A SIMPLE CRITERION FOR ESTABLISHING AN UPPER LIMIT TO THE HARMONIC EXCITATION LEVEL OF THE DUFFING OSCILLATOR USING THE VOLTERRA SERIES

1996 ◽  
Vol 190 (5) ◽  
pp. 751-762 ◽  
Author(s):  
G.R. Tomlinson ◽  
G. Manson ◽  
G.M. Lee
Keyword(s):  
Volterra Series ◽  
Duffing Oscillator ◽  
Harmonic Excitation ◽  
Excitation Level ◽  
Simple Criterion ◽  
Upper Limit

scholarly journals Nonlinear vibration of knitted spacer fabric under harmonic excitation

2020 ◽  
Vol 15 ◽  
pp. 155892502098356
Author(s):  
Fuxing Chen ◽  
Hong Hu
Keyword(s):  
Nonlinear Vibration ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Polyurethane Foams ◽  
Excitation Level ◽  
Harmonic Amplitude ◽  
Damping Force ◽  
Spacer Fabric ◽  
Fabric System ◽  
Quadratic Stiffness

Knitted spacer fabrics can be an alternative material to typical rubber sponges and polyurethane foams for the protection of the human body from vibration exposure, such as automotive seat cushions and anti-vibration gloves. To provide a theoretical basis for the understanding of the nonlinear vibration behavior of the mass-spacer fabric system under harmonic excitation, experimental, analytical and numerical methods are used. Different from a linear mass-spring-damper vibration model, this study builds a phenomenological model with the asymmetric elastic force and the fractional derivative damping force to describe the periodic solution of the mass-spacer fabric system under harmonic excitation. Mathematical expression of the harmonic amplitude versus frequency response curve (FRC) is obtained using the harmonic balance method (HBM) to solve the equation of motion of the system. Parameter values in the model are estimated by performing curve fit between the modeled FRC and the experimental data of acceleration transmissibility. Theoretical analysis concerning the influence of varying excitation level on the FRCs is carried out, showing that nonlinear softening resonance turns into nonlinear hardening resonance with the increase of excitation level, due to the quadratic stiffness term and the cubic stiffness term in the model, respectively. The quadratic stiffness term also results in biased vibration response and causes an even order harmonic distortion. Besides, the increase of excitation level also results in elevated peak transmissibility at resonance.

Superharmonic Resonance of Fractional-Order Mathieu–Duffing Oscillator

2019 ◽  
Vol 14 (7) ◽  
Author(s):  
Jiangchuan Niu ◽  
Xiaofeng Li ◽  
Haijun Xing
Keyword(s):  
Fractional Order ◽  
Order Term ◽  
Duffing Oscillator ◽  
Steady State Solution ◽  
Harmonic Excitation ◽  
Frequency Equation ◽  
Superharmonic Resonance ◽  
Duffing System ◽  
Resonance Response ◽  
Kbm Method

The superharmonic resonance of fractional-order Mathieu–Duffing oscillator subjected to external harmonic excitation is investigated. Based on the Krylov–Bogolubov–Mitropolsky (KBM) asymptotic method, the approximate analytical solution for the third superharmonic resonance under parametric-forced joint resonance is obtained, where the unified expressions of the fractional-order term with fractional order from 0 to 2 are gained. The amplitude–frequency equation for steady-state solution and corresponding stability condition are also presented. The correctness of the approximate analytical results is verified by numerical results. The effects of the fractional-order term, excitation amplitudes, and nonlinear stiffness coefficient on the superharmonic resonance response of the system are analyzed in detail. The results show that the KBM method is effective to analyze dynamic response in a fractional-order Mathieu–Duffing system.

Investigation of Vibration Energy Harvesting Using Two Cantilevers With Random Input

2017 ◽  
Author(s):  
Wei Yang ◽  
Panagiotis Alevras ◽  
Shahrzad Towfighian
Keyword(s):  
Mechanical Energy ◽  
Duffing Oscillator ◽  
Electrical Energy ◽  
Potential Energy Function ◽  
Excitation Level ◽  
Vibration Energy ◽  
Random Input ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Low Performance

There is a growing interest to convert ambient mechanical energy to electrical energy by vibration energy harvesters. Realistic vibrations are random and spread over a large frequency range. Most energy harvesters are linear with narrow frequency bandwidth and show low performance, which led to creation of nonlinear harvesters that have larger bandwidth. This article presents a simulation study of a nonlinear energy harvester that contains two cantilever beams coupled by magnetic force. One of the cantilever beam is covered partially by piezoelectric material, while the other beam is normal to the first one and is used to create a variable potential energy function. The variable double-well potential function enables optimum conversion of the kinetic energy and thus larger output. The system is modeled by coupled Duffing oscillator equations. To represent the ambient vibrations, the response to Gaussian random input signal (generated by Shinozuka formula) is studied using power spectral density. The effects of different parameters on the system are also investigated. The results show that the double cantilever harvester has a threshold distance, where the harvester can perform optimally regardless of the excitation level. This observation is opposite to that of the conventional fixed magnet cantilever system where the optimal distance varies with the excitation level. Results of this study can be used to enhance energy efficiency of vibration energy harvesters.

scholarly journals Limiting Phase Trajectories and Resonance Energy Transfer in a System of Two Coupled Oscillators

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
L. I. Manevitch ◽  
A. S. Kovaleva ◽  
E. L. Manevitch
Keyword(s):  
Energy Transfer ◽  
Coupled Oscillators ◽  
Energy Exchange ◽  
Duffing Oscillator ◽  
Normal Modes ◽  
Resonance Energy ◽  
Harmonic Excitation ◽  
Conservation Of Energy ◽  
Phase Trajectories ◽  
Limiting Phase Trajectories

We study a problem of energy exchange in a system of two coupled oscillators subject to 1 : 1 resonance. Our results exploit the concept of limiting phase trajectories (LPTs). The LPT, associated with full energy transfer, is, in certain sense, an alternative to nonlinear normal modes characterized by conservation of energy. We consider two benchmark examples. As a first example, we construct an LPT and examine the convergence to stationary oscillations for a Duffing oscillator subjected to resonance harmonic excitation. As a second example, we treat resonance oscillations in a system of two nonlinearly coupled oscillators. We demonstrate the reduction of the equations of motion to an equation of a single oscillator. It is shown that the most intense energy exchange and beating arise when motion of the equivalent oscillator is close to an LPT. Damped beating and the convergence to rest in a system with dissipation are demonstrated.

Excitation-Induced Stability in a Bistable Duffing Oscillator: Analysis and Experiments

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Z. Wu ◽  
R. L. Harne ◽  
K. W. Wang
Keyword(s):  
Perturbation Theory ◽  
Harmonic Balance ◽  
Duffing Oscillator ◽  
Excitation Level ◽  
Frequency Range ◽  
Numerical Studies ◽  
Method Of Harmonic Balance ◽  
Mathieu’S Equation ◽  
Excitation Conditions ◽  
Good Agreement

The excitation-induced stability (EIS) phenomenon in a harmonically excited bistable Duffing oscillator is studied in this paper. Criteria to predict system and excitation conditions necessary to maintain EIS are derived through a combination of the method of harmonic balance, perturbation theory, and stability theory for Mathieu's equation. Accuracy of the criteria is verified by analytical and numerical studies. We demonstrate that damping primarily determines the likelihood of attaining EIS response when several dynamics coexist while excitation level governs both the existence and frequency range of the EIS region, providing comprehensive guidance for realizing or avoiding EIS dynamics. Experimental results are in good agreement regarding the comprehensive influence of excitation conditions on the inducement of EIS.

scholarly journals The Influence of Voids in the Vibrations of Bodies with Dipolar Structure

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1804
Author(s):  
Marin Marin ◽  
Sorin Vlase ◽  
Adina Chirila
Keyword(s):  
Elastic Material ◽  
Lateral Surface ◽  
Harmonic Excitation ◽  
Excitation Level ◽  
The Other ◽  
Spatial Decay ◽  
Dipolar Structure

In our study we analyse the vibration of a right cylinder which consists of an elastic material with dipolar structure and has pores. One end of this cylinder is subjected to an excitation, harmonically in time. The other end of the cylinder and its lateral surface are free of loads. We prove that the presence of the voids does not affect the spatial decay of effects away from the excited end, if the harmonic excitation level is below a predetermined threshold.

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