The Response of Nonlinear Single-Degree-of-Freedom Systems to Modulated High-Frequency Input

In this paper we study the response of single-degree-of-freedom with cubic, quartic and quintic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contains frequencies much lower than the carrier frequency of the excitation. The method of multiple scales is used to derive two coupled first-order ordinary differential equations that describe the evolution of the amplitude and phase with damping, nonlinearities and resonances. The evolution equations are used to determine the steady-state motions, while representative frequency-response curves are presented for each resonance. Stability analysis of the amplitude and phase modulation equations for both cases are performed. The bending of the response curves leads to multi-valued solutions and hence to jump phenomena.

Download Full-text

The Response of Nonlinear Systems to Modulated High-Frequency Input

14th Biennial Conference on Mechanical Vibration and Noise: Dynamics and Vibration of Time-Varying Systems and Structures ◽

10.1115/detc1993-0130 ◽

1993 ◽

Author(s):

S. A. Nayfeh ◽

A. H. Nayfeh

Keyword(s):

Nonlinear Systems ◽

Natural Frequency ◽

Amplitude Modulation ◽

Carrier Frequency ◽

High Frequency ◽

Degree Of Freedom ◽

Resonant Excitation ◽

Single Degree Of Freedom ◽

Single Degree ◽

Different Types

Abstract We study the response of a single-degree-of-freedom system with cubic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contain frequencies much lower than the carrier frequency of the excitation. We apply the theory to different types of amplitude modulation and find that resonant excitation of the system may occur under some conditions.

Download Full-text

Approximate Gaussian representation of evolution equations I. Single degree of freedom nonlinear equations

Journal of Statistical Physics ◽

10.1007/bf01009681 ◽

1983 ◽

Vol 30 (3) ◽

pp. 633-648 ◽

Cited By ~ 14

Author(s):

Bruce J. West ◽

Galina Rovner ◽

Katja Lindenberg

Keyword(s):

Nonlinear Equations ◽

Evolution Equations ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Single Degree ◽

Gaussian Representation

Download Full-text

Resonances of a Nonlinear Single-Degree-of-Freedom System with Time Delay in Linear Feedback Control

Zeitschrift für Naturforschung A ◽

10.1515/zna-2010-0501 ◽

2010 ◽

Vol 65 (5) ◽

pp. 357-368 ◽

Cited By ~ 1

Author(s):

Atef F. El-Bassiouny ◽

Salah El-Kholy

Keyword(s):

Steady State ◽

Time Delay ◽

Feedback Control ◽

Fixed Points ◽

Multiple Scales ◽

Degree Of Freedom ◽

Linear Feedback ◽

Single Degree Of Freedom ◽

Single Degree ◽

Subharmonic Resonances

The primary and subharmonic resonances of a nonlinear single-degree-of-freedom system under feedback control with a time delay are studied by means of an asymptotic perturbation technique. Both external (forcing) and parametric excitations are included. By means of the averaging method and multiple scales method, two slow-flow equations for the amplitude and phase of the primary and subharmonic resonances and all other parameters are obtained. The steady state (fixed points) corresponding to a periodic motion of the starting system is investigated and frequency-response curves are shown. The stability of the fixed points is examined using the variational method. The effect of the feedback gains, the time-delay, the coefficient of cubic term, and the coefficients of external and parametric excitations on the steady-state responses are investigated and the results are presented as plots of the steady-state response amplitude versus the detuning parameter. The results obtained by two methods are in excellent agreement

Download Full-text

Equivalent Linkages and Dead Center Positions of Planar Single-Degree-of-Freedom Complex Linkages

Journal of Mechanisms and Robotics ◽

10.1115/1.4029187 ◽

2015 ◽

Vol 7 (4) ◽

Cited By ~ 3

Author(s):

Jun Wang ◽

Kwun-Lon Ting ◽

Daxing Zhao

Keyword(s):

General Concept ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

First Order ◽

Single Degree ◽

Kinematic Loops ◽

The Dead ◽

Planar Linkages ◽

Four Bar Linkage ◽

First Time

This paper proposes a simple and general approach for the identification of the dead center positions of single-degree-of-freedom (DOF) complex planar linkages. This approach is implemented through the first order equivalent four-bar linkages. The first order kinematic properties of a complex planar linkage can be represented by their instant centers. The condition for the occurrence of a dead center position of a single-DOF planar linkage can be designated as when the three passive instantaneous joints of any equivalent four-bar linkage become collinear. By this way, the condition for the complex linkage at the dead center positions can be easily obtained. The proposed method is a general concept and can be systematically applied to analyze the dead center positions for more complex single-DOF planar linkages regardless of the number of kinematic loops or the type of the kinematic pairs involved. The velocity method for the dead center analysis is also used to verify the results. The proposed method extends the application of equivalent linkage and is presented for the first time. It paves a novel and straightforward way to analyze the dead center positions for single-DOF complex planar linkages. Examples of some complex planar linkages are employed to illustrate this method in this paper.

Download Full-text