scholarly journals Approximate Super- and Sub-harmonic Response of a Multi-DOFs System with Local Cubic Nonlinearities under Resonance

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Yang CaiJin
Keyword(s):  
Nonlinear Response ◽  
Numerical Solutions ◽  
Resonance Theory ◽  
Subharmonic Excitation ◽  
Linearized System ◽  
Natural Resonance Theory ◽  
Direct Numerical Integration ◽  
Mass Spring ◽  
Discrete Mass ◽  
Harmonic Resonance

A multi-degree-of-freedom dynamical system with local cubic nonlinearities subjected to super/subharmonic excitation is considered in this paper. The purpose of this paper is to approximate the nonlinear response of system at super/sub harmonic resonance. For many situations, single resonance mode is often observed to be leading as system enters into super/sub harmonic resonance. In this case, the single modal natural resonance theory can be applied to reduce the system model and a simplified model with only a single DOF is always obtained. Thus, an approximate solution and the analytical expression of frequency response relation are then derived using classical perturbation analysis. While the system is controlled by multiple modes, modal analysis for linearized system is used to decide dominant modes. The reduced model governed by these relevant modes is found and results in an approximate numerical solutions. An illustrative example of the discrete mass-spring-damper nonlinear vibration system with ten DOFs is examined. The approximation results are validated by comparing them with the calculations from direct numerical integration of the equation of motion of the original nonlinear system. Comparably good agreements are obtained.

Analytical Study of a Piezoelectric Frequency Up-Conversion Harvester Under Sawtooth Wave Excitation

2018 ◽  
Author(s):  
Saeed Onsorynezhad ◽  
Amin Abedini ◽  
Fengxia Wang
Keyword(s):  
Numerical Solutions ◽  
Excitation Frequency ◽  
Dynamics Analysis ◽  
Periodic Motions ◽  
Lumped Model ◽  
Sawtooth Wave ◽  
Piezoelectric Beam ◽  
Period 2 ◽  
Mass Spring ◽  
The Impact

In this work, an impact based frequency up-conversion mechanism is studied via discontinuous dynamics analysis. The mechanism consists of a moving stopper and a piezoelectric beam. The repeated free vibration of the piezoelectric beam achieved through the impaction between the stopper and the beam, With the stopper excited by a sawtooth wave. Due to the impact, the system contains complex discontinuous dynamics, hence to better understand the energy harvesting performance of the piezoelectric beam, we seek the simple periodic motions of the system. As the system parameter varies, the output voltage and power of the piezoelectric beam with periodic motions is obtained. These results were also compared with those obtained when the piezoelectric beam is directly subjected to the same sawtooth wave. The piezoelectric beam was modeled as a mass-spring-damper system, and the linear piezoelectric constitutive equations have been used to obtain the lumped model of the piezoelectric beam. In this study, numerical solutions of the generated power and voltage were obtained via discontinuous dynamics analysis. When the excitation frequency is low, the effect of frequency-up-conversion is demonstrated by comparing the generated power of two cases: piezoelectric beam excited via impact and beam directly subject to the sawtooth wave. The stable and unstable periodic motions and bifurcation trees of the impact parameters are predicted analytically versus varying excitation frequency for period-1 and period-2.

Stability of Sliding in a System Excited by a Rough Moving Surface

1997 ◽  
Vol 119 (4) ◽  
pp. 672-680 ◽  
Author(s):  
E. J. Berger ◽  
C. M. Krousgrill ◽  
F. Sadeghi
Keyword(s):  
Parametric Resonance ◽  
Normal Force ◽  
Surface Velocity ◽  
Force System ◽  
Periodic Surface ◽  
Linearized System ◽  
Friction Curve ◽  
The Stability ◽  
Small Periodic ◽  
Harmonic Resonance

A two-degree-of-freedom translational system has been developed to study the influence of normal force oscillations on the stability of the steady sliding position. Excited by a small, periodic surface roughness, the normal and tangential motion are coupled through a velocity-dependent friction law. The linearized system has been examined using the first-order averaging technique of Krylov and Boguliubov. In addition to the primary forced resonance, a 2:1 parametric resonance and a 1/2 sub-harmonic resonance have been encountered. Arising from velocity-dependent coupling of the normal and tangential modes and the periodic normal force variations, the parametric resonance has been found to produce locally unstable responses in some cases. Conditions for the stability of the local response based upon local friction curve slope, static normal force, system damping, and surface velocity have been derived for a broad range of frequency.

scholarly journals Application of Input–State of the System Transformation for Linearization of Selected Electrical Circuits

2016 ◽  
Vol 67 (3) ◽  
pp. 199-205 ◽  
Author(s):  
Andrzej Zawadzki ◽  
Sebastian Różowicz
Keyword(s):  
Nonlinear System ◽  
Feedback Loop ◽  
Numerical Solutions ◽  
Necessary Conditions ◽  
Electric Circuit ◽  
Input State ◽  
System Transformation ◽  
State Equations ◽  
Local Diffeomorphism ◽  
Linearized System

Abstract The paper presents a transformation of nonlinear electric circuit into linear one through changing coordinates (local diffeomorphism) with the use of closed feedback loop. The necessary conditions that must be fulfilled by nonlinear system to enable carrying out linearizing procedures are presented. Numerical solutions of state equations for the nonlinear system and equivalent linearized system are included.

Mesoscopic fabric models using a discrete mass-spring approach: Yarn-yarn interactions analysis

2005 ◽  
Vol 40 (22) ◽  
pp. 5925-5932 ◽  
Author(s):  
Bilel Ben Boubaker ◽  
Bernard Haussy ◽  
Jean-Francois Ganghoffer
Keyword(s):  
Mass Spring ◽  
Discrete Mass

ESTIMATION OF DYNAMIC SYSTEM'S EXCITATION FORCES BY THE INDEPENDENT COMPONENT ANALYSIS

2012 ◽  
Vol 04 (03) ◽  
pp. 1250032 ◽  
Author(s):  
ALI AKROUT ◽  
DHOUHA TOUNSI ◽  
MOHAMED TAKTAK ◽  
MOHAMED SLIM ABBÈS ◽  
MOHAMED HADDAR
Keyword(s):  
Independent Component Analysis ◽  
Numerical Procedure ◽  
Component Analysis ◽  
Independent Component ◽  
Dynamic Responses ◽  
Statistical Criterion ◽  
Mass Spring ◽  
Discrete Mass ◽  
Signal Sources ◽  
Good Agreement

This paper deals with a numerical investigation for the estimation of dynamic system's excitation sources using the independent component analysis (ICA). In fact, the ICA concept is an important technique of the blind source separation (BSS) method. In this case, only the dynamic responses of a given mechanical system are supposed to be known. Thus, the main difficulty of such problem resides in the existence of any information about the excitation forces. For this purpose, the ICA concept, which consists on optimizing a fourth-order statistical criterion, can be highlighted. Hence, a numerical procedure based on the signal sources independency in the ICA concept is developed. In this work, the analytical or the finite element (FE) dynamic responses are calculated and exploited in order to identify the excitation forces applied on discrete (mass-spring) and continuous (beam) systems. Then, estimated results obtained by the ICA concept are presented and compared to those achieved analytically or by the FE and the modal recombination methods. Since a good agreement is obtained, this approach can be used when the vibratory responses of a dynamic system are obtained through sensor's measurements.

Sign in / Sign up

Export Citation Format

Share Document