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Meccanica

, Volume 51, Issue 4, pp 921–937 | Cite as

Three dimensional static and free vibration analysis of cross-ply laminated plate bonded with piezoelectric layers using differential quadrature method

  • M. Feri
  • A. Alibeigloo
  • A. A. Pasha Zanoosi
Article

Abstract

This paper illustrates static and free vibration analysis of a cross-ply laminated composite plate embedded in piezoelectric layers based on three dimensional theory of elasticity. In this approach, a semi-analytical solution is presented for the hybrid plate with arbitrary boundary condition. For analysis a differential quadrature method (DQM) is used in two directions and state space method is employed along the thickness direction. The method is validated by comparing numerical results with the one obtained in the literature and also the results of DQM are compared with the results of analytical solution obtained by Fourier series solution. In parametric study, the effect of boundary condition, mechanical load, electric voltage, length to thickness ratio and piezoelectric thickness on both vibration and static behavior of plate are investigated.

Keywords

Static Free vibration Three dimensional Laminated Piezoelectric DQM 

List of symbols

a, b, h

Plate dimensions in x, y and z directions

\( C_{ij} \,\left( {{\text{i}},{\text{j}} = 1,2, \ldots ,6} \right) \)

Material elastic constants

\( D_{x} ,{\text{D}}_{\text{y}} \,{\text{and}}\,{\text{D}}_{\text{z}} \)

Electric displacement components

\( E_{x} ,{\text{E}}_{\text{y}} \,{\text{and}}\,{\text{E}}_{\text{z}} \, \)

Electric field components

E22

Young’s modulus composite along the y-direction

\( \eta_{i} \,\left( {i = 1,2,3} \right) \)

Dielectric constants

ρsρaρc

Density of sensor, actuator and composite layers

\( \sigma_{i} (i = x,y,z) \)

Normal stresses

τxyτyzτxz

Shear stresses

e

Piezoelectric constant

V0

Applied electric voltage

\( {{\updelta}} \)

State vector

hc, hp

Thicknesses of the composite and piezoelectric layers

UVW

Displacements in the x-, y- and z-direction, respectively

γzyγzxγxy

Shear strains

\( {{\upvarepsilon}}_{i} \,(i = x,y,z) \)

Normal strains

\( \omega \)

Frequency

\( {{\updelta}}_{c} \), \( {{\updelta}}_{p} \)

State vectors of the elastic and piezoelectric layers

ψ

Electric voltage

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentBu Ali Sina UniversityHamedanIran
  2. 2.Mechanical Engineering Department, Faculty of EngineeringTarbiat Modares UniversityTehranIran
  3. 3.Faculty of Industrial and Mechanical Engineering, Qazvin BranchIslamic Azad UniversityQazvinIran

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