scholarly journals Power Flow in a Two-Stage Nonlinear Vibration Isolation System with High-Static-Low-Dynamic Stiffness

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Ze-Qi Lu ◽  
Dong Shao ◽  
Hu Ding ◽  
Li-Qun Chen
Keyword(s):  
Nonlinear Vibration ◽  
Power Flow ◽  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Resonant Peak ◽  
Nonlinear Stiffness ◽  
Two Stage ◽  
Force Transmissibility

The manuscript concerns the power flow characterization in a two-stage nonlinear vibration isolator comprising three springs, which are configured so that each stage of the system has a high-static-low-dynamic stiffness. To demonstrate the distinction of evaluation for vibration isolation using power flow, force transmissibility is used for comparison. The dynamic behavior of the isolator subject to harmonic excitation, however, is of interest here. The harmonic balance method (HBM) could be used to analyze the frequency response curve (FRC) of the strong nonlinear vibration system. A suggested stability analysis to distinguish the stable and the unstable HBM solutions is described. Increasing both upper and lower nonlinear stiffness could bend the first resonant peak to the left. The isolation range in the power and the force transmissibility plot could be extended to the lower frequencies when the nonlinear stiffness is increased, but the rate of roll-off for the power transmissibility is twice the rate for the force transmissibility at each horizontal stiffness setting. An explanation for this phenomenon is given in the paper.

scholarly journals Characteristic analysis of a new high-static-low-dynamic stiffness vibration isolator based on the buckling circular plate

2020 ◽  
pp. 146134842090486
Author(s):  
Zhirong Yang ◽  
Yan Wang ◽  
Ziming Huang ◽  
Zhushi Rao
Keyword(s):  
Equilibrium Point ◽  
Circular Plate ◽  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Harmonic Balance Method ◽  
Installation Space ◽  
Vibration Isolator ◽  
Characteristic Analysis ◽  
Linear Spring ◽  
Force Transmissibility

The high-static-low-dynamic stiffness vibration isolator has great advantages in vibration isolation because it can decrease the natural frequency of the system while keeping the load capability, but it is usually difficult to implement because of its complex structures and installation space constraints. A high-static-low-dynamic stiffness vibration isolator composed of a buckling circular plate and a traditional linear spring is proposed in this paper. The buckling circular plate works as the negative stiffness corrector paralleled with the linear spring, which can be integrated into the sleeve. If the load is chosen properly, the static equilibrium point will be at the initial quasi-zero stiffness point. However, any changes of the load will lead the equilibrium point deviating from the initial equilibrium point. The nonlinear mathematical model of high-static-low-dynamic stiffness vibration isolator considering load imperfection is developed and its force transmissibility is analyzed with the harmonic balance method and homotopy perturbation method. The influence rule of the system parameters on it is analyzed and the corresponding results show that the force transmissibility will exhibit complicated characteristics, depending on the load imperfection, damper, and excitation force.

Experimental Investigation of a Two-Stage Nonlinear Vibration Isolation System With High-Static-Low-Dynamic Stiffness

2016 ◽  
Vol 84 (2) ◽  
Author(s):  
Zeqi Lu ◽  
Tiejun Yang ◽  
Michael J. Brennan ◽  
Zhigang Liu ◽  
Li-Qun Chen
Keyword(s):  
Nonlinear Vibration ◽  
Composite Plate ◽  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Composite Plates ◽  
Negative Stiffness ◽  
Two Stage ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Static Test

A novel design of a two-stage nonlinear vibration isolation system, with each stage having a high-static-low-dynamic stiffness (HSLDS), is studied experimentally in this paper. The positive stiffness in each stage is realized by a metallic plate, and the corresponding negative stiffness is realized by a bistable carbon fiber–metal (CF) composite plate. An analytical model is developed as an aid to design a bistable composite plate with the required negative stiffness, and a static test of the plate is conducted to measure the actual stiffness of the plate. Dynamic tests of the two-stage isolator are carried out to determine the effectiveness of the isolator. Two tests are conducted, one with the bistable composite plates removed so that the isolator behaves as a linear device and one with the bistable composite plates fitted. An improvement in the isolator transmissibility of about 13 dB at frequencies greater than about 100 Hz is achieved when the bistable composite plates are added.

Design and Analysis of a High-Static-Low-Dynamic Stiffness Isolator Using the Cam-Roller-Spring Mechanism

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Yuhui Yao ◽  
Xiaojian Wang ◽  
Hongguang Li
Keyword(s):  
Harmonic Balance ◽  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Damping Ratio ◽  
Harmonic Balance Method ◽  
Interaction Force ◽  
Linear Spring ◽  
Cam Profile ◽  
Force Transmissibility ◽  
Spring Mechanism

Abstract This paper presents a new design of a high-static-low-dynamic stiffness (HSLDS) isolator with an adjustable cam profile. The interaction force between the cam and roller provides the negative stiffness force and the linear spring provides the positive stiffness force in the HSLDS isolator. Unlike previous studies, the cam profile in this paper can be individually designed to meet different working conditions. Firstly, the harmonic balance method is used to acquire the dynamic response of the HSLDS isolator. Then, the effects of the damping ratio, stiffness ratio, and external force amplitude on the frequency response amplitude and force transmissibility are discussed. Finally, the frequency responses of four designed nonlinear HSLDS isolators and a linear isolator are acquired by the numerical method. The results show that the nonlinear isolator begins to achieve vibration isolation at 0.11 Hz and the linear one is 8.9 Hz. The proposed HSLDS isolator realizes lower vibration isolation frequency than the linear isolator.

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 Nonlinear vibration of knitted spacer fabric under harmonic excitation

2020 ◽  
Vol 15 ◽  
pp. 155892502098356
Author(s):  
Fuxing Chen ◽  
Hong Hu
Keyword(s):  
Nonlinear Vibration ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Polyurethane Foams ◽  
Excitation Level ◽  
Harmonic Amplitude ◽  
Damping Force ◽  
Spacer Fabric ◽  
Fabric System ◽  
Quadratic Stiffness

Knitted spacer fabrics can be an alternative material to typical rubber sponges and polyurethane foams for the protection of the human body from vibration exposure, such as automotive seat cushions and anti-vibration gloves. To provide a theoretical basis for the understanding of the nonlinear vibration behavior of the mass-spacer fabric system under harmonic excitation, experimental, analytical and numerical methods are used. Different from a linear mass-spring-damper vibration model, this study builds a phenomenological model with the asymmetric elastic force and the fractional derivative damping force to describe the periodic solution of the mass-spacer fabric system under harmonic excitation. Mathematical expression of the harmonic amplitude versus frequency response curve (FRC) is obtained using the harmonic balance method (HBM) to solve the equation of motion of the system. Parameter values in the model are estimated by performing curve fit between the modeled FRC and the experimental data of acceleration transmissibility. Theoretical analysis concerning the influence of varying excitation level on the FRCs is carried out, showing that nonlinear softening resonance turns into nonlinear hardening resonance with the increase of excitation level, due to the quadratic stiffness term and the cubic stiffness term in the model, respectively. The quadratic stiffness term also results in biased vibration response and causes an even order harmonic distortion. Besides, the increase of excitation level also results in elevated peak transmissibility at resonance.

Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness

2016 ◽  
Vol 87 (1) ◽  
pp. 633-646 ◽  
Author(s):  
Xinlong Wang ◽  
Jiaxi Zhou ◽  
Daolin Xu ◽  
Huajiang Ouyang ◽  
Yong Duan
Keyword(s):  
Vibration Isolation ◽  
Two Stage ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Force Transmissibility

Energy flow and performance evaluation of inerter-based vibration isolators mounted on finite and infinite flexible foundation structures

2022 ◽  
Vol 14 (1) ◽  
pp. 168781402110704
Author(s):  
Zhuang Dong ◽  
Jian Yang ◽  
Chendi Zhu ◽  
Dimitrios Chronopoulos ◽  
Tianyun Li
Keyword(s):  
Power Flow ◽  
Vibration Isolation ◽  
Vibration Suppression ◽  
Flow Behavior ◽  
Flexible Beam ◽  
Vibration Isolators ◽  
Force Transmissibility ◽  
And Performance ◽  
Flexible Foundation ◽  
Isolation Performance

This study investigates the vibration power flow behavior and performance of inerter-based vibration isolators mounted on finite and infinite flexible beam structures. Two configurations of vibration isolators with spring, damper, and inerter as well as different rigidities of finite and infinite foundation structures are considered. Both the time-averaged power flow transmission and the force transmissibility are studied and used as indices to evaluate the isolation performance. Comparisons are made between the two proposed configurations of inerter-based isolators and the conventional spring-damper isolators to show potential performance benefits of including inerter for effective vibration isolation. It is shown that by configuring the inerter, spring, and damper in parallel in the isolator, anti-peaks are introduced in the time-averaged transmitted power and force transmissibility at specific frequencies such that the vibration transmission to the foundation can be greatly suppressed. When the inerter is connected in series with a spring-damper unit and then in-parallel with a spring, considerable improvement in vibration isolation can be achieved near the original peak frequency while maintaining good high-frequency isolation performance. The study provides better understanding of the effects of adding inerters to vibration isolators mounted on a flexible foundation, and benefits enhanced designs of inerter-based vibration suppression systems.

Dynamic Analysis of Multi-Supported Nonlinear Vibration Isolation System Mounted on Flexible Foundation

2013 ◽  
Vol 419 ◽  
pp. 223-227 ◽  
Author(s):  
Rui Huo ◽  
Hui Yu ◽  
Yan Feng Guan
Keyword(s):  
Numerical Solution ◽  
Nonlinear Vibration ◽  
Power Flow ◽  
Vibration Isolation ◽  
Engineering Application ◽  
System Dynamic ◽  
Dynamic Equations ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Flexible Foundation

In view of its prototype in engineering application, a theoretical model of multi-supported nonlinear vibration isolation system installed on flexible foundation is studied, including derivation of system dynamic equations and analysis of system dynamic characteristics. For effectiveness evaluation of nonlinear vibration isolation systems, a generalized time-averaged power is proposed as an extension of classical theory of vibratory power flow, and a numerical solution method of time-averaged power is probed accompanying with the numerical solution of nonlinear dynamic equations. In a further concrete calculation example, an air spring vibration isolation system of a small UAV engine is numerically simulated based on Runge-Kutta method, and dynamic behavior and power flow transmission characteristics influenced by system parameters are investigated.

On the Performance of a Two-Stage Vibration Isolation System Which has Geometrically Nonlinear Stiffness

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Zeqi Lu ◽  
Tiejun Yang ◽  
Michael J. Brennan ◽  
Xinhui Li ◽  
Zhigang Liu
Keyword(s):  
Resonance Frequency ◽  
Vibration Isolation ◽  
Low Frequency ◽  
Single Stage ◽  
Nonlinear Stiffness ◽  
Two Stage ◽  
Isolation System ◽  
Beneficial Effects ◽  
Isolation Systems ◽  
The Right

Linear single-stage vibration isolation systems have a limitation on their performance, which can be overcome passively by using linear two-stage isolations systems. It has been demonstrated by several researchers that linear single-stage isolation systems can be improved upon by using nonlinear stiffness elements, especially for low-frequency vibrations. In this paper, an investigation is conducted into whether the same improvements can be made to a linear two-stage isolation system using the same methodology for both force and base excitation. The benefits of incorporating geometric stiffness nonlinearity in both upper and lower stages are studied. It is found that there are beneficial effects of using nonlinearity in the stiffness in both stages for both types of excitation. Further, it is found that this nonlinearity causes the transmissibility at the lower resonance frequency to bend to the right, but the transmissibility at the higher resonance frequency is not affected in the same way. Generally, it is found that a nonlinear two-stage system has superior isolation performance compared to that of a linear two-stage isolator.

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