The Response of Nonlinear Systems to Modulated High-Frequency Input

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.

Demonstrator to show the effects of negative stiffness on the natural frequency of a simple oscillator

2008 ◽  
Vol 222 (7) ◽  
pp. 1189-1192 ◽  
Author(s):  
A Carrella ◽  
M J Brennan ◽  
T P Waters
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Degree Of Freedom ◽  
Negative Stiffness ◽  
Test Rig ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Horizontal Beam ◽  
Additional Correction

This article describes a demonstrator to show the effects of negative stiffness on the free vibration of a simple oscillator. The test rig consists of a horizontal beam that is hinged at one end and is supported by two coil springs to form a single-degree-of-freedom system. Additional correction springs, which provide negative stiffness, can be attached to lower the natural frequency of the system. The effect of the change in natural frequency can be easily seen visually, and it is shown that for one of the configurations of correction springs, the natural frequency can be reduced by a factor of about 4.

The Virtual Cam – Hexagon Method Authentication on Locating Key Instant Centers of All Planar Single Degree of Freedom Kinematically Indeterminate Linkages up to Ten-Bar

2018 ◽  
Author(s):  
Zhengqi Liu ◽  
Yin-ping Chang
Keyword(s):  
Degree Of Freedom ◽  
Universal Method ◽  
Single Degree Of Freedom ◽  
Graphical Approach ◽  
Single Degree ◽  
Wide Range ◽  
Different Types ◽  
Limited Application ◽  
Complete Sets ◽  
Improved Technique

At this moment all the methods which had been proposed have extremely limited application to only several specific constructions of kinematically indeterminate linkages, i.e. their complete sets of instant centers cannot be obtained simply from Kennedy Theorem due to lack of enough four-bar loop information in their constructions. Planar single degree of freedom linkages up to ten-bar include two different types of mechanisms, i.e. pure bar linkages, such as four-, six-, eight-, and ten-bar; and geared-bar linkages, i.e. geared-five, seven, and nine-bar. The huge varieties of different types and constructions can serve as great testbeds for these methods. This research systematically investigates and modifies the graphical approach, i.e. virtual cam method, whose employment will show it to be an almost-universal method which can be compliantly applied on very wide range of kinematically indeterminate linkages. The procedures and criteria of the methodology are proposed and examined thoroughly to help locate key instant centers of all planar single degree of freedom kinematically indeterminate linkages up to ten-bar so that their complete sets of instant centers can be located successfully. We call this modified and improved technique as Virtual Cam – Hexagon Method. The results are verified carefully against traditional Kennedy Theorem approach and CAD modeling.

Effectiveness of neoprene pad vibration isolators at high frequencies

2021 ◽  
Vol 263 (4) ◽  
pp. 2172-2183
Author(s):  
Jerry Lilly
Keyword(s):  
Natural Frequency ◽  
Insertion Loss ◽  
Dynamic Stiffness ◽  
Degree Of Freedom ◽  
Frequency Wave ◽  
Single Degree Of Freedom ◽  
High Frequencies ◽  
Vibration Isolators ◽  
Single Degree ◽  
Wide Range

The natural frequency, dynamic stiffness, and insertion loss of commercially available neoprene pad vibration isolators have been measured in a simple, single degree of freedom system over a wide range of pad loadings out to a maximum frequency of 10 kHz. The results reveal that dynamic stiffness can vary significantly with pad loading as well as the durometer of the material. It will also be shown that insertion loss follows the theoretical single degree of freedom curve only out to a frequency that is about 5 to 10 times the natural frequency, depending upon the pad durometer rating. Above that frequency wave resonances in the material cause the insertion loss to deteriorate significantly out to a frequency near 1 kHz, above which the insertion loss maintains a relatively constant value, again depending upon the pad durometer rating. In some instances the insertion loss values can approach 0 dB or even become negative at specific frequencies in the frequency region that is 10 to 20 times the natural frequency of the system.

Detection of Improper General Spatial Kinematic Chains With Different Types of Pairs

1994 ◽  
Author(s):  
Xian-Wen Kong ◽  
Ting-Li Yang
Keyword(s):  
Unsolved Problem ◽  
Degree Of Freedom ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Single Degree ◽  
Different Types ◽  
Necessary And Sufficient ◽  
Topological Synthesis

Abstract Improper general spatial kinematic chains (GSKCs) due to the effect of pair types may be generated during the process of topological synthesis of GSKCs with different types of pairs. Thus, detection of improper GSKCs is necessary in topological synthesis of GSKCs with different types of pairs. Unfortunately, it is still an unsolved problem. In this paper, a method for detecting improper GSKCs is presented. Both a necessary and sufficient condition and a sufficient condition for proper GSKCs with R, P, H, T and C pairs are introduced at first. Based on these two conditions, an algorithm to detect improper GSKCs is then developed which is very efficient and suitable for topological synthesis of GSKCs with R, P, H, T and C pairs. The proposed algorithm has been applied to topological synthesis of 1- and 2-loop, single degree of freedom GSKCs with R, P, H, T and C pairs and the corresponding atlas is obtained.

Effect of Waveform on the Effectiveness of Tangential Dither Forces to Cancel Friction-Induced Oscillations

2005 ◽  
Author(s):  
Michael A. Michaux ◽  
Aldo A. Ferri ◽  
Kenneth A. Cunefare
Keyword(s):  
Numerical Integration ◽  
High Frequency ◽  
Frictional Contact ◽  
Degree Of Freedom ◽  
System Response ◽  
Periodic Signal ◽  
Method Of Averaging ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree

High-frequency dither forces are often used to reduce unwanted vibration in frictional systems. This paper examines how the effectiveness of these dither-cancellation techniques is influenced by the type of periodic signal employed. The paper uses the method of averaging as well as numerical integration to study a single-degree-of-freedom (SDOF) system consisting of a mass in frictional contact with a translating surface. Recently, it was found that sinusoidal dither forces had the ability to stabilize or destabilize such a system, depending on the system and frictional characteristics as well as the amplitude and frequency of the dither signal [1]. This paper extends this analysis to general, periodic dither forces. In particular, the system response for sinusoidal dither waveforms is compared to that of triangular dither waveforms and square dither waveforms. It is found that, for a given amplitude and frequency of the dither signal, square waveforms are much more effective in canceling friction-induced oscillations than sinusoidal dither; likewise, sinusoidal waveforms are more effective than triangular waveforms for a given amplitude and frequency. A criterion is developed that relates the effectiveness of the waveform to the properties of the integral of the dither signal.

On the Use of Clearance in Viscous Dampers to Limit High Frequency Force Transmission

1961 ◽  
Vol 83 (1) ◽  
pp. 50-52 ◽  
Author(s):  
M. E. Gurtin
Keyword(s):  
Steady State ◽  
High Frequency ◽  
Degree Of Freedom ◽  
Viscous Damper ◽  
Force Transmission ◽  
Viscous Dampers ◽  
Single Degree Of Freedom ◽  
High Frequencies ◽  
Single Degree ◽  
Damped System

The steady-state vibration of a single degree of freedom system with clearance in the viscous damper is investigated. The results show that the clearance damper combines the low resonant force transmission feature of the viscous damped system and the characteristic of low force transmission at high frequencies of the undamped system.

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

2006 ◽  
Vol 61 (10-11) ◽  
pp. 541-555
Author(s):  
Atef F. El-Bassiouny
Keyword(s):  
Carrier Frequency ◽  
Phase Modulation ◽  
Evolution Equations ◽  
Multiple Scales ◽  
Degree Of Freedom ◽  
Response Curves ◽  
Single Degree Of Freedom ◽  
First Order ◽  
Single Degree ◽  
Jump Phenomena

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.

The Effect of Circumferential Aerodynamic Detuning on Coupled Bending-Torsion Unstalled Supersonic Flutter

1986 ◽  
Vol 108 (2) ◽  
pp. 253-260 ◽  
Author(s):  
D. Hoyniak ◽  
S. Fleeter
Keyword(s):  
Stability Analysis ◽  
Natural Frequency ◽  
Frequency Ratio ◽  
Center Of Gravity ◽  
Degree Of Freedom ◽  
Mode Analysis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Unsteady Aerodynamic ◽  
Supersonic Flutter

A mathematical model is developed to predict the enhanced coupled bending-torsion unstalled supersonic flutter stability due to alternate circumferential spacing aerodynamic detuning of a turbomachine rotor. The translational and torsional unsteady aerodynamic coefficients are developed in terms of influence coefficients, with the coupled bending-torsion stability analysis developed by considering the coupled equations of motion together with the unsteady aerodynamic loading. The effect of this aerodynamic detuning on coupled bending-torsion unstalled supersonic flutter as well as the verification of the modeling are then demonstrated by considering an unstable twelve-bladed rotor, with Verdon’s uniformly spaced Cascade B flow geometry as a baseline. It was found that with the elastic axis and center of gravity at or forward of the airfoil midchord, 10 percent aerodynamic detuning results in a lower critical reduced frequency value as compared to the baseline rotor, thereby demonstrating the aerodynamic detuning stability enhancement. However, with the elastic axis and center of gravity at 60 percent of the chord, this type of aerodynamic detuning has a minimal effect on stability. For both uniform and nonuniform circumferentially spaced rotors, a single degree of freedom torsion mode analysis was shown to be appropriate for values of the bending-torsion natural frequency ratio lower than 0.6 and higher than 1.2. However, for values of this natural frequency ratio between 0.6 and 1.2, a coupled flutter stability analysis is required. When the elastic axis and center of gravity are not coincident, the effect of detuning on cascade stability was found to be very sensitive to the location of the center of gravity with respect to the elastic axis. In addition, it was determined that when the center of gravity was forward of an elastic axis located at midchord, a single degree of freedom torsion model did not accurately predict cascade stability.

Aspects of creep buckling II. The effects of small deflexion approximations on predicted behaviour

1978 ◽  
Vol 364 (1718) ◽  
pp. 415-433 ◽  
Keyword(s):  
Constant Load ◽  
Buckling Analysis ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Creep Buckling ◽  
Different Types ◽  
Post Buckling

In creep buckling analysis, small deflexion approximations generally influence the calculated displacement‒time relations and may also result in the prediction of different phenomena from those indicated by exact analyses. Part II examines the nature of these approximations and the effects of using them. As in Part I, much significance is attached to the link between a structure’s creep buckling behaviour at constant load and its instantaneous buckling and post-buckling behaviour under varying load. Analyses of simple single degree of freedom models are used for illustration. Some general conclusions are drawn which permit a better understanding of the relationships between the different types of analysis that have been used in previous creep buckling studies.

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