The Size-Dependent Electromechanical Coupling Response in Circular Micro-Plate due to Flexoelectricity

2016 ◽  
Vol 33 (6) ◽  
pp. 873-883 ◽  
Author(s):  
X. Ji ◽  
A.-Q. Li
Keyword(s):  
Size Effect ◽  
Natural Frequency ◽  
Circular Plate ◽  
Electromechanical Coupling ◽  
Initial Conditions ◽  
Couple Stress Theory ◽  
Piezoelectric Response ◽  
Induced Voltage ◽  
Cylindrical Coordinates ◽  
Size Dependent

AbstractFlexoelectricity, the coupling of strain gradient to polarization, enhances the properties of piezoelectric response desirable for advanced MEMS dramatically even in centrosymmetric dielectrics. In this paper, the general formulations of the flexoelectric couple stress theory presented by Hadjesfandiari in orthogonal curvilinear coordinate system are derived, and are then specified for the case of cylindrical coordinates. A size-dependent flexoelectric model of circular plate is established based on the current formulations in cylindrical coordinates. The governing equations, boundary conditions and initial conditions are derived by applying Hamilton's principle. The static bending and free vibration problems of a simply supported axisymmetric circular plate are carried out to illustrate the applicability of the present model. Numerical results reveal that a homogeneous electric field between the up and down surfaces of the circular plate is induced indeed. The generated deflection, induced voltage and natural frequency show obvious size effect, but the size effect is almost diminishing as the thickness of the plate is far greater than the material length scale parameter. As the increase of the flexoelectric coefficient, the induced voltage increases evidently and the generated deflection and the natural frequency increase weakly.

Modeling size-dependent thermal-mechanical behaviors of shape memory polymer Timoshenko micro-beam

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Fei Zhao ◽  
Xueyao Zheng ◽  
Shichen Zhou ◽  
Bo Zhou ◽  
Shifeng Xue
Keyword(s):  
Size Effect ◽  
Shape Memory ◽  
Couple Stress Theory ◽  
Shape Memory Polymer ◽  
Modified Couple Stress Theory ◽  
Mechanical Behaviors ◽  
Equilibrium Equations ◽  
Content Type ◽  
Size Dependent ◽  
Beam Height

PurposeIn this paper, a three-dimensional size-dependent constitutive model of SMP Timoshenko micro-beam is developed to describe the micromechanical properties.Design/methodology/approachAccording to the Hamilton's principle, the equilibrium equations and boundary conditions of the model are established and according to the modified couple stress theory, the model is available to capturing the size effect because of the material length scale parameter. Based on the model, the simply supported beam was taken for example to be solved and simulated.FindingsResults show that the size effect of SMP micro-beam is more obvious when the dimensionless beam height is similar or the larger of the value of loading time. The rigidity and strength of the SMP beam decrease with the increasing of the dimensionless beam height or the loading time. The viscous property of SMP micro-beam plays a more important role with the larger dimensionless beam height. And the smaller the dimensionless beam height is, the more obvious the shape memory effect of the SMP micro-beam is.Originality/valueThis work implies prediction of size-dependent thermo-mechanical behaviors of the SMP micro-beam and will provide a theoretical basis for design SMP microstructures in the field of micro/nanomechanics.

Size Effect on Pull-In Behaviors of Electrostatically Actuated Cantilever Micro-Beams

2013 ◽  
Vol 300-301 ◽  
pp. 889-892
Author(s):  
Sheng Li Kong
Keyword(s):  
Size Effect ◽  
Couple Stress Theory ◽  
Ritz Method ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Electrostatically Actuated ◽  
Size Dependent ◽  
Deformation Problem ◽  
Approximate Analytical Solutions ◽  
Modified Couple Stress

For the deformation problem of an electrostatically actuated cantilever micro-beam, size effect on pull-in behaviors of the micro-beams have been studied based on modified couple stress theory. The approximate analytical solutions to the pull-in voltage and pull-in displacement of the micro-beam are derived by using the Rayleigh-Ritz method. The results show that the normalized pull-in voltage of the cantilever micro-beam is size-dependent and the normalized pull-in displacement of the micro-beam is size independence.

Nonlinear Vibration of Size Dependent Microresonators with an Electrostatically Actuated Proof Mass

2018 ◽  
Vol 18 (04) ◽  
pp. 1850057 ◽  
Author(s):  
Ehsan Sharifinsab ◽  
Mahdi Mojahedi
Keyword(s):  
Nonlinear Vibration ◽  
Microelectromechanical Systems ◽  
Proof Mass ◽  
Multiple Scales ◽  
Initial Conditions ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
System Response ◽  
Stress Theory ◽  
Size Dependent

In this paper, the dynamic and nonlinear vibration responses of a microresonator containing a microbridge with a proof mass located at its middle are studied. The proof mass of the microresonator is actuated by the electrostatic field in such a way that a direct voltage finds a certain equilibrium position and then be prompted to vibration under the alternative voltage. Due to the importance of the size dependency effect in analysis of the performance of microelectromechanical systems, the size dependent theory is used in the modeling of the microstructure. By adopting the modified couple stress theory and considering electrostatic actuation, the dynamic equation of motion is derived using the extended Hamilton’s principle. Further, with the approximation by Galerkin’s method, the governing equation for the static and oscillatory motion is reduced and the resultant equation is solved by analytical (multiple-scales) and numerical methods. In the analytical and numerical results, the effects of various parameters on the system response, including the midplane stretching and size dependent effects, and dependency of vibration response to initial conditions, are analyzed in detail.

scholarly journals Size-dependent vibration analysis of graphene-PMMA lamina based on non-classical continuum theory

2019 ◽  
Vol 26 (1) ◽  
pp. 491-501 ◽  
Author(s):  
Mehran Karimi Zeverdejani ◽  
Yaghoub Tadi Beni
Keyword(s):  
Natural Frequency ◽  
Couple Stress ◽  
Volume Fraction ◽  
Couple Stress Theory ◽  
Shear Deformation Theory ◽  
Continuum Theory ◽  
Dynamics Simulation ◽  
Physical Parameters ◽  
Stress Theory ◽  
Size Dependent

AbstractThis paper studies the free vibration of polymer nanocomposite reinforced by graphene sheet. In this work, the new size dependent formulation is presented for nanocomposites based on couple stress theory. For this purpose, the first shear deformation theory is applied. The effect of scale parameter is investigated based on anisotropic couple stress theory. Vibration equations of the composite lamina are extracted using Hamilton’s principle. Numerical results are provided for Poly methyl methacrylate/graphene composite.Mechanical properties of the composite are obtained from molecular dynamics simulation. Based on eigenvalue procedure, an analytical solution is obtained for the natural frequency of composite lamina. In the results section, the effect of dimensional and physical parameters are investigated on lamina natural frequency. It is observed that graphene defects caused to diminish the lamina frequency. Furthermore, it is revealed that the increase in graphene volume fraction leads to natural frequency be greater.

scholarly journals Size-Dependent Dynamic Behavior of a Microcantilever Plate

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Xiaoming Wang ◽  
Fei Wang
Keyword(s):  
Size Effect ◽  
Dynamic Behavior ◽  
Size Effects ◽  
Numerical Solutions ◽  
Couple Stress Theory ◽  
Differential Quadrature Method ◽  
Modified Couple Stress Theory ◽  
Cantilever Plate ◽  
Size Dependent ◽  
Material Length Scale

Material length scale considerably affects the mechanical properties of microcantilever components. Recently, cantilever-plate-like structures have been commonly used, whereas the lack of studies on their size effects constrains the design, testing, and application of these structures. We have studied the size-dependent dynamic behavior of a cantilever plate based on a modified couple stress theory and the differential quadrature method in this note. The numerical solutions of microcantilever plate equation involving the size effect have been presented. We have also analyzed the bending and vibration of the microcantilever plates considering the size effect and discussed the dependence of the size effect on their geometric dimensions. The results have shown that (1) the mechanical characteristics of the cantilever plate show obvious size effects; as a result, the bending deflection of a microcantilever plate reduces whereas the natural frequency increases effectively and (2) for the plates with the same material, the size effect becomes more obvious when the plates are thinner.

Size Effect on Natural Frequency of Cantilever Micro-Beams Based on a Modified Couple Stress Theory

2013 ◽  
Vol 694-697 ◽  
pp. 221-224 ◽  
Author(s):  
Sheng Li Kong
Keyword(s):  
Size Effect ◽  
Natural Frequency ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
The Difference

The natural frequency of cantilever micro-beams is solved analytically on the basis of modified couple stress theory. The governing equations are obtained by a combination of the basic equations of modified couple stress theory and Hamiltons principle. The size effect on natural frequencies of the cantilever micro-beams is analyzed. It is found that the natural frequencies of the cantilever micro-beams predicted by the newly model are size-dependent. The difference between the natural frequencies predicted by the newly established model and classical beam model is assessed.

A size-dependent model for shear deformable laminated micro-nano plates based on couple stress theory

2021 ◽  
Vol 259 ◽  
pp. 113457
Author(s):  
Zanhang He ◽  
Jianghong Xue ◽  
Sishi Yao ◽  
Yongfu Wu ◽  
Fei Xia
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Stress Theory ◽  
Size Dependent ◽  
Dependent Model ◽  
Shear Deformable

Sol-Gel Derived PZT Thick Films with Nano-Sized Microstructure

2002 ◽  
Vol 748 ◽  
Author(s):  
C. L. Zhao ◽  
Z. H. Wang ◽  
W. Zhu ◽  
O. K. Tan ◽  
H. H. Hng
Keyword(s):  
Lead Zirconate Titanate ◽  
Electromechanical Coupling ◽  
Thick Films ◽  
Sol Gel ◽  
Essential Element ◽  
Processing Parameters ◽  
Lead Zirconate ◽  
Piezoelectric Response ◽  
Coupling Coefficients ◽  
Pzt Films

ABSTRACTLead zirconate titanate (PZT) films are promising for acoustic micro-devices applications because of their extremely high electromechanical coupling coefficients and excellent piezoelectric response. Thicker PZT films are crucial for these acoustic applications. A hybrid sol-gel technology has been developed as a new approach to realize simple and cost-effective fabrication of high quality PZT thick films. In this paper, PZT53/47 thick films with a thickness of 5–50 μm are successfully deposited on Pt-coated silicon wafer by using the hybrid sol-gel technology. The obtained PZT thick films are dense, crack-free, and have a nano-sized microstructure. The processing parameters of this technology have been evaluated. The microstructure of the film has been observed using field-emission scanning electron microscopy and the crystallization process has been monitored by the X-ray diffraction. The thick films thus made are good candidates for fabrication of piezoelectric diaphragm which will be an essential element of microspeaker and microphone arrays.

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