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.

The Steady-State Response of the Double Bilinear Hysteretic Model

1965 ◽  
Vol 32 (4) ◽  
pp. 921-925 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
Steady State Solution ◽  
Degree Of Freedom ◽  
State Solution ◽  
Steady State Response ◽  
Hysteretic Model ◽  
Jump Phenomenon ◽  
State Response ◽  
The Stability

The steady-state response of a one-degree-of-freedom double bilinear hysteretic model is investigated and it is shown that this model gives rise to the jump phenomenon which is associated with certain nonlinear systems. The stability of the steady-state solution is discussed and it is shown that the model predicts an unbounded resonance for finite excitation.

Analytical Method of Response of Piping System With Nonlinear Support

2000 ◽  
Vol 122 (4) ◽  
pp. 437-442
Author(s):  
Shigeru Aoki ◽  
Takeshi Watanabe
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Analytical Method ◽  
Mode Shapes ◽  
Piping System ◽  
Steady State Response ◽  
Response Curves ◽  
State Response ◽  
Damping Characteristics ◽  
Nonlinear Support

This paper deals with steady-state response of the piping system with nonlinear support having hysteresis damping characteristics. Considering the energy loss for contact with a support, an analytical method of approximate solution for the beam, a one-span model of the piping system, with quadrilateral hysteresis loop characteristics is presented. Some numerical results of the approximate solution for the response curves and the mode shapes are shown. [S0094-9930(00)00204-3]

Forced Response of Continuous System With Hysteresis Loop Characteristics: System With Quadrilateral Hysteresis Loop Characteristics

2005 ◽  
Author(s):  
Shigeru Aoki ◽  
Takeshi Watanabe
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Energy Loss ◽  
Hysteresis Loop ◽  
Nonlinear Response ◽  
Continuous System ◽  
Forced Response ◽  
Steady State Response ◽  
State Response ◽  
Discontinuous Line

This paper deals with steady-state response of a continuous system with collision characteristics. Considering the energy loss in a collision, an analytical method of approximate solution for the continuous system with symmetrical hysteresis loop characteristics is presented. The resonance curves of nonlinear response obtained from approximate solution are shown as discontinuous line, and are discussed the phenomenon.

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.

Stability Analysis and Complex Dynamics of a Gear-Pair System Supported by a Squeeze Film Damper

1997 ◽  
Vol 119 (1) ◽  
pp. 85-88 ◽  
Author(s):  
Chin-Shong Chen ◽  
S. Natsiavas ◽  
H. D. Nelson
Keyword(s):  
Steady State ◽  
Periodic Solutions ◽  
Squeeze Film ◽  
Time Behavior ◽  
Steady State Response ◽  
Squeeze Film Damper ◽  
State Response ◽  
Mass Unbalance ◽  
Periodic Steady State ◽  
The Stability

The stability properties of periodic steady state response of a nonlinear geared rotordynamic system are investigated. The nonlinearity arises because one support of the system includes a cavitated squeeze film damper, while the excitation is caused by mass unbalance. The dynamical model and the procedure which leads to periodic steady state response of the system examined have been developed in an earlier paper. Here, the emphasis is placed on analyzing the stability characteristics of located periodic solutions. Also, within ranges of the excitation frequency where no stable periodic solutions are detected, the long time behavior of the system is investigated by direct integration of the equations of motion. It is shown that large order subharmonic, quasiperiodic and chaotic motions may coexist with unstable periodic response in these frequency ranges. Finally, attention is focused on practical consequences of these motions.

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.

Steady-State Response of a Trilinear Hysteretic System

2011 ◽  
Vol 4 (3) ◽  
pp. 1137-1142
Author(s):  
Jiduo Jin ◽  
Yufei Zhang ◽  
Xiaodong Yang
Keyword(s):  
Steady State ◽  
Steady State Response ◽  
Hysteretic System ◽  
State Response

scholarly journals An Evaluation of the Fixed Point Method of Vibration Analysis for a Particular System With Initial Damping

1963 ◽  
Vol 85 (3) ◽  
pp. 233-236 ◽  
Author(s):  
D. B. Bogy ◽  
P. R. Paslay
Keyword(s):  
Steady State ◽  
Approximate Method ◽  
Fixed Point Method ◽  
Steady State Response ◽  
Vibratory System ◽  
State Response ◽  
System Use ◽  
Two Degree Of Freedom ◽  
Maximum Steady State

The maximum steady-state response of a particular linear damped two-degree-of-freedom vibratory system is minimized by determining the optimum damping constant for a single damper. This is accomplished by both a well-known approximate method and by an exact numerical method. Since the approximate method does not take into account the damping which is initially in the system, attention in this analysis is directed to determining the influence of the initial damping on the optimum value for the single damper. In order to make direct comparison of the methods, a system was chosen in which an exact numerical determination of the optimum damping was possible. The results of the investigation show for the particular case considered that, although the value of the damping constant for the optimum damper increases considerably as initial damping is included in the system, use of the value obtained for the initially undamped case would give values of the maximum steady-state response within 10 percent of the optimized value for the range of initial damping commonly encountered.

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