Size-dependent nonlinear vibration of nonhomogeneous shell embedded with a piezoelectric layer based on surface/interface theory

2017 ◽  
Vol 160 ◽  
pp. 1191-1197 ◽  
Author(s):  
Xue-Qian Fang ◽  
Chang-Song Zhu
Keyword(s):  
Nonlinear Vibration ◽  
Piezoelectric Layer ◽  
Size Dependent ◽  
Interface Theory

scholarly journals Research on nonlinear vibration control of laminated cylindrical shells with discontinuous piezoelectric layer

2021 ◽  
Author(s):  
Chaofeng Li ◽  
Peiyong Li ◽  
Xueyang Miao
Keyword(s):  
Cylindrical Shell ◽  
Vibration Control ◽  
Nonlinear Vibration ◽  
Piezoelectric Layer ◽  
Cylindrical Shells ◽  
Harmonic Balance Method ◽  
Amplitude Response ◽  
Nonlinear Vibration Control ◽  
Laminated Cylindrical Shell ◽  
Laminated Cylindrical Shells

Abstract In this paper, the nonlinear vibration control of the piezoelectric laminated cylindrical shell with point supported elastic boundary condition is analyzed, in which the geometric nonlinearity is considered by the first-order shear nonlinear shell theory. In the model, different boundary conditions are simulated by introducing a series of artificial springs. The elastic-electrically coupled differential equations of piezoelectric laminated cylindrical shells are obtained based on the Chebyshev polynomials and Lagrange equation, and decoupled by using the negative velocity feedback adjustment. Later, the Incremental Harmonic Balance Method (IHBM) is deduced, and the frequency-amplitude response of the piezoelectric laminated cylindrical shell is obtained by IHBM. Finally, the influence of the constant gain, size and position of the piezoelectric layer on frequency-amplitude response are investigated. The results show that the position, size and constant gain of the piezoelectric layer have a significant influence on its nonlinear vibration control.

scholarly journals Nonlinear Vibration Analysis of Curved Piezoelectric-Layered Nanotube Resonator

Energies ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 8031
Author(s):  
Zia Saadatnia
Keyword(s):  
Nonlinear Vibration ◽  
Piezoelectric Layer ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Point Load ◽  
Vibration Response ◽  
Structural Vibration ◽  
Small Scale ◽  
Sensors And Actuators ◽  
Harmonic Voltage

Piezoelectric-based nano resonators are smart structures that can be used for mechanical sensors and actuators in miniature systems. In this study, the nonlinear vibration behavior of a curved piezoelectric-layered nanotube resonator was investigated. The curved structure comprises a core nanotube and a slender layer of piezoelectric material covering the inner nanotube where a harmonic voltage is applied to the piezoelectric layer. Applying the energy method and Hamiltonian principle in association with non-local theories, the governing equations of motion of the targeted system are obtained. Then, the problem is solved using the Galerkin and multiple scales methods, and the system responses under external excitation and parametric load are found. Various resonance conditions are investigated including primary and parametric resonances, and the frequency responses are obtained considering steady state motions. The effects of different parameters such as applied voltage, piezoelectric thickness, and structural curvature on the system responses are investigated. It is shown that the applied harmonic voltage to the piezoelectric layer can cause a parametric resonance in the structural vibration, and the applied harmonic point load to the structure can cause a primary resonance in the vibration response. Considering two structural curvatures including quadratic and cubic curves, it is also found that the waviness and curve shape parameters can tune the nonlinear hardening and softening behaviors of the system and at specific curve shapes, the vibration response of the targeted structure acts similar to that of a linear system. This study can be targeted toward the design of curved piezoelectric nano-resonators in small-scale sensing and actuation systems.

Interaction Between an Edge Dislocation and a Crack With Surface Elasticity

2015 ◽  
Vol 82 (2) ◽  
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Edge Dislocation ◽  
Analytical Study ◽  
Surface Elasticity ◽  
Image Force ◽  
Size Dependent ◽  
Interface Theory ◽  
Singular Integrodifferential Equations ◽  
Finite Crack ◽  
Crack Tips ◽  
The Continuum

We undertake an analytical study of the interaction of an edge dislocation with a finite crack whose faces are assumed to have separate surface elasticity. The surface elasticity on the faces of the crack is described by a version of the continuum-based surface/interface theory of Gurtin and Murdoch. By using the Green's function method, we obtain a complete exact solution by reducing the problem to three Cauchy singular integrodifferential equations of the first-order, which are solved by means of Chebyshev polynomials and a collocation method. The correctness of the solution is rigorously verified by comparison with existing analytical solutions. Our analysis shows that the stresses and the image force acting on the edge dislocation are size-dependent and that the stresses exhibit both the logarithmic and square root singularities at the crack tips when the surface tension is neglected.

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.

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