and geometrical properties of the mentioned nanostructures for SWPENS can be seen in work done by Hashemi Kachapi et al in reference [11,13].…”

“…Within the framework of Gurtin-Murdoch surface/interface elasticity theory, the normal stresses and can be written as [4,[10][11][12][13][14] (1) ( , ) = 11( , )…”

“…(1)-(4) such as nonlinear deflection, displacement fields and curvatures, relations of Gurtin-Murdoch surface/interface elasticity theory and etc. can be expressed in full detail in reference [11][12][13].…”

“…In Eq. 5, the forces ( ) and moment ( ) resultants are defined in reference Hashemi Kachapi et al [13] for SWPENS. And, as explained, all the sentences mentioned in reference [13] belong to the last wall (in this article, the third wall), which is considered a nanoshell with two piezoelectric layers, and in the other walls (in this article, the first and second walls) are not considered piezoelectric effects.…”

“…Also, vibration analysis of viscoelastic doublewalled carbon nanotube (DWCNT) unified with ZnO layers and subjected to magnetic and electric fields are studied by Fereidoon et al [9]. Recently, Hashemi Kachapi et al presented Gurtin-Murdoch surface/interface theory to investigate linear and nonlinear vibration analysis of piezoelectric nanostructures [10][11][12][13]. Also, nonlinear buckling and postbuckling behavior of functionally graded piezoelectric cylindrical nanoshells under lateral pressure are studied by Fang et al using surface energy effect [14].…”