The Steady State Response of Systems With Hardening Hysteresis

1978 ◽  
Vol 100 (1) ◽  
pp. 193-198 ◽  
Author(s):  
R. K. Miller
Keyword(s):  
Steady State ◽  
Degree Of Freedom ◽  
General Nature ◽  
Model Parameters ◽  
Steady State Response ◽  
Single Degree Of Freedom ◽  
Analytical Technique ◽  
State Response ◽  
Single Degree ◽  
Critical Model

A physical model for hardening hysteresis is presented. An approximate analytical technique is used to determine the steady-state response of a single-degree-of-freedom system and a multi-degree-of-freedom system incorporating this model. Certain critical model parameters which determine the general nature of the responses are identified.

Predictions of the Periodic Response of a Single-Degree-of-Freedom Foam-Mass System by Using Incremental Harmonic Balance

2012 ◽  
Author(s):  
Yousof Azizi ◽  
Patricia Davies ◽  
Anil K. Bajaj
Keyword(s):  
Steady State ◽  
Harmonic Balance ◽  
Driving Frequency ◽  
Steady State Response ◽  
Base Excitation ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
State Response ◽  
Single Degree ◽  
Incremental Harmonic Balance

Vehicle occupants are exposed to low frequency vibration that can cause fatigue, lower back pain, spine injuries. Therefore, understanding the behavior of a seat-occupant system is important in order to minimize these undesirable vibrations. The properties of seating foam affect the response of the occupant, so there is a need for good models of seat-occupant systems through which the effects of foam properties on the dynamic response can be directly evaluated. In order to understand the role of flexible polyurethane foam in characterizing the complex seat-occupant system behavior better, the response of a single-degree-of-freedom foam-mass system, which is the simplest model representing a seat-occupant system, is studied. The incremental harmonic balance method is used to determine the steady-state behavior of the foam-mass system subjected to sinusoidal base excitation. This method is used to reduce the time required to generate the steady-state response at the driving frequency and at harmonics of the driving frequency from that required when using direct time-integration of the governing equations to determine the steady state response. Using this method, the effects of different viscoelastic models, riding masses, base excitation levels and damping coefficients on the response are investigated.

Reduction of Harmonic Response of Cylindrical Shells

1975 ◽  
Vol 97 (4) ◽  
pp. 1371-1377 ◽  
Author(s):  
G. B. Warburton
Keyword(s):  
Cantilever Beams ◽  
Steady State Response ◽  
Optimum Conditions ◽  
Harmonic Force ◽  
Shell Surface ◽  
Single Degree Of Freedom ◽  
Harmonic Response ◽  
State Response ◽  
Single Degree ◽  
Mode Method

The normal mode method is used to investigate the reduction in the steady-state response of a simply supported cylindrical shell when conventional absorbers are attached to the shell. Two types of excitation are considered: (a) a single radial harmonic force, and (b) a harmonic pressure distributed over the shell surface. The effect upon response of varying the absorber parameters is studied. Optimum conditions for specific cases are obtained and compared with those required to minimize response when absorbers are added to cantilever beams and to the classical single degree of freedom system.

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

2010 ◽  
Vol 65 (5) ◽  
pp. 357-368 ◽  
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

Dynamic Response of Eccentric Face Seals to Synchronous Shaft Whirl

2004 ◽  
Vol 126 (2) ◽  
pp. 301-309 ◽  
Author(s):  
J. Wileman
Keyword(s):  
Steady State ◽  
Dynamic Response ◽  
Solution Technique ◽  
Steady State Response ◽  
Analytical Technique ◽  
State Response ◽  
Flexible Supports ◽  
Simple Matrix ◽  
The Stability ◽  
Degenerate Cases

This work provides an analytical technique for computing the seal face misalignment which results from synchronous whirl of the shaft. The eccentric dynamic response is obtained for seals in which both mating faces are mounted on flexible supports. Responses for seals with a single flexibly mounted stator or rotor are also obtained as degenerate cases of the more general result. Synchronous shaft whirl is shown to have a significant effect on the steady-state response of all these seals, while not affecting the stability threshold. The steady-state response is obtained by solution of a simple matrix equation for the general case, and can be obtained in closed form for the degenerate cases of the flexibly mounted stator or flexibly mounted rotor. A numerical example of the solution technique is presented, and the influence of speed is examined. Extension of the method to shaft motions other than synchronous whirl is briefly discussed.

Probabilistic Analysis and Design of a MEMS Re-Entry Switch

2005 ◽  
Author(s):  
R. V. Field ◽  
S. Reese
Keyword(s):  
Probabilistic Analysis ◽  
Random Variables ◽  
Degree Of Freedom ◽  
Model Parameters ◽  
Rigid Barrier ◽  
Single Degree Of Freedom ◽  
Analysis And Design ◽  
Mems Switch ◽  
Single Degree ◽  
System A

The probabilistic analysis and design of a MEMS switch during atmospheric re-entry is discussed. The switch is modeled as a classical vibro-impact system: a single degree-of-freedom oscillator subject to impact with a single rigid barrier. The excitation is assumed stationary, Gaussian, with prescribed PSD to represent the re-entry environment. A subset of the model parameters are described as random variables to represent the significant unit-to-unit variability observed during fabrication and testing of the device. The metric of performance is the amount of time the switch remains closed during the re-entry event.

The Steady-State Response of a Two-Degree-of-Freedom Bilinear Hysteretic System

1965 ◽  
Vol 32 (1) ◽  
pp. 151-156 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Degree Of Freedom ◽  
Finite Limit ◽  
Steady State Response ◽  
Varying Parameters ◽  
Hysteretic System ◽  
State Response ◽  
The Stability ◽  
Two Degree Of Freedom

The method of slowly varying parameters is used to obtain an approximate solution for the steady-state response of a two-degree-of-freedom bilinear hysteretic system. The stability of the system is investigated and it is shown that such a system exhibits unbounded amplitude resonance when the level of excitation is increased beyond a certain finite limit.

Forced Vibrations of a Single-Degree-of-Freedom System With Coulomb Bearing Friction

1969 ◽  
Vol 36 (4) ◽  
pp. 871-873 ◽  
Author(s):  
E. V. Wilms
Keyword(s):  
Coulomb Friction ◽  
Degree Of Freedom ◽  
Half Cycle ◽  
Piecewise Linearization ◽  
Single Degree Of Freedom ◽  
State Response ◽  
Single Degree ◽  
Forcing Function ◽  
Bearing Friction

The equation of motion of a single-degree-of-freedom mechanical system with Coulomb friction acting at two bearings is derived. The equation is nonlinear, but may be solved by piecewise linearization. For the case of transient oscillations, the amplitude decreases by a constant ratio every half cycle and, in this respect, the behavior resembles that of viscous damping rather than the type of Coulomb damping which has previously been investigated. The steady-state response with a forcing function is determined for the case of small damping. In addition to the amplitude and phase angle of the motion, a solution requires the determination of a second angle which defines the linearized regions.

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