Analysis of Subharmonic Resonance Response of the Time-Delayed System

2010 ◽  
Vol 163-167 ◽  
pp. 2910-2915 ◽  
Author(s):  
Hong Zhang ◽  
Xiao Hong Wu ◽  
Lei Zhang
Keyword(s):  
Amplitude Ratio ◽  
Harmonic Balance Method ◽  
Subharmonic Resonance ◽  
Feedback Gain ◽  
Incremental Harmonic Balance Method ◽  
Third Harmonic ◽  
System Parameters ◽  
Resonance Response ◽  
Exciting Frequency ◽  
The One

The subharmonic resonance response of the strongly nonlinear delay differential equation is solved using the incremental harmonic balance method. The value of the exciting frequency when the subharmonic resonance occurs is discussed. The influences of the time delay and the feedback gain on the system subharmonic resonance response are studied. The variation of the subharmonic resonance response with the system parameters is obtained. The results show that the value of the exciting frequency when the subharmonic resonance occurs is affected by the system parameters. The proportion of the one third harmonic in the amplitude increases rapidly with the increase of the exciting frequency. The variation of the amplitude ratio of the one third harmonic and the first harmonic is wavy type. The proportion of the one third harmonic in the amplitude decreases with increasing the displacement feedback gain and increases with increasing the velocity feedback gain. The proportion of the one third harmonic in the amplitude occupies a dominant position in the subharmonic resonance response.

scholarly journals Time-Delayed Feedback Control of Piezoelectric Elastic Beams under Superharmonic and Subharmonic Excitations

2019 ◽  
Vol 9 (8) ◽  
pp. 1557 ◽  
Author(s):  
Jian Peng ◽  
Mingjiao Xiang ◽  
Luxin Li ◽  
Hongxin Sun ◽  
Xiuyong Wang
Keyword(s):  
Feedback Control ◽  
Elastic Beam ◽  
Delayed Feedback ◽  
Subharmonic Resonance ◽  
Delayed Feedback Control ◽  
Feedback Gain ◽  
Control Gain ◽  
Resonance Response ◽  
And Control ◽  
Time Delayed Feedback

The time-delayed displacement feedback control is provided to restrain the superharmonic and subharmonic response of the elastic support beams. The nonlinear equations of the controlled elastic beam are obtained with the help of the Euler–Bernoulli beam principle and time-delayed feedback control strategy. Based on Galerkin method, the discrete nonlinear time-delayed equations are derived. Using the multiscale method, the first-order approximate solutions and stability conditions of three superharmonic and 1/3 subharmonic resonance response on controlled beams are derived. The influence of time-delayed parameters and control gain are obtained. The results show that the time-delayed displacement feedback control can effectively suppress the superharmonic and subharmonic resonance response. Selecting reasonably the time-delayed quantity and control gain can avoid the resonance region and unstable multi-solutions and improve the efficiency of the vibration control. Furthermore, with the purpose of suppressing the amplitude peak and governing the resonance stability, appropriate feedback gain and time delay are derived.

scholarly journals Dynamic and Stability Analysis of the Machine Hydrostatic Slide with Magnetorheological Damper

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Zhongkui Zhang ◽  
Feng Gao ◽  
Yan Li ◽  
Han Zhang
Keyword(s):  
Chaotic Behavior ◽  
Harmonic Balance Method ◽  
Mr Damper ◽  
Harmonic Excitation ◽  
Magnetorheological Damper ◽  
Incremental Harmonic Balance Method ◽  
Resonance Response ◽  
Incremental Harmonic Balance ◽  
Combined Action ◽  
Mr Fluid Damper

Tangential dynamic behaviors of the machine hydrostatic slide with a magnetorheological (MR) fluid damper are studied, and the effect of the MR damper to control the vibration of the hydrostatic slide is discussed. The dynamic model of the hydrostatic slide with the MR damper is established, and the tangential vibration equation of linear and nonlinear is derived. The multidimensional incremental harmonic balance method (MIHBM) with discrete Fourier transform (DFT) is derived by which the nonlinear response and stability of the system are studied. The resonance response of the Duffing equation under the combined action of harmonic excitation and constant excitation is obtained. In order to investigate the vibration response of the hydrostatic slide with the MR damper in detail, the bifurcation diagram, phase diagram, and Poincaré map are given. Finally, the dynamic response of the machine hydrostatic slide with the MR damper is discussed, and it is verified that the MR damper can suppress the tangential vibration of the hydrostatic slide effectively and the constant controller can control the chaotic behavior of the system well.

Effects of nonlinear interactions of flexural modes on the performance of a beam autoparametric vibration absorber

2019 ◽  
Vol 26 (7-8) ◽  
pp. 459-474
Author(s):  
Saeed Mahmoudkhani ◽  
Hodjat Soleymani Meymand
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Continuation Method ◽  
Harmonic Balance Method ◽  
Vibration Absorber ◽  
Primary System ◽  
Lumped Mass ◽  
Response Curves ◽  
Internal Resonances ◽  
The One

The performance of the cantilever beam autoparametric vibration absorber with a lumped mass attached at an arbitrary point on the beam span is investigated. The absorber would have a distinct feature that in addition to the two-to-one internal resonance, the one-to-three and one-to-five internal resonances would also occur between flexural modes of the beam by tuning the mass and position of the lumped mass. Special attention is paid on studying the effect of these resonances on increasing the effectiveness and extending the range of excitation amplitudes at which the autoparametric vibration absorber remains effective. The problem is formulated based on the third-order nonlinear Euler–Bernoulli beam theory, where the assumed-mode method is used for deriving the discretized equations of motion. The numerical continuation method is then applied to obtain the frequency response curves and detect the bifurcation points. The harmonic balance method is also employed for detecting the type of internal resonances between flexural modes by inspecting the frequency response curves corresponding to different harmonics of the response. Parametric studies on the performance of the absorber are conducted by varying the position and mass of the lumped mass, while the frequency ratio of the primary system to the first mode of the beam is kept equal to two. Results indicated that the one-to-five internal resonance is especially responsible for the considerable enhancement of the performance.

scholarly journals Dynamic Characteristics of the Bouc–Wen Nonlinear Isolation System

2021 ◽  
Vol 11 (13) ◽  
pp. 6106
Author(s):  
Zhiying Zhang ◽  
Xin Tian ◽  
Xin Ge
Keyword(s):  
Dynamic Characteristics ◽  
Seismic Isolation ◽  
Influence Factors ◽  
Harmonic Balance Method ◽  
Control Parameters ◽  
Hysteretic Model ◽  
Incremental Harmonic Balance Method ◽  
Isolation System ◽  
Nonlinear Dynamic Characteristics ◽  
Incremental Harmonic Balance

The Bouc–Wen nonlinear hysteretic model has many control parameters, which has been widely used in the field of seismic isolation. The isolation layer is the most important part of the isolation system, which can be effectively simulated by the Bouc–Wen model, and the isolation system can reflect different dynamic characteristics under different control parameters. Therefore, this paper mainly studies and analyzes the nonlinear dynamic characteristics of the isolation system under different influence factors based on the incremental harmonic balance method, which can provide the basis for the dynamic design of the isolation system.

scholarly journals Comparison of Common Methods in Dynamic Response Predictions of Rotor Systems with Malfunctions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongliang Yao ◽  
Qian Zhao ◽  
Qi Xu ◽  
Bangchun Wen
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Newmark Method ◽  
Incremental Harmonic Balance Method ◽  
Rotor Systems ◽  
Double Frequency ◽  
Frequency Domain Methods ◽  
Incremental Harmonic Balance

The efficiency and accuracy of common time and frequency domain methods that are used to simulate the response of a rotor system with malfunctions are compared and analyzed. The Newmark method and the incremental harmonic balance method are selected as typical representatives of time and frequency domain methods, respectively. To improve the simulation efficiency, the fixed interface component mode synthesis approach is combined with the Newmark method and the receptance approach is combined with the incremental harmonic balance method. Numerical simulations are performed for rotor systems with single and double frequency excitations. The inherent characteristic that determines the efficiency of the two methods is analyzed. The results of the analysis indicated that frequency domain methods are suitable single and double frequency excitation rotor systems, whereas time domain methods are more suitable for multifrequency excitation rotor systems.

Nonlinear Dynamics of One-Way Clutches in Belt-Pulley Systems

2003 ◽  
Author(s):  
Farong Zhu ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Excitation Amplitude ◽  
Relative Displacement ◽  
Second Primary ◽  
Arc Length ◽  
The One

One-way clutches are frequently used in the serpentine belt accessory drives of automobiles and heavy vehicles. The clutch plays a role similar to a vibration absorber in order to reduce belt/pulley vibration and noise and increase belt life. This paper analyzes a two-pulley system where the driven pulley has a one-way clutch between the pulley and accessory shaft that engages only for positive relative displacement between these components. The belt is modeled with linear springs that transmit torque from the driving pulley to the accessory pulley. The one-way clutch is modeled as a piecewise linear spring with discontinuous stiffness that separates the driven pulley into two degrees of freedom (DOF). The harmonic balance method (HBM) combined with arc-length continuation is employed to illustrate the nonlinear dynamic behavior of the one-way clutch. HBM with arc-length continuation yields the stable and unstable periodic solutions for given parameters. These solutions are examined across a range of excitation frequencies. The results are confirmed by numerical integration and the widely used bifurcation software AUTO. At the first primary resonance, most of the responses are aperiodic, including quasiperiodic and chaotic solutions. At the second primary resonance, the peak bends to the left with classical softening nonlinearity because clutch disengagement decouples the pulley and the accessory over portions of the response period. The dependence on system parameters such as clutch stiffness, excitation amplitude, and inertia ratio between the pulley and accessory is studied to characterize the nonlinear dynamics across a range of conditions.

scholarly journals Friction Damper Optimisation: Simulation of Rainbow Tests

1999 ◽  
Author(s):  
Kenan Y. Sanliturk ◽  
David J. Ewins ◽  
Robert Elliott ◽  
Jeff S. Green
Keyword(s):  
Harmonic Balance Method ◽  
Lumped Parameter Model ◽  
Friction Damper ◽  
Blade Vibration ◽  
Friction Dampers ◽  
Lumped Parameter ◽  
Engine Order ◽  
Resonance Response ◽  
Theoretical Predictions ◽  
Different Characteristics

Friction dampers have been used to reduce turbine blade vibration levels for a considerable period of time. However, optimal design of these dampers has been quite difficult due both to a lack of adequate theoretical predictions and to difficulties in conducting reliable experiments. One of the difficulties of damper weight optimisation via the experimental route has been the inevitable effects of mistuning. Also, conducting separate experiments for different damper weights involves excessive cost. Therefore, current practice in the turbomachinery industry has been to conduct so-called ‘rainbow tests’ where friction dampers with different weights are placed between blades with a predefined configuration. However, it has been observed that some rainbow test results have been difficult to interpret and have been inconclusive for determining the optimum damper weight for a given bladed-disc assembly. A new method of analysis — a combination of Harmonic Balance Method and structural modification approaches — is presented in this paper for the analysis of structures with friction interfaces and the method is applied to search for qualitative answers about the so-called ‘rainbow tests’ in turbomachinery applications. A simple lumped-parameter model of a bladed-disc model was used and different damper weights were modelled using friction elements with different characteristics. Resonance response levels were obtained for bladed discs with various numbers of blades under various engine-order excitations. It was found that rainbow tests, where friction dampers with different weights are used on the same bladed-disc assembly, can be used to find the optimum damper weight if the mode of vibration concerned has weak blade-to-blade coupling (the case where the disc is almost rigid and blades vibrate almost independently from each other). Otherwise, it is very difficult to draw any reliable conclusion from such expensive experiments.

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