Nonlinear study of large deflection of simply supported piezoelectric layered-plate under initial tension

2009 ◽  
Author(s):  
Chun-Fu Chen ◽  
John-Han Chen
Keyword(s):  
Large Deflection ◽  
Layered Plate ◽  
Initial Tension ◽  
Simply Supported

Sensitivity in Large Deflection of Bossed and Pre-Tensioned Layered Plate under Lateral Load

2008 ◽  
Vol 47-50 ◽  
pp. 33-36
Author(s):  
Chun Fu Chen ◽  
Yu Chou Wu
Keyword(s):  
Large Deflection ◽  
Plate Theory ◽  
Single Layer ◽  
Radial Force ◽  
Iteration Scheme ◽  
Layered Plate ◽  
Mechanical Sensitivity ◽  
Initial Tension ◽  
Numerical Iteration ◽  
Over The Top

Mechanical sensitivity of a bossed and clamped layered isotropic circular plate with pretension in large deflection is evaluated. The approach extends Von-Karman’s plate theory for large deflection to a symmetrically layered plate with a center boss. The derived nonlinear governing equations are solved using a finite difference method incorporating a numerical iteration scheme in finding the lateral slope and radial force resultant. The obtained geometrical responses are further manipulated to calculate the associated mechanical sensitivity. For a 3-layered plate with nearly the same layer moduli, the results correlate well with those following available formulation for a single-layer isotropic plate. The developed approach is then implemented for various initial tensions, lateral pressures as well as different boss sizes and ratios between the layer moduli. The obtained numerical results show that, initial tension appears to have the strongest influence upon the radial variation of mechanical sensitivity over the top surface of the bossed layered plate. While both the size of center boss and magnitude of lateral pressure can still have a significant effect, the mechanical sensitivity seems to be insensitive to the change of the ratio between layer moduli for a bossed and symmetrically layered plate.

Analytical Study of Piezoelectric Effect on Curvature and Mechanical Sensitivity in Large Deflection of Pre-Stressed Layered Plate Including a Piezoelectric Layer

2015 ◽  
Vol 775 ◽  
pp. 324-328
Author(s):  
Chun Fu Chen ◽  
John Han Chen
Keyword(s):  
Piezoelectric Layer ◽  
Large Deflection ◽  
Piezoelectric Effect ◽  
Low Voltage ◽  
Threshold Value ◽  
Layered Plate ◽  
Mechanical Sensitivity ◽  
Initial Tension ◽  
Bessel Equation ◽  
Lateral Curvature

This study explores the curvature and mechanical sensitivity of a pre-stressed layered plate embedded with a piezoelectric layer in large deflection. Piezoelectric effect was included in deriving the nonlinear governing equations but the arising nonlinear terms are neglected, yielding a standard Bessel equation or a modified Bessel equation for the lateral slope. Analytical solutions are developed and further manipulated to obtain lateral curvature and mechanical sensitivity. The results for a nearly monolithic plate under low pretension and low voltage applied across the piezoelectric layer agree well with those of CPT for a single-layered plate under pure mechanical loading. For typical symmetric 3-layered piezoelectric plates, the solutions show that, piezoelectric effect is apparent only up to a moderate initial tension. Beyond a moderate threshold value, the pretension turns to be dominant, resulting in nearly zero curvature and uniform mechanical sensitivity throughout the entire plate.

Linear Analytical Study of Large Deflection of Piezoelectric Layered Plate Under Initial Tension

2013 ◽  
Vol 29 (3) ◽  
pp. 517-526 ◽  
Author(s):  
C.-F. Chen ◽  
B.-C. Huang
Keyword(s):  
Piezoelectric Layer ◽  
Large Deflection ◽  
Piezoelectric Effect ◽  
Plate Theory ◽  
Layered Plate ◽  
Initial Tension ◽  
Bessel Equation ◽  
Structural Responses ◽  
Clamped Edge ◽  
Good Agreement

AbstractThe linear problem of large deflection of a clamped and layered piezoelectric circular plate under initial tension due to lateral pressure is solved. Von Karman plate theory for large deflection is extended to a symmetrically laminated case including a piezoelectric layer. The thus derived nonlinear governing equations are simplified by neglecting the arising nonlinear terms, yielding a modified Bessel equation or a standard Bessel equation for the lateral slope. These equations are solved analytically by imposing boundary conditions for the clamped edge. For a 3-layered nearly monolithic plate with a low applied voltage upon the piezoelectric layer, the results are in a good agreement with those available in literature for a single-layered plate under pure mechanical loading, thus validates the present approach. Typical 3-layered piezoelectric plates are then implemented and the results show that, piezoelectric effect seems to be apparent only up to a moderate initial tension. For a relatively high pretension, the effect of initial tension appears to be dominant, yielding nearly the same results for the structural responses, regardless of the piezoelectric effect, i.e., the magnitude of voltage applied upon the piezo-electric layer.

Nonlinear Analysis of Large Deflection of Elastically-Bossed Sensor Plate under Initial Tension

2012 ◽  
Vol 152-154 ◽  
pp. 970-975
Author(s):  
Chun Fu Chen ◽  
Nai Di Gao
Keyword(s):  
Large Deflection ◽  
Lateral Pressure ◽  
Plate Theory ◽  
Nonlinear Behavior ◽  
Iteration Scheme ◽  
Isotropic Case ◽  
Layered Plate ◽  
Initial Tension ◽  
Structural Responses ◽  
Silicon Based

The nonlinear problem of large deflection of an elastically-bossed layered plate under pretension due to lateral load is studied. The approach follows von Karman plate theory for large deflection for a symmetrically layered isotropic case. The thus derived nonlinear governing equations are solved using a numerical finite difference method with the aid of an iteration scheme. For a nearly monolithic plate with a thin boss, the obtained solutions correlate well with those available in literature for a single-layered flat plate, thus validates the presented approach. For three layered symmetric plates made of typical silicon based materials, various initial tension and lateral pressure are implemented. The results indicate that, edge behavior may appear at both the boss edge and the clamped end of the plate, thereby revealing severe variations for the structural responses. Varying the central boss size and relative thickness may have a sensible influence upon the behavior of the bossed layered plate. Furthermore, lateral pressure appears to have a sensible effect upon the nonlinear behavior of the bossed layered plate. For a relatively large initial tension, however, the pretension effect dominates, yielding a total membrane behavior for the bossed plate, regardless of the size of the center boss, except in the vicinity of the clamped edge.

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

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