Parametric Resonance Based Piezoelectric Micro-Scale Resonators: Modeling and Theoretical Analysis

2011 ◽  
Author(s):  
Pooya Ghaderi ◽  
Andrew J. Dick
Keyword(s):  
Parametric Resonance ◽  
Multiple Scales ◽  
Single Mode ◽  
Electric Signal ◽  
Dynamic Force ◽  
Mode Behavior ◽  
Out Of Plane ◽  
Three Degree Of Freedom ◽  
Plane Oscillations ◽  
Beam Component

In this study, a two-component auto-parametric resonator utilizing piezoelectric actuation is proposed. The resonator consists of a plate component which serves as the exciter and a beam component which serves as the oscillator. When an electric signal is applied, the plate component experiences in-plane oscillations which serve to provide axial excitation to the beam component. The system is designed to operate in auto-parametric resonance with a plate to beam principal frequency ratio of 1:2. Due to the oscillations of the beam component, a dynamic force and a moment are applied to the plate and can cause out-of-plane oscillations of the plate component. Internal-resonance can also exist between the beam oscillations and the out-of-plane vibrations of the plate component. A model is derived in order to describe these three motions and the coupling between them. By assuming single mode behavior for each motion, the model is discretized and represented with a three degree-of-freedom model. The model is solved analytically by using the method of multiple scales. Results of the perturbation method agree well with the numerical simulation. The results for the system with strong and weak coupling between the resonator components are presented and compared.

Parametric Resonance Based Piezoelectric Micro-Scale Resonators: Modeling and Theoretical Analysis

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Pooya Ghaderi ◽  
Andrew J. Dick
Keyword(s):  
Multiple Scales ◽  
Single Mode ◽  
Electric Signal ◽  
Dynamic Force ◽  
Operational Conditions ◽  
Mode Behavior ◽  
Out Of Plane ◽  
Nominal Performance ◽  
Plane Oscillations ◽  
Beam Component

In this study, a two-component autoparametric resonator utilizing piezoelectric actuation is proposed. The resonator consists of a plate component which serves as the exciter and a beam component which serves as the oscillator. When an electric signal is applied, the plate component experiences in-plane oscillations which serve to provide axial excitation to the beam component. The system is designed to operate in autoparametric resonance with a plate to beam principal frequency ratio of 1:2. Due to the oscillations of the beam component, a dynamic force and a moment are applied to the plate and can cause out-of-plane oscillations of the plate component. The possibility of internal-resonance between the beam oscillations and the out-of-plane vibrations of the plate component are also considered. A model is derived in order to describe these three motions and the coupling between them. By assuming single mode behavior for each motion, the model is discretized and represented with a three degree-of-freedom model. The model is solved analytically by using the method of multiple scales and results are verified with the numerical simulations. Also, the influence of system parameters on response behavior is studied and the ideal operational conditions and parameter values for nominal performance are obtained.

Single-mode cylindrical graphene plasmon waveguide

2016 ◽  
Vol 30 (22) ◽  
pp. 1650268
Author(s):  
Jianfeng Yang ◽  
Jingjing Yang ◽  
Ming Huang
Keyword(s):  
Cutoff Frequency ◽  
Single Mode ◽  
Graphene Sheets ◽  
Fem Simulations ◽  
Graphene Surface ◽  
Single Mode Operation ◽  
Mode Behavior ◽  
Novel Applications ◽  
Large Tunability ◽  
Single Mode Condition

A cylindrical graphene plasmon waveguide (CGPW) which consists of two rolled graphene ribbons, a dielectric core and a dielectric interlayer is proposed. An analytical model for the single-mode condition and cutoff frequency of high-order graphene surface plasmon (GSP) modes is presented and verified by finite element method (FEM) simulations. Single-mode operation region of CGPW is identified in the frequency–radius space. By varying the separation between two graphene sheets and the Fermi level of graphene, a large tunability of the mode behavior is also demonstrated. The proposed structure may provide a new freedom to manipulate GSPs, and would lead to novel applications in optics.

scholarly journals Fiber Optical Hydrogen Sensor Based on WO3-Pd2Pt-Pt Nanocomposite Films

Nanomaterials ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 128
Author(s):  
Jixiang Dai ◽  
Yi Li ◽  
Hongbo Ruan ◽  
Zhuang Ye ◽  
Nianyao Chai ◽  
...  
Keyword(s):  
Optical Power ◽  
Single Mode ◽  
Hydrogen Sensor ◽  
Single Mode Fiber ◽  
Nanocomposite Films ◽  
Electric Signal ◽  
Hydrogen Sensing ◽  
Air Atmosphere ◽  
Sensing Material ◽  
Wide Range

In this paper, WO3-Pd2Pt-Pt nanocomposite films were deposited on a single mode fiber as the hydrogen sensing material, which changes its reflectivity under different hydrogen concentration. The reflectivity variation was probed and converted to an electric signal by a pair of balanced InGaAs photoelectric detectors. In addition, the performance of the WO3-Pd2Pt-Pt composite film was investigated under different optical powers, and the irrigating power was optimized at 5 mW. With the irrigation of this optical power, the hydrogen sensitive film exhibits quick response toward 100 ppm hydrogen in air atmosphere at a room temperature of 25 °C. The experimental results demonstrate a high resolution at 5 parts per million (ppm) within a wide range from 100 to 5000 ppm in air. This simple and compact sensing system can detect hydrogen concentrations far below the explosion limit and provide early alert for hydrogen leakage, showing great potential in hydrogen-related applications.

Nonlinear Coupled Transverse and Axial Vibration of Variable Cross-Section Beam Flexures Interconnecting Rigid Body

2016 ◽  
Author(s):  
Hasan Malaeke ◽  
Hamid Moeenfard ◽  
Amir H. Ghasemi
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Cross Section ◽  
Multiple Scales ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Closed Form Solutions ◽  
Dynamic Performances

The objective of this paper is to analytically study the nonlinear behavior of variable cross-section beam flexures interconnecting an eccentric rigid body. Hamilton’s principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. Using a single mode approximation, the governing equations are reduced to a set of two nonlinear ordinary differential equations in terms of end displacement components of the beam which are coupled due to the presence of the transverse eccentricity. The method of multiple scales are employed to obtain parametric closed-form solutions. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. These analytical expressions provide design insights for modeling and optimization of more complex flexure mechanisms for improved dynamic performances.

Energy harvesting from aeroelastic vibrations induced by discrete gust loads

2016 ◽  
Vol 28 (1) ◽  
pp. 47-62 ◽  
Author(s):  
Claudia Bruni ◽  
James Gibert ◽  
Giacomo Frulla ◽  
Enrico Cestino ◽  
Pier Marzocca
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Flow Region ◽  
Rotational Displacement ◽  
Reduced Order ◽  
Piezoelectric Elements ◽  
Out Of Plane ◽  
Gust Loads ◽  
Three Degree Of Freedom ◽  
Euler Bernoulli Beam

This article evaluates the amount of energy that can be extracted from a gust using an aeroelastic energy harvester composed of a flexible wing with attached piezoelectric elements. The harvester operates in a subcritical flow region. It is modeled as a linear Euler–Bernoulli beam sandwiched between two piezoceramics. The extended Hamilton’s principle is used to derive the harvester’s equations of motion and an eigenfunction expansion is used to form a three-degree-of-freedom reduced-order model. The degrees of freedom retained in the model are two flexural degrees for the in-plane and out-of-plane displacements, and a torsional degree for the rotational displacement. Wagner and Küssner functions are used to represent the unsteady aerodynamic and gust loading, respectively. The amount of energy extracted from the system is then compared for two different deterministic gust profiles, 1-COSINE and two sharp-edged gusts forming a square gust, for various magnitudes and durations. The results show that the harvester is able to extract more energy from the square gust profile, although for both profiles the harvester extracts more power after the gust has subsided.

Principal parametric resonance of axially accelerating viscoelastic strings with an integral constitutive law

2005 ◽  
Vol 461 (2061) ◽  
pp. 2701-2720 ◽  
Author(s):  
Li-Qun Chen
Keyword(s):  
Steady State ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Constitutive Law ◽  
Transverse Motion ◽  
Viscoelastic Parameters ◽  
Principal Parametric Resonance ◽  
Linearized Stability ◽  
Speed Fluctuation ◽  
Axial Speed

The steady-state transverse responses and the stability of an axially accelerating viscoelastic string are investigated. The governing equation is derived from the Eulerian equation of motion of a continuum, which leads to the Mote model for transverse motion. The Kirchhoff model is derived from the Mote model by replacing the tension with the averaged tension over the string. The method of multiple scales is applied to the two models in the case of principal parametric resonance. Closed-form expressions of the amplitudes and the existence conditions of steady-state periodical responses are presented. The Lyapunov linearized stability theory is employed to demonstrate that the first (second) non-trivial steady-state response is always stable (unstable). Numerical calculations show that the two models are qualitatively the same, but quantitatively different. Numerical results are also presented to highlight the effects of the mean axial speed, the axial-speed fluctuation amplitude, and the viscoelastic parameters.

Frequency Response of Parametric Resonance of Electrostatically Actuated Circular Plates Under Hard Excitations

2019 ◽  
Author(s):  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Frequency Response ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Reduced Order Model ◽  
Circular Plates ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Modes Of Vibration

Abstract In this paper, the Method of Multiple Scales, and the Reduced Order Model method of two modes of vibration are used to investigate the amplitude-frequency response of parametric resonance of electrostatically actuated circular plates under hard excitations. Results show that the Method of Multiple Scales is accurate for low voltages. However, it starts to separate from the Reduced Order Model results as the voltage values are larger. The Method of Multiple Scales is good for low amplitudes and weak non-linearities. Furthermore the Reduced Order Model running with AUTO 07p is validated and calibrated using the 2 Term ROM time responses.

Bifurcation and Chaos in Externally Excited Circular Cylindrical Shells

1996 ◽  
Vol 63 (3) ◽  
pp. 565-574 ◽  
Author(s):  
Char-Ming Chin ◽  
A. H. Nayfeh
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Multiple Scales ◽  
Period Doubling ◽  
Single Mode ◽  
Equilibrium Solutions ◽  
Multiple Attractors ◽  
Partial Differential ◽  
Quadratic Nonlinearities ◽  
Mode Solution

The nonlinear response of an infinitely long cylindrical shell to a primary excitation of one of its two orthogonal flexural modes is investigated. The method of multiple scales is used to derive four ordinary differential equations describing the amplitudes and phases of the two orthogonal modes by (a) attacking a two-mode discretization of the governing partial differential equations and (b) directly attacking the partial differential equations. The two-mode discretization results in erroneous solutions because it does not account for the effects of the quadratic nonlinearities. The resulting two sets of modulation equations are used to study the equilibrium and dynamic solutions and their stability and hence show the different bifurcations. The response could be a single-mode solution or a two-mode solution. The equilibrium solutions of the two orthogonal third flexural modes undergo a Hopf bifurcation. A combination of a shooting technique and Floquet theory is used to calculate limit cycles and their stability. The numerical results indicate the existence of a sequence of period-doubling bifurcations that culminates in chaos, multiple attractors, explosive bifurcations, and crises.

Asymptotic analysis of the forced vibrations of a one-disc rotor on a non-linear flexible base

2010 ◽  
Vol 224 (8) ◽  
pp. 1593-1604 ◽  
Author(s):  
K V Avramov
Keyword(s):  
Asymptotic Analysis ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Forced Vibrations ◽  
Linear Dynamics ◽  
Non Linear ◽  
Out Of Plane ◽  
Symmetric Rotor ◽  
Flexible Base ◽  
Steady Motions

Equations of motion for a four-degree-of-freedom dynamical system describing the vibrations of a one-disc elastic rotor taking into account gyroscopic moments on a non-linear flexural base are derived. A new version of the multiple scales method is developed and applied to analyse the non-linear dynamics of such a system for different resonances. The steady motions of the rotor are analysed. From the asymptotic analysis, it is shown that out-of-plane motions of the disc exist in the symmetric rotor.

Analytical and experimental studies on out-of-plane dynamic instability of shallow circular arch based on parametric resonance

2016 ◽  
Vol 87 (1) ◽  
pp. 677-694 ◽  
Author(s):  
Airong Liu ◽  
Hanwen Lu ◽  
Jiyang Fu ◽  
Yong-Lin Pi ◽  
Youqin Huang ◽  
...  
Keyword(s):  
Parametric Resonance ◽  
Dynamic Instability ◽  
Experimental Studies ◽  
Circular Arch ◽  
Out Of Plane
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