scholarly journals On some aspects of the dynamic behavior of the softening Duffing oscillator under harmonic excitation

2016 ◽  
Vol 86 (8) ◽  
pp. 1383-1390 ◽  
Author(s):  
Utz von Wagner ◽  
Lukas Lentz
Keyword(s):  
Dynamic Behavior ◽  
Duffing Oscillator ◽  
Harmonic Excitation

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.

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.

scholarly journals Dynamic behavior of an AMB supported rotor subject to harmonic excitation

2008 ◽  
Vol 32 (7) ◽  
pp. 1370-1380 ◽  
Author(s):  
M.H. Eissa ◽  
U.H. Hegazy ◽  
Y.A. Amer
Keyword(s):  
Dynamic Behavior ◽  
Harmonic Excitation

Study on Dynamic Response of Visco-elastic Plate Under Transverse Periodic Load

2012 ◽  
Vol 13 (3-4) ◽  
Author(s):  
Xiaopeng Yan ◽  
Nianmei Zhang ◽  
Guitong Yang
Keyword(s):  
Dynamic Response ◽  
Dynamic Behavior ◽  
Thin Plate ◽  
Elastic Plate ◽  
Harmonic Excitation ◽  
Rectangular Thin Plate ◽  
Periodic Load ◽  
Compressive Loads

AbstractThe dynamic behavior of simple supported rectangular thin plate subjected to transverse harmonic excitation is investigated in this paper. The compressive loads

Nonlinear Modeling and Identification of the Dynamic Behavior of Polyurethane Foam

2001 ◽  
Author(s):  
R. Singh ◽  
P. Davies ◽  
A. K. Bajaj
Keyword(s):  
Dynamic Behavior ◽  
Polyurethane Foam ◽  
Nonlinear Modeling ◽  
Viscoelastic Model ◽  
Harmonic Excitation ◽  
Relaxation Kernel ◽  
Mass System ◽  
Response Data ◽  
State Response ◽  
Linear Viscoelastic

Abstract The analysis of the steady-state response of a polyurethane foam and mass system to harmonic excitation is given. The foam’s uni-directional dynamic behavior motion is modeled by using nonlinear stiffness, linear viscoelastic and velocity proportional damping components. The relaxation kernel for the viscoelastic model is assumed to be a sum of exponentials. Harmonic balance is used to develop one- and two-term solution approximations that are utilized for system identification. The identification process is based on least-squares minimization of a sub-optimal cost function that uses response data at various excitation frequencies and amplitudes. The effect of number, spacing and amplitudes of the harmonic input on the results of the model parameter estimation is discussed. Model-order choice and the feasibility of describing the system behavior at several input amplitudes with a single set of parameters are also addressed.

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