scholarly journals Linear Analytical Solutions of Mechanical Sensitivity in Large Deflection of Unsymmetrically Layered Piezoelectric Plate under Pretension

2014 ◽  
Vol 6 ◽  
pp. 403827
Author(s):  
Chun-Fu Chen ◽  
I-Wei Li
Keyword(s):  
Analytical Solutions ◽  
Large Deflection ◽  
Piezoelectric Plate ◽  
Mechanical Sensitivity

Analytical Solutions for Large Deflections of Functionally Graded Beams Based on Layer-Graded Beam Model

2018 ◽  
Vol 10 (09) ◽  
pp. 1850098 ◽  
Author(s):  
Peng Zhou ◽  
Ying Liu ◽  
Xiaoyan Liang
Keyword(s):  
Intensity Factor ◽  
Analytical Solutions ◽  
Large Deflection ◽  
Yield Criterion ◽  
Functionally Graded ◽  
Beam Model ◽  
Large Deflections ◽  
Transverse Loading ◽  
Functionally Graded Beam ◽  
Gradient Variation

The objective of this paper is to investigate the large deflection of a slender functionally graded beam under the transverse loading. Firstly, by modeling the functionally graded beam as a layered structure with graded yield strength, a unified yield criterion for a functionally graded metallic beam is established. Based on the proposed yielding criteria, analytical solutions (AS) for the large deflections of fully clamped functionally graded beams subjected to transverse loading are formulated. Comparisons between the present solutions with numerical results are made and good agreements are found. The effects of gradient profile and gradient intensity factor on the large deflections of functionally graded beams are discussed in detail. The reliability of the present analytical model is demonstrated, and the larger the gradient variation ratio near the loading surface is, the more accurate the layer-graded beam model will be.

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.

Weakly Nonlinear Characteristics of a Three-Layer Circular Piezoelectric Plate-Like Power Harvester Near Resonance

2013 ◽  
Vol 30 (1) ◽  
pp. 97-102 ◽  
Author(s):  
H. R. Wang ◽  
X. Xie ◽  
Y. T. Hu ◽  
J. Wang
Keyword(s):  
Large Deflection ◽  
Piezoelectric Plate ◽  
Nonlinear Effects ◽  
Energy Scavenging ◽  
Nonlinear Characteristics ◽  
Weakly Nonlinear ◽  
Simply Supported ◽  
Near Resonance ◽  
Jump Phenomena ◽  
Power Harvester

ABSTRACTThe nonlinear characteristics of a simply-supported three-layer circular piezoelectric plate-like power harvester near resonance are examined in the paper, where the energy-scavenging structure consists of two properly poled piezoceramic layers separated by a central metallic layer. The structure is subjected to a uniform harmonic pressure on the upper surface. Nonlinear effects of large deflection near resonance to induce the incidental in-plane extension are considered. Results on output powers are presented, which exhibit multi-valuedness and jump phenomena.

scholarly journals Design and Mechanical Sensitivity Analysis of a MEMS Tuning Fork Gyroscope with an Anchored Leverage Mechanism

Sensors ◽  
2019 ◽  
Vol 19 (16) ◽  
pp. 3455 ◽  
Author(s):  
Li ◽  
Gao ◽  
Jin ◽  
Liu ◽  
Guan ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Analytical Solutions ◽  
Tuning Fork ◽  
Fem Simulation ◽  
Micro Electro Mechanical System ◽  
Stiffness Ratio ◽  
Sense Mode ◽  
Mechanical Sensitivity ◽  
Improvement Rate ◽  
Theoretical Results

This paper presents the design and analysis of a new micro-electro-mechanical system (MEMS) tuning fork gyroscope (TFG), which can effectively improve the mechanical sensitivity of the gyroscope sense-mode by the designed leverage mechanism. A micromachined TFG with an anchored leverage mechanism is designed. The dynamics and mechanical sensitivity of the design are theoretically analyzed. The improvement rate of mechanical sensitivity (IRMS) is introduced to represent the optimization effect of the new structure compared with the conventional one. The analytical solutions illustrate that the IRMS monotonically increases with increased stiffness ratio of the power arm (SRPA) but decreases with increased stiffness ratio of the resistance arm (SRRA). Therefore, three types of gyro structures with different stiffness ratios are designed. The mechanical sensitivities increased by 79.10%, 81.33% and 68.06% by theoretical calculation. Additionally, FEM simulation demonstrates that the mechanical sensitivity of the design is in accord with theoretical results. The linearity of design is analyzed, too. Consequently, the proposed new anchored leverage mechanism TFG offers a higher displacement output of sense mode to improve the mechanical sensitivity.

Application of Groebner Basis Methodology to Nonlinear Analysis of an Underwater Cable

2011 ◽  
Author(s):  
Y. Jane Liu ◽  
George R. Buchanan
Keyword(s):  
Galerkin Method ◽  
Nonlinear Analysis ◽  
Analytical Solutions ◽  
Large Deflection ◽  
Geometrically Nonlinear ◽  
Groebner Basis ◽  
Governing Equations ◽  
Geometrically Nonlinear Analysis ◽  
Highly Nonlinear ◽  
The Galerkin Method

The governing equations for a large deflection cable analysis have a highly nonlinear and coupled nature. As a result, analytical solutions are unavailable or limited to a few simplified cases. The present study is to apply the Groebner Basis methodology combined with the Galerkin method to a geometrically nonlinear analysis of an underwater cable as an example.

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