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.

An experimental study on vibration isolation performance of weft-knitted spacer fabrics

2016 ◽  
Vol 86 (20) ◽  
pp. 2225-2235 ◽  
Author(s):  
Fuxing Chen ◽  
Yanping Liu ◽  
Hong Hu
Keyword(s):  
Experimental Study ◽  
Vibration Isolation ◽  
Nonlinear Behavior ◽  
Harmonic Excitation ◽  
Excitation Level ◽  
Spacer Fabric ◽  
Spacer Fabrics ◽  
Vibration Isolation Performance ◽  
Isolation Performance ◽  
Load Mass

This paper presents an experimental study on the vibration isolation performance of weft-knitted spacer fabrics under forced harmonic excitation. The weft-knitted spacer fabrics with two different thicknesses were first designed by varying the linking distance of the spacer monofilament and fabricated using an electronic flat knitting machine. Then, their vibration isolation performance was tested under forced vibration condition via sinusoidal sweeps from low to high frequencies. The typical acceleration transmissibility curve and effects of fabric thickness, load mass and excitation level were discussed in detail. The results obtained show that the thicker spacer fabric has a lower resonance frequency than the thinner fabric due to lower stiffness, and thus can isolate the vibration at a lower frequency level. The results also show that changing the load mass and excitation level changes the loading conditions of the fabric structure, and thus also changes fabric stiffness and vibration isolation performance due to nonlinear behavior of spacer fabrics. It is expected that this study could provide some useful information to promote the application of weft-knitted spacer fabrics for vibration isolation.

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.

Nonlinear Vibration by Asynchronous Excitation Force in Friction Damper of Turbine Blade

2020 ◽  
Author(s):  
Ryuichi Umehara ◽  
Haruko Shiraishi ◽  
Naoki Onozato ◽  
Tetsuya Shimmyo
Keyword(s):  
Nonlinear Vibration ◽  
Turbine Blade ◽  
Gas Turbines ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Time History ◽  
Harmonic Excitation ◽  
Friction Damper ◽  
Excitation Force ◽  
Force Components

Abstract Turbine blades are now being used under increasingly severe conditions in order to increase the thermal efficiency of gas turbines. Friction dampers are often used to reduce the vibration of the blade and improve the plant reliability. This is a general study dealing with resonance passing where the natural frequency of the turbine blade coincides with the frequency of specific harmonic excitation forces while increasing the turbine rotation speed. Asynchronous components of excitation forces are also considered in addition to the synchronous components caused by specific harmonic excitation forces. In this study, a new method for predicting the characteristics of nonlinear vibration under excitation force including both synchronous and asynchronous force components is developed. In order to investigate the effect of additional asynchronous loading, time history response analyses considering nonlinear vibration using simulated turbine blades were conducted. Results showed that friction damper slip can be induced by the presence of the additional asynchronous excitation force components even for low values of synchronous excitation force. It is shown that it is possible to use a calibration factor to predict vibration characteristics considering friction slipping by estimating the ratio of the total excitation force to the single harmonic excitation force. To verify the effect of asynchronous excitation force and the validity of the proposed correction method, verification tests were conducted experimentally. The experimental results show that friction slipping occurred under small harmonic excitation force when there was asynchronous excitation force and show good agreement with the numerical results. Moreover, the validity of the proposed method which corrects the dynamic characteristics obtained using of the first order harmonic balance method is confirmed.

Vibration Suppression of a Harmonically Forced Oscillator Using a Passive Nonlinear Vibration Absorber

2020 ◽  
Author(s):  
Bo Yu
Keyword(s):  
Nonlinear Vibration ◽  
Analytical Solutions ◽  
Vibration Suppression ◽  
Harmonic Balance Method ◽  
Vibration Absorber ◽  
Harmonic Amplitude ◽  
Periodic Motions ◽  
Nonlinear Vibration Absorber ◽  
Approximate Analytical Solutions ◽  
Forced Oscillator

Abstract In this paper, the performance of a nonlinear vibration absorber with different nonlinearity is studied. The analytical solutions of periodic motions are obtained using the general harmonic balance method. As the nonlinear strength is weak, the effectiveness of the absorber is discussed. For strong nonlinearities, unstable parodic motions can be obtained and stabilities of the periodic motions are determined through the eigenvalue analysis. The Hopf and saddle bifurcations are observed. Numerical simulations are illustrated for both masses at the resonance peaks. The harmonic amplitude spectrums show the harmonic effects on periodic motions, and the corresponding accuracy of approximate analytical solutions.

Nonlinear Vibration Analysis of MEMS Micro-Beam Structure Acting by Multi-Couplings Factors

2011 ◽  
Author(s):  
Dengwei Huang ◽  
Shoujian Li ◽  
Changping Chen ◽  
Liming Dai
Keyword(s):  
Frequency Response ◽  
Nonlinear Vibration ◽  
Geometric Nonlinearity ◽  
Harmonic Balance Method ◽  
Beam Theory ◽  
Response Characteristic ◽  
Frequency Response Characteristic ◽  
Beam Structure ◽  
Damping Force ◽  
Air Damping

In this paper, the nonlinear vibration characteristics of the micro-beam structure acting by multi-couplings factors are investigated. Taking the nonlinear air damping force, alternating voltage excitation as well as the geometric nonlinearity of the micro-beam into account, the nonlinear vibration governing equations of the micro-beam are derived on the basis of the Euler-Bernoulli beam theory. The Galerkin method and harmonic balance method are adopted to obtain the amplitude-frequency response characteristic and phase-frequency response characteristic of the micro-beam structure. Then the effects of the nonlinear air damping force and the geometric nonlinearity on the resonance frequency and stiffness of micro-beam structure are analyzed.

Periodic Motion in a Nonlinear Vibration Isolator Under Harmonic Excitation

2017 ◽  
Author(s):  
Bo Yu ◽  
Albert C. J. Luo
Keyword(s):  
Nonlinear Vibration ◽  
Analytical Solutions ◽  
Periodic Motion ◽  
Harmonic Excitation ◽  
Eigenvalue Analysis ◽  
Harmonic Amplitude ◽  
Vibration Isolator ◽  
Periodic Motions ◽  
Approximate Analytical Solutions ◽  
Forced Oscillator

In this paper, periodic motions of a periodically forced oscillator with a nonlinear isolator are studied through generalized harmonic balanced method. Both symmetric and asymmetric period-1 motions are obtained. Stability and bifurcation of the periodic motions are determined through eigenvalue analysis. Numerical illustrations of both symmetric and asymmetric are given. From the harmonic amplitude spectrums, the harmonic effects on periodic motions are determined, and the corresponding accuracy of approximate analytical solutions can be observed.

Nonlinear vibration characteristics of the rotor bearing system with bolted flange joints

2019 ◽  
Vol 233 (4) ◽  
pp. 910-930
Author(s):  
Yifu Zhou ◽  
Zhong Luo ◽  
Zifang Bian ◽  
Fei Wang
Keyword(s):  
Nonlinear Vibration ◽  
Time Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Vibration Characteristics ◽  
Rotor System ◽  
Rotor Bearing ◽  
Bolted Flange ◽  
Bearing System

As sophisticated mechanical equipment, the rotor system of aero-engine is assembled by various parts; bolted flange joints are one of the essential ways of joints. Aiming at the analysis of the nonlinear vibration characteristics of the rotor-bearing system with bolted flange joints, in this paper, a finite element modeling method for a rotor-bearing system with bolted flange joints is proposed, and an incremental harmonic balance method combined with arc length continuation is proposed to solve the dynamic solution of the rotor system. In order to solve the rotor system with rolling bearing nonlinearity, the alternating frequency/time-domain process of the rolling bearing element is deduced. Compared with the conventional harmonic balance method and the time-domain method, this method has the characteristics of fast convergence and high computational efficiency; solving the rotor system with nonlinear bearing force; overcome the shortcoming that the frequency–response curve of the system is too sharp to continue solving. By using this method, the influence of bearing clearance and stiffness on vibration characteristics of the rotor system with bolted flange joints is studied. The evolution law of the state of the rotor system with bolt flange is investigated through numerical simulation and experimental data. The results indicated that the modeling and solving method proposed in this paper could accurately solve the rotor-bearing system with bolted flange joints and analyze its vibration characteristics.

scholarly journals Nonlinear Vibration Analysis of Damaged Microplate considering Size Effect

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jihai Yuan ◽  
Xiangmin Zhang ◽  
Changping Chen
Keyword(s):  
Size Effect ◽  
Frequency Response ◽  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Couple Stress Theory ◽  
Harmonic Balance Method ◽  
Damage Effect ◽  
Physical Parameters ◽  
Response Curves ◽  
Electrically Actuated

Since microplates are extensively used in MEMS devices such as microbumps, micromirrors, and microphones, this work aims to study nonlinear vibration of an electrically actuated microplate whose four edges are clamped. Based on the modified couple stress theory (MCST) and strain equivalent assumption, size effect and damage are taken into consideration in the present model. The dynamic governing partial differential equations of the microplate system were obtained using Hamilton’s principle and solved using the harmonic balance method after they are transformed into ordinary differential equation with regard to time. Size effect and damage effect on nonlinear free vibration of the microplate under DC voltage are discussed using frequency-response curve. In the forced vibration analysis, the frequency-response curves were also employed for the purpose of highlighting the influence of different physical parameters such as external excitation, damping coefficient, material length scale parameter, and damage variable when the system is under AC voltage. The results presented in this study may be helpful and useful for the dynamic stability of a electrically actuated microplate system.

scholarly journals The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Y. H. Qian ◽  
J. L. Pan ◽  
S. P. Chen ◽  
M. H. Yao
Keyword(s):  
Exact Solutions ◽  
Nonlinear Vibration ◽  
Harmonic Balance ◽  
Nonlinear Dynamical Systems ◽  
Harmonic Balance Method ◽  
Time History ◽  
Approximate Solutions ◽  
Balance Method ◽  
Lumped Mass ◽  
Strongly Nonlinear

The exact solutions of the nonlinear vibration systems are extremely complicated to be received, so it is crucial to analyze their approximate solutions. This paper employs the spreading residue harmonic balance method (SRHBM) to derive analytical approximate solutions for the fifth-order nonlinear problem, which corresponds to the strongly nonlinear vibration of an elastically restrained beam with a lumped mass. When the SRHBM is used, the residual terms are added to improve the accuracy of approximate solutions. Illustrative examples are provided along with verifying the accuracy of the present method and are compared with the HAM solutions, the EBM solutions, and exact solutions in tables. At the same time, the phase diagrams and time history curves are drawn by the mathematical software. Through analysis and discussion, the results obtained here demonstrate that the SRHBM is an effective and robust technique for nonlinear dynamical systems. In addition, the SRHBM can be widely applied to a variety of nonlinear dynamic systems.

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