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.

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.

scholarly journals Dynamic analysis and experiment of QZS system with nonlinear hysteretic damping

2021 ◽  
Author(s):  
Xiaoying Hu ◽  
Chunyan Zhou
Keyword(s):  
Vibration Isolation ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Primary Response ◽  
Nonlinear Phenomena ◽  
Isolation Frequency ◽  
Hysteretic Damping ◽  
Isolation Systems ◽  
The One ◽  
Vibration Tests

Abstract Nonlinear Quasi-zero-stiffness (QZS) vibration isolation systems with linear damping cannot lead to displacement isolation with different excitation levels. In this study, a QZS system with nonlinear hysteretic damping was investigated. The Duffing-Ueda equation with a coupling nonlinear parameter 𝜂 was proposed to describe the dynamic motion of the QZS system. By using the harmonic balance method (HBM), the primary and secondary harmonic responses were obtained and verified by numerical simulations. The results indicated that nonlinear damping can guarantee a bounded response for different excitation levels. The one-third subharmonic response was found to affect the isolation frequency range even when the primary response was stable. To evaluate the performance of the QZS system, the effective isolation frequency Ω𝑒 and maximum transmissibility 𝑇𝑝 were proposed to represent the vibration isolation range and isolation effect, respectively. By discussing the effect of 𝜂 on Ω𝑒 and 𝑇𝑝, the conditions to avoid nonlinear phenomena and improve the isolation performance are provided. A prototype of the QZS system was then constructed for vibration tests, which verified the theoretical analysis.

scholarly journals An Asymmetric Quasi-zero Stiffness Vibration Isolator with Long Stroke and Large Bearing Capacity

2021 ◽  
Author(s):  
Xinghua Zhou ◽  
Dingxuan Zhao ◽  
Xiao Sun ◽  
Xiao Yang ◽  
Jianhai Zhang ◽  
...  
Keyword(s):  
Bearing Capacity ◽  
Vibration Isolation ◽  
Geometrical Nonlinearity ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Vibration Isolator ◽  
Plate Spring ◽  
Supporting Force ◽  
Vibration Isolation Performance ◽  
Isolation Performance

Abstract A novel passive asymmetric quasi-zero stiffness vibration isolator (AQZS-VI) comprising two linear springs acting in parallel with one negative stiffness element (NSE) is proposed, of which the NSE is mainly constructed by the combination of cantilever plate spring and L-shaped lever (CPS-LSL). The static model of the isolator is deduced considering the geometrical nonlinearity of the NSE and the bending deformation of plate spring. The nonlinear stiffness properties of the CPS-LSL and the AQZS-VI, as well as the nonlinear damping properties of the AQZS-VI are discussed. The absolute displacement transmissibility of the AQZS-VI under base displacement excitation is obtained using Harmonic Balance Method, and the effects of different excitation amplitudes and damping factors on the vibration isolation performance are analyzed. Better than other quasi-zero stiffness vibration isolators (QZS-VI) whose NSEs do not provide supporting force at zero stiffness point, the NSE of the AQZS-VI provides more supporting force than the parallel connected linear springs, which is very beneficial for improving the bearing capacity of the isolator. Compared with a typical symmetric QZS-VI with same damping property, the AQZS-VI has longer stroke with low stiffness and lower peak value of displacement transmissibility. The prototype experiments indicate that the AQZS-VI outperforms the linear counterpart with much smaller starting frequency of vibration isolation and lower displacement transmissibility. The proposed AQZS-VI has great potential for applying in various engineering practices with superior vibration isolation performance.

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.

scholarly journals Nonlinear damping and quasi-linear modelling

2015 ◽  
Vol 373 (2051) ◽  
pp. 20140402 ◽  
Author(s):  
S. J. Elliott ◽  
M. Ghandchi Tehrani ◽  
R. S. Langley
Keyword(s):  
Vibration Isolation ◽  
Mechanical Response ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Random Excitation ◽  
Damping Force ◽  
Control Engineering ◽  
Equivalent Linear ◽  
Physical Insight ◽  
Bifurcation Behaviour

The mechanism of energy dissipation in mechanical systems is often nonlinear. Even though there may be other forms of nonlinearity in the dynamics, nonlinear damping is the dominant source of nonlinearity in a number of practical systems. The analysis of such systems is simplified by the fact that they show no jump or bifurcation behaviour, and indeed can often be well represented by an equivalent linear system, whose damping parameters depend on the form and amplitude of the excitation, in a ‘quasi-linear’ model. The diverse sources of nonlinear damping are first reviewed in this paper, before some example systems are analysed, initially for sinusoidal and then for random excitation. For simplicity, it is assumed that the system is stable and that the nonlinear damping force depends on the n th power of the velocity. For sinusoidal excitation, it is shown that the response is often also almost sinusoidal, and methods for calculating the amplitude are described based on the harmonic balance method, which is closely related to the describing function method used in control engineering. For random excitation, several methods of analysis are shown to be equivalent. In general, iterative methods need to be used to calculate the equivalent linear damper, since its value depends on the system’s response, which itself depends on the value of the equivalent linear damper. The power dissipation of the equivalent linear damper, for both sinusoidal and random cases, matches that dissipated by the nonlinear damper, providing both a firm theoretical basis for this modelling approach and clear physical insight. Finally, practical examples of nonlinear damping are discussed: in microspeakers, vibration isolation, energy harvesting and the mechanical response of the cochlea.

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.

scholarly journals Research and Analysis of Quasi-Zero-Stiffness Isolator with Geometric Nonlinear Damping

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Qingguo Meng ◽  
Xuefeng Yang ◽  
Wei Li ◽  
En Lu ◽  
Lianchao Sheng
Keyword(s):  
Vibration Isolation ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Vibration Isolator ◽  
Rehabilitation Robots ◽  
Geometric Nonlinear ◽  
Low Frequency Vibration ◽  
Linear Spring ◽  
The Relationship

This paper presents a novel quasi-zero-stiffness (QZS) isolator designed by combining a tension spring with a vertical linear spring. In order to improve the performance of low-frequency vibration isolation, geometric nonlinear damping is proposed and applied to a quasi-zero-stiffness (QZS) vibration isolator. Through the study of static characteristics first, the relationship between force displacement and stiffness displacement of the vibration isolation mechanism is established; it is concluded that the parameters of the mechanism have the characteristics of quasi-zero stiffness at the equilibrium position. The solutions of the QZS system are obtained based on the harmonic balance method (HBM). Then, the force transmissibility of the QZS vibration isolator is analyzed. And the results indicate that increasing the nonlinear damping can effectively suppress the transmissibility compared with the nonlinear damping system. Finally, this system is innovative for low-frequency vibration isolation of rehabilitation robots and other applications.

scholarly journals A Variable Parameter Ambient Vibration Control Method Based on Quasi-Zero Stiffness in Robotic Drilling Systems

Machines ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 67
Author(s):  
Laixi Zhang ◽  
Chenming Zhao ◽  
Feng Qian ◽  
Jaspreet Singh Dhupia ◽  
Mingliang Wu
Keyword(s):  
Vibration Control ◽  
Vibration Isolation ◽  
Control Method ◽  
Control Strategies ◽  
Equations Of Motion ◽  
Variable Parameter ◽  
Harmonic Balance Method ◽  
Variable Stiffness ◽  
Ambient Vibration ◽  
Robotic Drilling

Vibrations in the aircraft assembly building will affect the precision of the robotic drilling system. A variable stiffness and damping semiactive vibration control mechanism with quasi-zero stiffness characteristics is developed. The quasi-zero stiffness of the mechanism is realized by the parallel connection of four vertically arranged bearing springs and two symmetrical horizontally arranged negative stiffness elements. Firstly, the quasi-zero stiffness parameters of the mechanism at the static equilibrium position are obtained through analysis. Secondly, the harmonic balance method is used to deal with the differential equations of motion. The effects of every parameter on the displacement transmissibility are analyzed, and the variable parameter control strategies are proposed. Finally, the system responses of the passive and semiactive vibration isolation mechanisms to the segmental variable frequency excitations are compared through virtual prototype experiments. The results show that the frequency range of vibration isolation is widened, and the stability of the vibration control system is effectively improved without resonance through the semiactive vibration control method. It is of innovative significance for ambient vibration control in robotic drilling systems.

Theoretical and Experimental Research of Viscoelastic Damping Limb-Like-Structure Device with Coupling Nonlinear Characteristics

2021 ◽  
pp. 2130002
Author(s):  
Zhen-Hua He ◽  
Zhao-Dong Xu ◽  
Jian-Yang Xue ◽  
Xing-Jian Jing ◽  
Yao-Rong Dong ◽  
...  
Keyword(s):  
Vibration Isolation ◽  
Harmonic Balance Method ◽  
Viscoelastic Damping ◽  
Static Stiffness ◽  
Viscoelastic Damper ◽  
Stiffness Analysis ◽  
Nonlinear Dynamic Equation ◽  
New Type ◽  
Geometrical Effects ◽  
Theoretical Results

The nonlinear characteristic of vibration control systems has attracted increasing attention for its advantage in improving structural performance. In this paper, a new type of viscoelastic damping limb-like-structure (VE-LLS) device is proposed by combing the viscoelastic (VE) damper and limb-like-structure (LLS) together, which possesses coupling nonlinearity characteristic caused by geometric and material factors, as well as a remarkable advantage in improving the control performance. First, to explore the nonlinear geometrical effects on the static stiffness of the VE-LLS device, a formula is derived from static stiffness, and the results are discussed. Second, dynamic analysis is performed of the proposed device considering the coupling geometrical and material nonlinearities in frequency domain, with the real-time effect of frequency and temperature on the mechanical properties of the viscoelastic damper considered in solving the nonlinear vibration equation. The harmonic balance method (HBM) is used to solve the nonlinear dynamic equation. Then, the displacement transmissibility of the VE-LLS device is calculated and assessed. The results indicate that the proposed device possesses excellent vibration isolation performance, and the geometric parameters of the viscoelastic damper have significant nonlinear effect on the performance. Finally, an experiment is carried out of the VE-LLS device to verify the accuracy of the static stiffness analysis. The results show that the theoretical results agree well the experimental ones, and that the theoretical results have high accuracy and reliability.

scholarly journals Identification and Removal of Non-acoustic Noise in Towed Array Sonar Using F-Κ Transform for Enhanced Torpedo Detection

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Vibration Isolation ◽  
Acoustic Noise ◽  
Detection System ◽  
Mechanical Vibration ◽  
Low Frequency ◽  
Acoustic Energy ◽  
Noise Sources ◽  
Towed Array ◽  
Spatio Temporal ◽  
Towed Arrays

Low frequency passive towed array sonar is an essential component in a torpedo detection system for surface ships. Compact towed arrays are used for torpedo detection and they will be towed at higher towing speeds compared to conventional towed array sonars used for surveillance. Presence of non-acoustic noise in towed array sensors at higher towing speeds degrades torpedo detection capability at lower frequencies. High wavenumber mechanical vibrations are induced in the array by vortex shedding associated with hydrodynamic flow over the array body and cable scope. These vibrations are known to couple into the hydrophone array as nonacoustic noise sources and can impair acoustic detection performance, particularly in the forward end fire direction. Lengthy mechanical vibration isolation modules can isolate vibration induced noise in towed arrays, but this is not recommended in a towed array which is towed at high speeds as it will increase the drag and system complexity. An algorithm for decomposing acoustic and non-acoustic components of signals received at sensor level using well known frequency-wavenumber transform (F-K transform) is presented here. Frequency-wavenumber diagrams can be used for differentiating between acoustic and non-acoustic signals. An area of V shape is identified within the F-K spectrum where acoustic energy is confined. Energy outside this V will highlight non-acoustic energy. Enhanced simultaneous spatio-temporal and spatio-amplitude detection is possible with this algorithm. Performance of this algorithm is validated through simulation and experimental data.

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