Semi-Analytical Solution for Vibration of Nonlocal Piezoelectric Kirchhoff Plates Resting on Viscoelastic Foundation

Semi-analytical solutions for vibration analysis of nonlocal piezoelectric Kirchhoff plates resting on viscoelastic foundation with arbitrary boundary conditions are derived by developing Galerkin strip distributed transfer function method. Based on the nonlocal elasticity theory for piezoelectric materials and Hamilton's principle, the governing equations of motion and boundary conditions are first obtained, where external electric voltage, viscoelastic foundation, piezoelectric effect, and nonlocal effect are considered simultaneously. Subsequently, Galerkin strip distributed transfer function method is developed to solve the governing equations for the semi-analytical solutions of natural frequencies. Numerical results from the model are also presented to show the effects of nonlocal parameter, external electric voltages, boundary conditions, viscoelastic foundation, and geometric dimensions on vibration responses of the plate. The results demonstrate the efficiency of the proposed methods for vibration analysis of nonlocal piezoelectric Kirchhoff plates resting on viscoelastic foundation.

[1]  Mohammed Sid Ahmed Houari,et al.  Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept , 2016 .

[2]  Abdelouahed Tounsi,et al.  Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory , 2017 .

[3]  A. Zenkour.  Nonlocal transient thermal analysis of a single-layered graphene sheet embedded in viscoelastic medium , 2016 .

[4]  S. R. Mahmoud,et al.  On the Thermal Buckling Characteristics of Armchair Single-Walled Carbon Nanotube Embedded in an Elastic Medium Based on Nonlocal Continuum Elasticity , 2015 .

[5]  Mohammed Sid Ahmed Houari,et al.  A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams , 2017 .

[6]  Lin-zhi Wu,et al.  Non-local theory solution for a Mode I crack in piezoelectric materials , 2006 .

[7]  A. Zenkour,et al.  Size-dependent free vibration and dynamic analyses of piezo-electro-magnetic sandwich nanoplates resting on viscoelastic foundation , 2017 .

[8]  Y. Lei,et al.  Vibration analysis of viscoelastic single-walled carbon nanotubes resting on a viscoelastic foundation , 2017 .

[9]  Biao Wang,et al.  The scattering of harmonic elastic anti-plane shear waves by a Griffith crack in a piezoelectric material plane by using the non-local theory , 2002 .

[10]  S. R. Mahmoud,et al.  A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams , 2017 .

[11]  A. Farajpour,et al.  Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM , 2014 .

[12]  S. R. Mahmoud,et al.  Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect , 2015 .

[13]  Sondipon Adhikari,et al.  Non-local finite element analysis of damped beams , 2007 .

[14]  L. Ke,et al.  Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory , 2012 .

[15]  A. Eringen.  Theories of nonlocal plasticity , 1983 .

[16]  Ser Tong Quek,et al.  On dispersion relations in piezoelectric coupled-plate structures , 2000 .

[17]  R. Kolahchi,et al.  Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods , 2017 .

[18]  Sondipon Adhikari,et al.  A Galerkin method for distributed systems with non-local damping , 2006 .

[19]  S. Kitipornchai,et al.  Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory , 2013 .

[20]  S. R. Mahmoud,et al.  On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model , 2015 .

[21]  Steven G. Louie,et al.  Stability and Band Gap Constancy of Boron Nitride Nanotubes , 1994 .

[22]  A. Tounsi,et al.  A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation , 2016 .

[23]  I. Elishakoff,et al.  Comparison of nonlocal continualization schemes for lattice beams and plates , 2017 .

[24]  Chen Liu,et al.  Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions , 2015 .

[25]  A. Eringen,et al.  Nonlocal Continuum Field Theories , 2002 .

[26]  Chih‐Ping Wu,et al.  Free vibration of an embedded single-walled carbon nanotube with various boundary conditions using the RMVT-based nonlocal Timoshenko beam theory and DQ method , 2015 .

[27]  R. Kolahchi,et al.  Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories , 2016 .