Challenges in Exact Response of Piecewise Linear Vibration Isolator

2014 ◽  
pp. 59-79 ◽  
Author(s):  
Oleksandr Pogorilyi ◽  
Reza N. Jazar ◽  
Pavel M. Trivailo
Keyword(s):  
Piecewise Linear ◽  
Vibration Isolator ◽  
Linear Vibration

Sensitivity of Jump Avoidance Condition of Piecewise Linear Vibration Isolator to Dynamical Parameters

2005 ◽  
Author(s):  
Sagar Deshpande ◽  
Sudhir Mehta ◽  
G. Nakhaie Jazar
Keyword(s):  
Piecewise Linear ◽  
System Response ◽  
Structural Constraints ◽  
Vibration Isolator ◽  
Linear Vibration ◽  
Vibration Isolators ◽  
Non Linear ◽  
Dynamical Parameters ◽  
Non Linear System ◽  
Stiffness And Damping

An adapted averaging method is employed to obtain an implicit function for frequency response of a bilinear vibration isolator system under steady state. This function is examined for jump-avoidance and a condition is derived which when met ensures that the undesirable phenomenon of ‘Jump’ does not occur and the system response is functional and unique. The jump avoidance and sensitivity of the condition are examined and investigated as the dynamic parameters vary. The results of this investigation can be directly employed in design of effective piecewise linear vibration isolators. A linear vibration system is defined as one in which the quantities of mass (or inertia), stiffness, and damping are linear in behavior and do not vary with time [1]. Although mathematical models employing a linear ordinary differential equation with constant coefficients portray a simple and manageable system for analytical scrutiny, in most cases they are an incomplete representation simplified for the sake of study. Most real physical vibration systems are more accurately depicted by non-linear governing equations, in which the non-linearity may stem from structural constraints causing a change in stiffness and damping characteristics, or from inherent non-linear behavior of internal springs and dampers. This paper focuses on a general form of such a non-linear system. This study of piecewise-linear systems will allow hazardous system behavior over operating frequency ranges to be gauged and controlled in order to avoid premature fatigue damage, and prolong the life of the system.

Design of a piecewise linear vibration isolator for jump avoidance

2007 ◽  
Vol 221 (3) ◽  
pp. 441-449 ◽  
Author(s):  
G N Jazar ◽  
M Mahinfalah ◽  
S Deshpande
Keyword(s):  
Piecewise Linear ◽  
Harmonic Excitation ◽  
System Response ◽  
Structural Constraints ◽  
Vibration Isolator ◽  
Linear Vibration ◽  
Vibration Isolators ◽  
Non Linear ◽  
Non Linear System ◽  
Stiffness And Damping

Piecewise linear isolators are smart passive vibration isolators that provide effective isolation for high frequency/low amplitude excitation. This can be done by introducing a soft primary suspension and a relatively damped secondary suspension. Such a piecewise isolator prevents the system from a high relative displacement in low frequency/high amplitude excitation. By employed an averaging method it is possible to obtain an implicit function for frequency response of a symmetric bilinear vibration isolator system under steady-state harmonic excitation. This function is examined for jump avoidance. A condition is derived which when met ensures that the undesirable phenomenon of ‘jump’ does not occur and the system response is functional. The jump avoidance and sensitivity of the condition are examined and investigated as the dynamic parameters vary. The results of this investigation can be directly employed in design of effective piecewise linear vibration isolators. A linear vibration system is defined as one in which the quantities of mass (or inertia), stiffness, and damping are linear in behaviour and do not vary with time [1]. Although mathematical models employing a linear ordinary differential equation with constant coefficients portray a simple and manageable system for analytical study, in most cases they are an incomplete representation simplified for the sake of analysis. Most real physical vibration systems are more accurately depicted by non-linear governing equations, in which the non-linearity may stem from structural constraints causing a change in stiffness and damping characteristics, or from inherent non-linear behaviour of internal springs and dampers. This paper focuses on a general form of such a non-linear system. This study of piecewise-linear systems will allow hazardous system behaviour over operating frequency ranges to be gauged and controlled in order to avoid premature fatigue damage, and prolong the life of the system.

On the Piecewise Linear Exact Solution

2014 ◽  
Vol 3 (4) ◽  
Author(s):  
Oleksandr Pogorilyi ◽  
Pavel M. Trivailo ◽  
Reza N. Jazar
Keyword(s):  
Mathematical Modeling ◽  
Exact Solution ◽  
Frequency Response ◽  
Piecewise Linear ◽  
Vibration Isolator ◽  
Linear Vibration ◽  
Transcendental Equations

AbstractIn this paper we will show how the exact frequency response of the piecewise linear vibration isolator can be reduced to be found by solving only two transcendental equations. Adopting a new nondimensionalization method, the mathematical modeling of the system is presented and the mathematics to determine the exact steadystate response of the system is explained.

Jump Avoidance Conditions for Piecewise Linear Vibration Isolator

2005 ◽  
Author(s):  
Sagar Deshpande ◽  
Sudhir Mehta ◽  
G. Nakhaie Jazar
Keyword(s):  
Steady State ◽  
Frequency Response ◽  
Perturbation Methods ◽  
Averaging Method ◽  
Piecewise Linear ◽  
Bilinear System ◽  
System Response ◽  
Implicit Function ◽  
Vibration Isolator ◽  
Linear Vibration

Piecewise linear systems being highly non-linear, standard perturbation methods cannot produce an analytical expression for the frequency response. Hence, an adapted averaging method is employed to obtain an implicit function for frequency response of a bilinear system under steady state. This function is examined for jump-avoidance and a condition is derived which when met ensures that the undesirable phenomenon of ‘Jump’ does not occur and the system response is functional and unique.

Sensitivity analysis of piecewise linear vibration isolator with dual rate spring and damper

2015 ◽  
Vol 4 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Oleksandr Pogorilyi ◽  
Pavel Trivailo ◽  
Mohammad Fard ◽  
Reza N. Jazar
Keyword(s):  
Sensitivity Analysis ◽  
Frequency Response ◽  
Piecewise Linear ◽  
Peak Amplitude ◽  
Vibration Isolator ◽  
Linear Vibration ◽  
The Impact

AbstractIn this paper the exact frequency response of symmetric piecewise linear vibration isolator has been revised and reviewed. The frequency response of the system is calculated and detailed sensitivity analysis is presented. The method of obtaining the exact frequency response of the isolator is based on combining together the liner solutions of different segments within the cycle of motion of the system. In this paper set of graphs for different parameters of the system that illustrates the sensitivity of the system have been provided. The analysis of the impact of parameters of the system on its behavior has been presented. The sensitivity analysis is required to be able to determine the working domain of the parameters. Jump avoidance and peak amplitude minimization are the main aspects of parameter working domain.

Frequency Response of a Piecewise Linear Vibration Isolator

2004 ◽  
Vol 10 (12) ◽  
pp. 1775-1794 ◽  
Author(s):  
A. Narimani ◽  
M. E. Golnaraghi ◽  
G. Nakhaie Jazar
Keyword(s):  
Frequency Response ◽  
Averaging Method ◽  
Dominant Role ◽  
Piecewise Linear ◽  
Damping Ratio ◽  
Vibration Isolator ◽  
Linear Vibration ◽  
Vibration Isolators ◽  
Piecewise Linear System ◽  
Response Equation

Piecewise linear vibration isolators are designed to optimally balance the competing goals of motion control and isolation. The piecewise linear system represents a hard nonlinearity, which cannot be assumed small, and hence standard perturbation methods are unable to provide a complete analytical solution. To date there is no frequency response equation reported for piecewise linear isolator systems to include both dual damping and stiffness behavior. In this investigation an averaging method was adopted to explore the frequency response of a symmetric piecewise linear isolator at resonance. The result obtained by an averaging method is in agreement with numerical simulation and experimental measurements. Preliminary sensitivity analysis is conducted to find the effect of system parameters. It appears that the damping ratio plays a more dominant role than stiffness in piecewise linear vibration isolators.

On the Effects of Mistuning a Force-Excited System Containing a Quasi-Zero-Stiffness Vibration Isolator

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Ali Abolfathi ◽  
M. J. Brennan ◽  
T. P. Waters ◽  
B. Tang
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Vibration Isolator ◽  
Linear Vibration ◽  
Vibration Isolators ◽  
Zero Dynamic ◽  
Low Frequency Vibration ◽  
Excited System ◽  
Better Than

Nonlinear isolators with high-static-low-dynamic-stiffness have received considerable attention in the recent literature due to their performance benefits compared to linear vibration isolators. A quasi-zero-stiffness (QZS) isolator is a particular case of this type of isolator, which has a zero dynamic stiffness at the static equilibrium position. These types of isolators can be used to achieve very low frequency vibration isolation, but a drawback is that they have purely hardening stiffness behavior. If something occurs to destroy the symmetry of the system, for example, by an additional static load being applied to the isolator during operation, or by the incorrect mass being suspended on the isolator, then the isolator behavior will change dramatically. The question is whether this will be detrimental to the performance of the isolator and this is addressed in this paper. The analysis in this paper shows that although the asymmetry will degrade the performance of the isolator compared to the perfectly tuned case, it will still perform better than the corresponding linear isolator provided that the amplitude of excitation is not too large.

A New Criterion for Optimizing Linear Vibration Isolator Systems Subject to Random Input

1969 ◽  
Vol 91 (4) ◽  
pp. 1005-1010 ◽  
Author(s):  
A. K. Trikha ◽  
D. C. Karnopp
Keyword(s):  
Optimization Problem ◽  
Performance Criterion ◽  
Weighted Sum ◽  
Mean Square ◽  
Vibration Isolator ◽  
Linear Vibration ◽  
Random Input ◽  
Random Inputs ◽  
New Criterion ◽  
Operational Time

A new performance criterion is proposed for the synthesis of optimum linear isolators subject to random inputs. This criterion is based upon the values of displacement and acceleration; the probability of exceeding which, during the operational time, will be less than a desired value. A method is developed to solve this optimization problem for the case of stationary, Gaussian random input. Finally, systems optimized on the basis of the proposed criterion are compared with systems optimized according to the commonly used criterion which involves minimization of a weighted sum of the expected mean square values of displacement and acceleration.

Vibration Analysis of Nonlinear Isolator’s Characteristics by ADAMS

2012 ◽  
Vol 152-154 ◽  
pp. 1077-1081 ◽  
Author(s):  
Zhao Qi He ◽  
Yu Chao Song ◽  
Hong Liang Yu
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Isolation ◽  
Excitation Frequency ◽  
Vibration Isolator ◽  
Vibration System ◽  
Linear Vibration ◽  
External Excitation ◽  
Mass Model ◽  
Adams Software ◽  
Isolation Systems

A nonlinear spring-mass model is established to study the dynamic characteristics of nonlinear vibration isolator. By use of ADAMS software, the influence of stiffness, foundation displacement excitation and frequency of external excitation on the nonlinear vibration isolation systems are analyzed. Results indicate that the linear vibration system needs 4s to achieve stability, but the nonlinear vibration system only needs 0.1s. The response value increases with the increase of excitation frequency, the response pick value increases by 61.58% and 102.35% and each corresponding stable value increases by 159.35% and 309.87%.

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