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.

Nonlinear Vibrations in Contact Atomic Force Microscopy

2003 ◽  
Author(s):  
Joseph A. Turner
Keyword(s):  
Nonlinear Vibration ◽  
Multiple Scales ◽  
Contact Stiffness ◽  
Vibration Response ◽  
Hertzian Contact ◽  
Force Microscopy ◽  
Softening Behavior ◽  
Atomic Force ◽  
Frequency Relation ◽  
Frequency Curves

The nonlinear vibration response of an atomic force microscope cantilever in contact with a vibrating sample is investigated. The tip-sample contact is modeled using Hertzian contact mechanics. The method of multiple scales is used to analyze this problem in which it is assumed that the beam remains in contact with the moving surface at all times. The primary result from this analysis is the amplitude-frequency relation for the various flexural modes. The amplitude-frequency curves exhibit softening behavior as expected. The amount of softening is shown to depend on the linear contact stiffness as well as the specific mode. The modal sensitivity to nonlinearity is the result of the nonlinearity being restricted to a single position. The mode shape greatly affects the degree to which the nonlinearity influences the frequency response. The Hertzian restriction is then loosened slightly such that variations in nonlinear contact stiffness are examined. These results depend on the linear contact stiffness and mode number as well. The nonlinear vibration response is expected to provide new insight on the nonlinear tip mechanics present in these systems.

scholarly journals Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT

2021 ◽  
Author(s):  
Reza Mohammadi
Keyword(s):  
Nonlinear Vibration ◽  
Frequency Ratio ◽  
Vibration Analysis ◽  
Multiple Scales ◽  
Numerical Technique ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Nonlinear Frequency

Abstract In this paper, the nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT is studied. Nonlocal elasticity theory is applied to consider the small scale effect. The nonlinear equations of motion are derived using Hamilton’s principle. First, a Galerkin-based numerical technique is applied to reduce the nonlinear governing equation into a set of Duffing-type time-dependent differential equations. Afterward, the analytical solutions are derived based on the method of multiple scales (MMS) and perturbation technique. All of the mechanical properties of the beam are temperature dependent. The impacts of the several variables are investigated on the nonlinear frequency ratio of the nanobeams. The results illustrate that when maximum deflection is smaller/ greater than 0.2, its impact on the nonlinear frequency ratio will decrease/increase.

Nonlinear Vibration Analysis of a Fractional Viscoelastic Euler-Bernoulli Microbeam

2018 ◽  
Author(s):  
Firooz Bakhtiari-Nejad ◽  
Ehsan Loghman ◽  
Mostafa Pirasteh
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Multiple Scales ◽  
Scale Effects ◽  
Viscoelastic Model ◽  
Harmonic Excitation ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Harmonic Resonance

Nonlinear vibration of a simply-supported Euler-Bernoulli microbeam with fractional Kelvin-Voigt viscoelastic model subjected to harmonic excitation is investigated in this paper. For small scale effects the modified strain gradient theory is used. For take into account geometric nonlinearities the Von karman theory is applied. Beam equations are derived from Hamilton principle and the Galerkin method is used to convert fractional partial differential equations into fractional ordinary differential equations. Problem is solved by using the method of multiple scales and amplitude-frequency equations are obtained for primary, super-harmonic and sub-harmonic resonance. Effects of force amplitude, fractional parameters and nonlinearity on the frequency responses for primary, super-harmonic and sub-harmonic resonance are investigated. Finally results are compared with ordinary Kelvin-Voigt viscoelastic model.

USING ENERGY-PHASE METHOD TO STUDY GLOBAL BIFURCATIONS AND SHILNIKOV TYPE MULTIPULSE CHAOTIC DYNAMICS FOR A NONLINEAR VIBRATION ABSORBER

2012 ◽  
Vol 22 (01) ◽  
pp. 1250001 ◽  
Author(s):  
S. B. LI ◽  
W. ZHANG ◽  
M. H. YAO
Keyword(s):  
Nonlinear Vibration ◽  
Chaotic Dynamics ◽  
Multiple Scales ◽  
Standard Form ◽  
Primary Resonance ◽  
Phase Method ◽  
Vibration Absorber ◽  
Global Bifurcations ◽  
Modulation Equation ◽  
Nonlinear Vibration Absorber

Global bifurcations and Shilnikov type multipulse chaotic dynamics for a nonlinear vibration absorber are investigated by using the energy-phase method for the first time. A two-degree-of-freedom model of a nonlinear vibration absorber is considered. After the nonlinear nonautonomous equations of this model are given, the method of multiple scales is used to derive four first-order nonlinear ordinary differential equations governing the modulation of the amplitudes and phases of the two interacting modes in the presence of 1:1 internal resonance and primary resonance. Using several coordinate transformations to transform the modulation equation into a standard form, we can apply the energy-phase method to show the existence of the multipulse chaotic dynamics by identifying Shilnikov-type multipulse orbits in the perturbed phase space. We are able to obtain the explicit restriction on the damping, forcing excitation and the detuning parameters, under which the multipulse chaotic dynamics is expected. These multipulse orbits represent the repeated departure from purely vertical oscillations for the nonlinear vibration absorber. Numerical simulations also indicate that there exist different forms of the multipulse chaotic responses and jumping phenomena for the nonlinear vibration absorber.

Nonlinear Vibration of Gear Pairs With Tooth Surface Modifications at Primary Resonance Using a Perturbation Method

2011 ◽  
Author(s):  
Tugan Eritenel ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Vibration ◽  
Half Space ◽  
Multiple Scales ◽  
Gear Tooth ◽  
Primary Resonance ◽  
Surface Modifications ◽  
Element Model ◽  
Elastic Behavior ◽  
Tooth Surface ◽  
Contact Vibrations

An analytical solution for the nonlinear vibration of gear pairs that exhibit partial and total contact loss is found. The gear teeth can have arbitrary tooth surface modifications. Such modifications and dynamic displacements separate parts of gear tooth surface otherwise designed to be in contact. This is partial contact loss. The excitation and the nonlinearity are not specified but are found from the force-deflection function of the gear pair, which comes from independent analysis, such as a finite element model. Fourier and Taylor series expansions of the force-deflection function capture the flexibility, nonlinearity, and the excitation in a few coefficients. The gear elastic behavior includes Hertz contact, bending, and shear. The nonlinearity arises chiefly from tooth surface modifications due to the dependence of contact upon the instantaneous dynamic mesh force. Although this work focuses on gear pairs with tooth surface modifications, the physical system from which the force-deflection function comes is not limited to gear pairs. Sphere/half-space contact vibrations are also analyzed. The dynamic frequency-amplitude relation at the steady-state is found using the method of multiple scales. Comparisons with experiments from the literature on gear vibrations and sphere/half-space contact vibrations verify the method.

Nonlinear vibration control of nano-beam based on capacitive acoustic sensors

2020 ◽  
Vol 64 (1-4) ◽  
pp. 421-429
Author(s):  
Lei Wan ◽  
Canchang Liu ◽  
Weixu Kong ◽  
Yingchao Zhou ◽  
Chicheng Ma
Keyword(s):  
Vibration Control ◽  
Nonlinear Vibration ◽  
Multiple Scales ◽  
Graphene Film ◽  
Primary Resonance ◽  
High Sensitivity ◽  
Vibration Signal ◽  
System Stability ◽  
Acoustic Sensors ◽  
Nonlinear Vibration Control

The nonlinear vibration control of the Euler–Bernoulli beam is studied based on capacitive micro-mechanical acoustic sensors The graphene film has the characteristics of high sensitivity and high accuracy which can be applied to sense the vibration signal. Capacitive micro-mechanical acoustic sensors can be used to detect the acoustic signal of the vibration of the nano-beam. The nonlinear vibration control equation of nano-beam can be established with the displacement and velocity voltage feedback controller based on capacitive micro-mechanical acoustic sensors. The amplitude-frequency response equation of the primary resonance of nano-beam can be gotten by using the multiple scales method. The relationship between the nonlinear vibration of nano-beam and system parameters is investigated. The influencing factors of how to weak system nonlinearity and enhance system stability are analyzed. The static bifurcation behavior of the system is discussed. The numerical results show that the nonlinearity of vibration can be reduced and the stability of the system can be improved by selecting the appropriate control gains and appropriately reducing the amplitude of DC and AC excitation voltages.

scholarly journals Accuracy Improvement of the Method of Multiple Scales for Nonlinear Vibration Analyses of Continuous Systems with Quadratic and Cubic Nonlinearities

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Akira Abe
Keyword(s):  
Nonlinear Vibration ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Primary Resonance ◽  
Harmonic Excitation ◽  
Continuous Systems ◽  
Driving Frequency ◽  
Accuracy Improvement ◽  
Definition Of ◽  
Quadratic And Cubic Nonlinearities

This paper proposes an accuracy improvement of the method of multiple scales (MMSs) for nonlinear vibration analyses of continuous systems with quadratic and cubic nonlinearities. As an example, we treat a shallow suspended cable subjected to a harmonic excitation, and investigate the primary resonance of the th in-plane mode () in which and are the driving and natural frequencies, respectively. The application of Galerkin's procedure to the equation of motion yields nonlinear ordinary differential equations with quadratic and cubic nonlinear terms. The steady-state responses are obtained by using the discretization approach of the MMS in which the definition of the detuning parameter, expressing the relationship between the natural frequency and the driving frequency, is changed in an attempt to improve the accuracy of the solutions. The validity of the solutions is discussed by comparing them with solutions of the direct approach of the MMS and the finite difference method.

scholarly journals Stress-driven two-phase integral elasticity for Timoshenko curved beams

2021 ◽  
pp. 239779142199051
Author(s):  
Marzia S Vaccaro ◽  
Francesco P Pinnola ◽  
Francesco Marotti de Sciarra ◽  
Marko Canadija ◽  
Raffaele Barretta
Keyword(s):  
Solution Procedure ◽  
Small Scale ◽  
Curved Beams ◽  
Sensors And Actuators ◽  
Two Phase ◽  
Design And Optimization ◽  
Local Responses ◽  
Size Dependent ◽  
Classical Boundary ◽  
Phase Integral

In this research, the size-dependent static behaviour of elastic curved stubby beams is investigated by Timoshenko kinematics. Stress-driven two-phase integral elasticity is adopted to model size effects which soften or stiffen classical local responses. The corresponding governing equations of nonlocal elasticity are established and discussed, non-classical boundary conditions are detected and an effective coordinate-free solution procedure is proposed. The presented mixture approach is elucidated by solving simple curved small-scale beams of current interest in Nanotechnology. The contributed results could be useful for design and optimization of modern sensors and actuators.

Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths

2017 ◽  
Vol 9 (6) ◽  
pp. 1485-1505
Author(s):  
Lingchang Meng ◽  
Fengming Li
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Composite Laminated Plate ◽  
Vibration Localization ◽  
Composite Laminated Plates ◽  
Localization Phenomenon ◽  
Harmonic Resonance

AbstractThe nonlinear transverse vibrations of ordered and disordered two-dimensional (2D) two-span composite laminated plates are studied. Based on the von Karman's large deformation theory, the equations of motion of each-span composite laminated plate are formulated using Hamilton's principle, and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin's method. The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales. The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out. The effects of the disorder ratio and ply angle on the two different resonances are analyzed. From the numerical results, it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon, and with the increase of the disorder ratio, the vibration localization phenomenon will become more obvious. Moreover, the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration, and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.

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