Nonlinear vibrations and stability analysis of a rotor on high-static-low-dynamic-stiffness supports using method of multiple scales

2017 ◽  
Vol 63 ◽  
pp. 259-265 ◽  
Author(s):  
H.M. Navazi ◽  
M. Hojjati
Keyword(s):  
Stability Analysis ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Dynamic Stiffness

Primary Resonance of the Current-Carrying Beam in Thermal-Magneto-Elasticity Field

2010 ◽  
Vol 29-32 ◽  
pp. 16-21 ◽  
Author(s):  
Xiao Yan Xi ◽  
Zhian Yang ◽  
Li Li Meng ◽  
Chang Jian Zhu
Keyword(s):  
Response Curve ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Primary Resonance ◽  
Response Curves ◽  
Bending Vibration ◽  
Approximation Solution ◽  
System Parameters ◽  
Practical Engineering

On base of the electro-magneto-elastic theory and the theory of the bending vibration of the electric beam, nonlinear vibration equation of current-carrying beam subjected to thermal-magneto-elasticity field is studied. The Lorentz force and thermal force on the beam are derived. According to the method of multiple scales for nonlinear vibrations the approximation solution of the primary resonance of the system is obtained. Numerical analysis results show that the amplitude changed with the system parameters. With the decrease of magnetic intensity, the amplitude increases rapidly. The response curve occurs bending phenomenon and soft features is increased gradually. Increasing current, the amplitudes increase. With the decrease of temperature, the peak of response curves decrease. With the increase of temperature, natural frequency decreased. It is useful in practical engineering.

Nonlinear Vibrations of a Beam-Spring-Mass System

1994 ◽  
Vol 116 (4) ◽  
pp. 433-439 ◽  
Author(s):  
M. Pakdemirli ◽  
A. H. Nayfeh
Keyword(s):  
Nonlinear Response ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Nonlinear Partial Differential Equations ◽  
Primary Resonance ◽  
Fast Time ◽  
Lagrange Equations ◽  
Response Curves ◽  
Mass System

The nonlinear response of a simply supported beam with an attached spring-mass system to a primary resonance is investigated, taking into account the effects of beam midplane stretching and damping. The spring-mass system has also a cubic nonlinearity. The response is found by using two different perturbation approaches. In the first approach, the method of multiple scales is applied directly to the nonlinear partial differential equations and boundary conditions. In the second approach, the Lagrangian is averaged over the fast time scale, and then the equations governing the modulation of the amplitude and phase are obtained as the Euler-Lagrange equations of the averaged Lagrangian. It is shown that the frequency-response and force-response curves depend on the midplane stretching and the parameters of the spring-mass system. The relative importance of these effects depends on the parameters and location of the spring-mass system.

Saturation and Its Application in the Vibration Control of Nonlinear Systems

Volume 2 ◽  
2004 ◽  
Author(s):  
Mohammad Shoeybi ◽  
Mehrdaad Ghorashi
Keyword(s):  
Singular Point ◽  
Degrees Of Freedom ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Approximate Solutions ◽  
Stability Of Solutions ◽  
Nonlinear Controller ◽  
Point Analysis ◽  
Good Agreement

An investigation on the nonlinear vibrations of a system with two degrees of freedom when subjected to saturation is presented. The method is especially applied to a system that consists of a DC motor with a nonlinear controller and subjected to a harmonic forcing voltage. Approximate solutions are sought using the method of multiple scales. Also, singular point analysis is used to study stability of solutions. These findings are then compared with the corresponding numerical results. Good agreement between the two is observed.

1/3 Subharmonic Resonance of the Electro-Conductive Beam in Thermal-Magneto-Elasticity Field

2012 ◽  
Vol 466-467 ◽  
pp. 814-818 ◽  
Author(s):  
Xiao Yan Xi ◽  
Zhian Yang ◽  
Gao Feng Li
Keyword(s):  
Numerical Analysis ◽  
Nonlinear Vibration ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Subharmonic Resonance ◽  
Bending Vibration ◽  
Approximation Solution ◽  
Vibration Equation ◽  
System Parameters

Based on the electro-magneto-elastic theory and the theory of the bending vibration of the electric beam, nonlinear vibration equation of current-carrying beam in thermal-magneto-elasticity field is studied. The Lorentz force and thermal force on the beam are derived. According to the method of multiple scales for nonlinear vibrations the approximation solution of 1/3 subharmonic resonance of the system is obtained. Numerical analysis results show that the amplitude changed with the system parameters.

Nonlinear Flexural Vibrations of Unshearable Elastic Rings

2013 ◽  
Author(s):  
Walter Lacarbonara ◽  
Andrea Arena ◽  
Stuart S. Antman
Keyword(s):  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Equations Of Motion ◽  
Cosserat Theory ◽  
Flexural Mode ◽  
Curved Rods ◽  
Deformation Modes ◽  
Nonlinear Motions ◽  
Planar Motions

Refined theories are employed to study nonlinear vibrations of elastic rings in the mth flexural mode away from autoparametric resonances involving other flexural modes. A top-down modeling approach is followed to describe the rings undergoing all deformation modes in space by the Special Cosserat theory of curved rods. The specialization to extensional-flexural-shearing, then to extensional-flexural, and finally to purely flexural planar motions is illustrated. Free undamped extensional-flexural nonlinear motions involving the mth mode and its companion mode are investigated via a direct asymptotic approach based on the method of multiple scales applied to the geometrically exact equations of motion and it is shown that these motions are softening for linearly elastic rings while there are thresholds in the constitutive laws separating softening from hardening behaviors.

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

scholarly journals Dynamic analysis of a parametrically excited golden Muga silk embedded pneumatic artificial muscle

2018 ◽  
Vol 211 ◽  
pp. 02008 ◽  
Author(s):  
Bhaben Kalita ◽  
S. K. Dwivedy
Keyword(s):  
Dynamic Analysis ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Quadratic Function ◽  
Artificial Muscle ◽  
Equation Of Motion ◽  
Time Response ◽  
Phase Portraits ◽  
Pneumatic Artificial Muscle ◽  
Pneumatic Muscle

In this work a novel pneumatic artificial muscle is fabricated using golden muga silk and silicon rubber. It is assumed that the muscle force is a quadratic function of pressure. Here a single degree of freedom system is considered where a mass is supported by a spring-damper-and pneumatically actuated muscle. While the spring-mass damper is a passive system, the addition of pneumatic muscle makes the system active. The dynamic analysis of this system is carried out by developing the equation of motion which contains multi-frequency excitations with both forced and parametric excitations. Using method of multiple scales the reduced equations are developed for simple and principal parametric resonance conditions. The time response obtained using method of multiple scales have been compared with those obtained by solving the original equation of motion numerically. Using both time response and phase portraits, variation of few systems parameters have been carried out. This work may find application in developing wearable device and robotic device for rehabilitation purpose.

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