Investigation of Damping Nonlinearity in Duffing-Type Vibration Isolation System With Geometric and Magnetic Stiffness Nonlinearities

2017 ◽  
Author(s):  
S. M. Mahdi Mofidian ◽  
Hamzeh Bardaweel
Keyword(s):  
Resonant Frequency ◽  
Dynamic Behavior ◽  
Vibration Isolation ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Resonant Peak ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Magnetic Stiffness ◽  
Sinusoidal Input

In this work, the effect of nonlinear damping in presence of geometric nonlinearities and magnetic stiffness nonlinearities in vibration isolation system is investigated. The dynamic behavior of the isolation system design is modeled. Harmonic Balance Method (HBM) is used to investigate the dynamic behavior of the vibration isolation system in response to sinusoidal input waveform. Results obtained using the HBM are compared to the results from numerical simulation attained using Runge-kutta method. Results show that introducing nonlinear viscous damping into the vibration isolation system suppresses frequency jump phenomena observed in Duffing-type vibration isolation systems. Additionally, results show that nonlinear damping can suppress transmissibility around resonant peak. For frequencies lower than resonant frequency the effect of nonlinear damping is minimum compared to a linear isolation system. Beyond resonant frequency higher nonlinear damping may slightly alter transmissibility of the isolation system.

Displacement transmissibility evaluation of vibration isolation system employing nonlinear-damping and nonlinear-stiffness elements

2017 ◽  
Vol 24 (18) ◽  
pp. 4247-4259 ◽  
Author(s):  
S M Mahdi Mofidian ◽  
Hamzeh Bardaweel
Keyword(s):  
Numerical Simulation ◽  
Vibration Isolation ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Resonant Peak ◽  
Engineering Practice ◽  
Nonlinear Stiffness ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Isolation Systems

Undesired oscillations commonly encountered in engineering practice can be harmful to structures and machinery. Vibration isolation systems are used to attenuate undesired oscillations. Recently, there has been growing interest in nonlinear approaches towards vibration isolation systems design. This work is focused on investigating the effect of nonlinear cubic viscous damping in a vibration isolation system consisting of a magnetic spring with a positive nonlinear stiffness, and a mechanical oblique spring with geometric nonlinear negative stiffness. Dynamic model of the vibration isolation system is obtained and the harmonic balance method (HBM) is used to solve the governing dynamic equation. Additionally, fourth order Runge–Kutta numerical simulation is used to obtain displacement transmissibility of the system under investigation. Results obtained from numerical simulation are in good agreement with those obtained using HBM. Results show that introducing nonlinear damping improves the performance of the vibration isolation system. Nonlinear damping purposefully introduced into the described vibration isolation system appears to eliminate undesired frequency jump phenomena traditionally encountered in quasi-zero-stiffness vibration isolation systems. Compared to its rival linear vibration isolation system, the described nonlinear system transmits less vibrations around resonant peak. At lower frequencies, both nonlinear and linear isolation systems show comparable transmissibility characteristics.

Two-Dimensional Linear Friction Damper Consisting of Concave Cone and Cylindrical Member (Investigation of Performance by Numerical Simulation and Experiment)

2015 ◽  
Author(s):  
Hideya Yamaguchi ◽  
Hidehisa Yoshida
Keyword(s):  
Numerical Simulations ◽  
Friction Force ◽  
Vibration Isolation ◽  
Two Dimensions ◽  
Resonant Peak ◽  
Friction Damper ◽  
Isolation System ◽  
Friction Forces ◽  
Vibration Isolation System ◽  
Linear Friction

A passive vibration isolation system consisting of a constant friction force has performance limitations; the isolation performance declines and the residual displacement becomes large in the case of the large friction force, while the resonant peak becomes large in the case of the small friction force. It is known that above drawbacks are avoidable when the friction force varies in proportion to the relative displacement. Recently, authors have proposed a simple linear friction damper mechanism that consists of a cylindrical block and a tilt lever supported with a pivot or a leaf spring. Performance of the vibration isolation system equipped with the proposed damper is investigated, and its effectiveness is confirmed by numerical simulations and the experiments. However, the motion of the mechanism is limited to one-dimension. This paper proposes an extended mechanism that can be applied to motion moving in two dimensions by combining the concave cone and the cylindrical member. The concave cone is supported with a universal joint on the apex side and its tilting motion is constrained by the restoring spring. The rounded edge of the cylindrical member is set up to contact the inside flank of the concave cone. When the cylindrical member moves in an arbitrary direction on the planar floor and pushes the concave cone, the normal and friction forces at the contact point vary depending on the displacement of the cylindrical member. The fundamental property and the performance of the proposed mechanism are investigated by numerical simulations and experiments.

Analysis and Experiment of an Air Vibration Isolation System with Auxiliary Chambers

2012 ◽  
Vol 226-228 ◽  
pp. 195-198
Author(s):  
Rong Wei Wen ◽  
Jiu Bin Tan ◽  
Lei Wang ◽  
Guan Hua Wang
Keyword(s):  
Resonant Frequency ◽  
Vibration Isolation ◽  
Excitation Frequency ◽  
Volume Ratio ◽  
Air Spring ◽  
Working Pressure ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Vibration Transmissibility ◽  
System Vibration

A mathematical model of a single degree of freedom air spring vibration isolation system is established. The model analyzes the influence of structural damping in the air spring vibration isolation system based on the traditional model. This paper establishes the relationship between the working pressure p, the volume ratio of n and system vibration transmissibility T under forced vibration. The experimental results are verified on different working pressure. The results showed that working pressure p has little effect on the resonant frequency of the system and the system vibration transmissibility. The smaller the ratio n, the lower the resonant frequency of the system and the system vibration transmissibility. The environmental excitation frequency range must be taken into account in designing.

Study on the Mechanism for Line Spectrum Reduction in Nonlinear Vibration Isolation System

2007 ◽  
Author(s):  
Jing-Jing Wang ◽  
Shi-Jian Zhu ◽  
Shu-Yong Liu
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Isolation ◽  
Harmonic Balance Method ◽  
Chaotic Signal ◽  
Dominant Frequency ◽  
Line Spectrum ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Chaotic Response ◽  
Frequency Components

The chaotic response and mechanism for line spectrum reduction in nonlinear vibration isolation system are studied. The harmonic balance method is applied to uncover the interaction between different harmonics. It is clear that the considerable energy transfers from the fundamental harmonic to the others by the nonlinear interactions, and thus the energy at the dominant frequency is reduced greatly. When the nonlinear vibration isolation system is in a chaotic state, the response is characteristic of the broadband spectrum, and thus the energy is distributed to all the frequency components. Chaotic attractor is different from the point, limit cycle and so on, and the fractal dimension can be applied to describe its characteristic. Furthermore, the chaotic signal is distinguished from the random one by the saturation of the correlation dimension. The former approaches to saturation with the increasing embedding dimension, but the latter does not. The phase space reconstruction based on wavelet transform can achieve the study of both the geometry and frequency characteristics of the chaos, so that provides a new way to study chaotic response.

scholarly journals Indirect Control of Oscillations: Elements of Theory

2018 ◽  
Vol 18 (1) ◽  
pp. 148-175
Author(s):  
Vladimir Chernyshev ◽  
Leonid Savin ◽  
Olga Fominova
Keyword(s):  
Vibration Isolation ◽  
Dynamic Properties ◽  
Harmonic Balance Method ◽  
Frequency Region ◽  
Optimal Sequence ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Basic Model ◽  
Indirect Control ◽  
Vibration Protection

A brief review of the main research areas in the field of controlled vibration protection systems is given. It is shown that Vibration systems with indirect control processes of oscillations allow with a minimum expenditure of energy to ensure programmable switching parameters and structures, in which the dissipative restoring and inertial forces generated on the basis of active impact. Within synthesis of indirect control the chains of new auxiliary mathematical constructs for finding optimal synthesizing functions of the elastic-damping units parameters control are obtained. It enabled to separate a base model with intermittent damping and base model with impulse trap. As a result of the study, based on the harmonic balance method, the dynamic properties of the basic model with intermittent damping, calculation formulas are obtained for determining the parameters of the compensation effect and calculating the dynamic coefficient. It is established that, with an optimal sequence of damping switching, the resonant phenomena are eliminated, and the transient processes decay within one period of the kinematic perturbation. The basic model with a pulse trap imitates the limiting variant of intermittent damping and realizes the process of superimposing constraining bonds, the sequence and duration of which are new variables essentially increasing controllability. And for indirect pulse control, there exicts a certain minimum of power consumption independent of the achieved effect of vibration protection. A regulated increase in the duration of the application of the restraining coupling in the low-frequency region and a decrease in this duration in the high-frequency region provides a monotonically decreasing dependence on the dynamic coefficients over the entire frequency range. An example of a solution to the optimization problem of controlling the damping process for a basic model of a vibration isolation system is considered. It is established that intermittent damping is an indispensable feature of the optimality of the vibration isolation system: the damper switches on when the sign of the object's speed has changed and turns off when the object's displacement sign has changed.

Synthesis of Mechanical Vibration Filters With Nonlinear Characteristics

1963 ◽  
Vol 85 (3) ◽  
pp. 247-253 ◽  
Author(s):  
Ruey-Wen Liu ◽  
Will J. Worley
Keyword(s):  
Vibration Isolation ◽  
Response Spectrum ◽  
Mechanical Vibration ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Space Vehicles ◽  
Nonlinear Characteristics ◽  
Steady State Condition ◽  
Sinusoidal Input ◽  
Fixed Reference

The synthesis of the desired nonlinear characteristics for the spring and damper used to isolate a single mass from a vibrating base is here investigated. The analysis is confined to the steady-state condition resulting from a sinusoidal input excitation. The purpose of this paper is to study the effect of oscillation due to nonlinear damping and the effect of the dynamic mean deflection of the nonlinear spring on the amplitude response spectrum. These factors are important in vibration isolation of equipment in space vehicles because of the variation in acceleration or in the effective weight of the isolated body. The solution for the displacement of the mass relative to its base was obtained by the harmonic balance method. The procedure has been extended to obtain the absolute displacement of the mass relative a fixed reference frame.

The Effect of Stiffness and Loading Deviations in a Nonlinear Isolator Having Quasi Zero Stiffness and Geometrically Nonlinear Damping

2017 ◽  
Author(s):  
Ata Donmez ◽  
Ender Cigeroglu ◽  
Gokhan O. Ozgen
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Nonlinear Differential Equations ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Geometrically Nonlinear ◽  
Algebraic Equations ◽  
Isolation System ◽  
Highly Nonlinear ◽  
Isolation Performance

Static deflections due to static loadings limit the isolation performance of linear vibration isolation systems. Therefore, quasi-zero stiffness (QZS) mechanisms, i.e. nonlinear isolators with high static and low dynamic stiffness characteristic, are used to decrease the natural frequency of the isolation structure and improve the isolation performance of the system while having the same loading capacity. However, the resulting system is highly nonlinear and unstable solutions may as well occur. Although increasing the amount of linear viscous damping in the system reduces the nonlinearity, it has adverse effect on the isolation region. Geometrically nonlinear damping is effective when the response of the isolation system increases; hence, isolation region is unaffected. Combination of position depended nonlinear damping and QZS mechanism eliminates highly input depended response of QZS mechanism. In this study, a single degree of freedom system with a nonlinear isolator having QZS mechanism and geometrically nonlinear damping is considered. The nonlinear differential equations of motion of the isolation system are converted into a set of nonlinear algebraic equations by using harmonic balance method, which are solved by using Newton’s method with arc-length continuation. Several case studies are performed and the effect of stiffness and loading deviations on the isolation performance is studied.

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