Pull-in instability and nonlinear vibration analysis of electrostatically piezoelectric nanoresonator with surface/interface effects

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].…”

“…Where all coefficients and phrases of Eqs. (7)-(9) can be seen in reference [11][12][13]. Also, the external work of the fluid can be written as [24] (10)…”

“…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].…”