Numerical Study of a New Variable Friction TMD

2011 ◽  
Vol 243-249 ◽  
pp. 5450-5457 ◽  
Author(s):  
Li Qin ◽  
Wei Ming Yan ◽  
Sheng Bo Guo
Keyword(s):  
Frequency Response ◽  
Numerical Study ◽  
Damping Ratio ◽  
Harmonic Balance Method ◽  
Structural Response ◽  
Harmonic Excitation ◽  
Response Curves ◽  
Equivalent Damping ◽  
Response Characteristics ◽  
Variable Friction

The paper proposes a new variable friction system, of which the friction force can increase linearly with the displacement of system. This new system can be used in TMD to avoid the disadvantage of Coulomb friction TMD. Using first order harmonic balance method, the equivalent damping ratio and frequency of SDOF variable friction system is deduced and analyzed. The frequency response characteristics of SDOF variable friction system is discussed. The control effectiveness of variable friction TMD under harmonic excitation is analyzed theoretically. The results demonstrate that the frequency response curves of variable friction TMD and classically damped TMD are similar and both can effectively reduce structural response under harmonic excitation.

Bifurcation Modes of Periodic Solution in a Duffing System Under Constant Force as Well as Harmonic Excitation

2019 ◽  
Vol 29 (13) ◽  
pp. 1950173 ◽  
Author(s):  
Lei Hou ◽  
Xiaochao Su ◽  
Yushu Chen
Keyword(s):  
Frequency Response ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Nonlinearity Parameter ◽  
Constant Force ◽  
Response Curves ◽  
Duffing System ◽  
Singularity Method

This paper focuses on the classification of the bifurcation modes of a Duffing system under the combined excitations of constant force and harmonic excitation. The Harmonic Balance method combined with the arc-length continuation is used to obtain the periodic solutions of the system, and the Floquet theory is employed to analyze the stability of the corresponding solutions. Accordingly, the frequency-response curves affected respectively by the constant force and the magnitude of the harmonic excitation are analyzed to show the basic dynamical properties of the system. Afterwards, the bifurcation investigations are carried out with the aid of the two-state variable singularity method. It is derived that there are a total of six different types of bifurcation modes due to the effects of the constant force and the magnitude of the harmonic excitation. At last, the effects of the nonlinearity parameter and the damping ratio on the bifurcation modes of the system are also discussed. The results obtained in this paper extend the findings in reference that the system can have markedly three types of frequency-response curves: with only one solution, or with maximum three or five solutions for a certain excitation frequency, and contribute to a better understanding of the significant influence of the constant force.

Analysis and experimental study on dynamic characteristics of an integrated quasi-zero stiffness isolator

2021 ◽  
pp. 1-28
Author(s):  
Haiping Liu ◽  
Kaili Xiao ◽  
Qi Lv ◽  
Yunlong Ma
Keyword(s):  
Frequency Response ◽  
High Reliability ◽  
Dynamic Performance ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Engineering Practice ◽  
Lumped Mass ◽  
Response Curves ◽  
Force Transmissibility ◽  
Force Excitation

Abstract The dynamic performance of an integrated quasi-zero stiffness (IQZS) isolator which is constructed by a single elastic structure is investigated in this study. This prototype exhibits the characteristics of the best simplicity, high reliability and without friction by using the minimum number of elements. For completeness, the static properties of the IQZS isolator are provided at first. And then, the dynamic behavior is analyzed and the frequency response under harmonic excitation is derived by using an equivalent mechanical model. Frequency response curves (FRCs) are obtained by using the harmonic balance method (HBM) under force excitation condition. Moreover, the dynamic performance of the nonlinear isolator supporting a lumped mass is investigated by using force transmissibility, which are derived by modelling and compared with an equivalent linear system with the same design parameter values. The isolation performance of the nonlinear isolator outperforms the linear counterpart for providing a larger isolation range. The effects of system parameters on the transmissibility are also examined. At last, the comparison between the analytical and experimental results under force excitation shows that the analytical model of the IQZS isolator is accuracy in terms of force transmissibility. The calculation results discussed may provide a theoretical basis for designing this class of IQZS isolator in engineering practice.

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 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.

Theoretical and experimental studies of a novel nested oscillator with a high-damping characteristic

2020 ◽  
pp. 107754632094378
Author(s):  
Haiping Liu ◽  
Kaili Xiao ◽  
PengPeng Zhao ◽  
Dongmei Zhu
Keyword(s):  
Resonant Frequency ◽  
Vibration Suppression ◽  
Damping Ratio ◽  
Experimental Studies ◽  
Harmonic Balance Method ◽  
Design Parameters ◽  
Base Excitation ◽  
Oscillation System ◽  
Equivalent Damping ◽  
Vibration Transmissibility

Stiffness and damping of a structure usually show the opposite change so that the resonant frequency and the static load bearing capacity of a mechanical system often exhibit contradiction. To solve this dilemma, a novel high-damping oscillator which is constructed by a nested diamond structure with the purpose of enhancing the damping property is proposed in this study without reducing the overall systematic stiffness. The mathematical model and geometrical relationships are established at first. And then, the steady-state solutions under base excitation are derived by using the harmonic balance method and further verified by numerical simulation. In addition, the effects of some design parameters on the equivalent damping ratio for the high-damping oscillator are studied to reveal the nonlinear characteristic. Besides, the natural frequency of the nonlinear oscillator is also presented and investigated. By using the displacement transmissibility and comparing with the traditional linear isolator with the same overall stiffness, the vibration suppression performance of the high-damping oscillator is addressed. The obtained calculating results demonstrate that the vibration control performance of the high-damping oscillator outperforms the linear counterpart around resonant frequency. Moreover, the influences of systematic parameters of the high-damping oscillator for the base excitation case on the vibration transmissibility are also discussed, respectively. Finally, an experimental campaign is conducted on an in-house-built test rig to corroborate the accuracy of the analytical solutions of the high-damping oscillation system. The results discussed in this study provide a useful guideline, which can help to design this class of high-damping oscillation system.

Dynamic response of a concrete dam impounding an ice-covered reservoir: Part II. Parametric and numerical study

2004 ◽  
Vol 31 (6) ◽  
pp. 965-976 ◽  
Author(s):  
Najib Bouaanani ◽  
Patrick Paultre ◽  
Jean Proulx
Keyword(s):  
Dynamic Response ◽  
Frequency Response ◽  
Parametric Study ◽  
Seismic Analysis ◽  
Numerical Study ◽  
Ice Cover ◽  
Concrete Dams ◽  
Response Curves ◽  
Concrete Dam ◽  
Structure Interaction

This paper presents a numerical and parametric study of the effect of an ice cover on the dynamic response of a concrete dam using the approach proposed in the companion paper in this issue. The method was programmed and implemented in a finite element code specialized for the seismic analysis of concrete dams. The 84-m-high Outardes 3 concrete gravity dam in northeastern Quebec was chosen as a model for this research. Some basic aspects of the numerical model are established in this paper and we show that the ice cover affects the dynamic response of the ice–dam–reservoir system. Main features of this influence are emphasized and discussed in a parametric study through the analysis of: (i) acceleration frequency response curves at the dam crest, (ii) hydrodynamic frequency response curves inside the reservoir, and (iii) the hydrodynamic pressure distribution on the upstream face of the dam. Key words: gravity dams, concrete dams, ice, reservoirs, mathematical models, ice–structure interaction, fluid–structure interaction, forced-vibration testing, finite elements modelling.

scholarly journals Serotonin 1B Receptor Modulates Frequency Response Curves and Spectral Integration in the Inferior Colliculus by Reducing GABAergic Inhibition

2008 ◽  
Vol 100 (3) ◽  
pp. 1656-1667 ◽  
Author(s):  
Laura M. Hurley ◽  
Jo Anne Tracy ◽  
Alexander Bohorquez
Keyword(s):  
Frequency Response ◽  
Inferior Colliculus ◽  
Extracellular Recording ◽  
Evoked Responses ◽  
Auditory Midbrain ◽  
Response Curves ◽  
Response Characteristics ◽  
Spectral Integration ◽  
Serotonin 1B Receptor

The selectivity of sensory neurons for stimuli is often shaped by a balance between excitatory and inhibitory inputs, making this balance an effective target for regulation. In the inferior colliculus (IC), an auditory midbrain nucleus, the amplitude and selectivity of frequency response curves are altered by the neuromodulator serotonin, but the changes in excitatory-inhibitory balance that mediate this plasticity are not well understood. Previous findings suggest that the presynaptic 5-HT1B receptor may act to decrease the release of GABA onto IC neurons. Here, in vivo extracellular recording and iontophoresis of the selective 5-HT1B agonist CP93129 were used to characterize inhibition within and surrounding frequency response curves using two-tone protocols to indirectly measure inhibition as a decrease in spikes relative to an excitatory tone alone. The 5-HT1B agonist attenuated such two-tone spike reduction in a varied pattern among neurons, suggesting that the function of 5-HT1B modulation also varies. The hypothesis that the 5-HT1B receptor reduces inhibition was tested by comparing the effects of CP93129 and the GABAA antagonists bicuculline and gabazine in the same neurons. The effects of GABAA antagonists on spike count, tuning bandwidth, two-tone ratio, and temporal response characteristics mimicked those of CP93129 across the neuron population. GABAA antagonists also blocked or reduced the facilitation of evoked responses by CP93129. These results are all consistent with the reduction of GABAA-mediated inhibition by 5-HT1B receptors in the IC, resulting in an increase in the level of evoked responses in some neurons, and a decrease in spectral selectivity in others.

scholarly journals Theoretical Design and Characteristics Analysis of a Quasi-Zero Stiffness Isolator Using a Disk Spring as Negative Stiffness Element

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Lingshuai Meng ◽  
Jinggong Sun ◽  
Wenjuan Wu
Keyword(s):  
Damping Ratio ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Steady State Solution ◽  
Excitation Amplitude ◽  
Response Curves ◽  
Disk Spring ◽  
Performance Effects ◽  
Characteristics Analysis ◽  
Isolation Performance

This paper presents a novel quasi-zero stiffness (QZS) isolator designed by combining a disk spring with a vertical linear spring. The static characteristics of the disk spring and the QZS isolator are investigated. The optimal combination of the configurative parameters is derived to achieve a wide displacement range around the equilibrium position in which the stiffness has a low value and changes slightly. By considering the overloaded or underloaded conditions, the dynamic equations are established for both force and displacement excitations. The frequency response curves (FRCs) are obtained by using the harmonic balance method (HBM) and confirmed by the numerical simulation. The stability of the steady-state solution is analyzed by applying Floquet theory. The force, absolute displacement, and acceleration transmissibility are defined to evaluate the isolation performance. Effects of the offset displacement, excitation amplitude, and damping ratio on the QZS isolator and the equivalent system (ELS) are studied. The results demonstrate that the QZS isolator for overloaded or underloaded can exhibit different stiffness characteristics with changing excitation amplitude. If loaded with an appropriate mass, excited by not too large amplitude, and owned a larger damper, the QZS isolator can possess better isolation performance than its ELS in low frequency range.

Vibration Control of Horizontally Excited Structures Utilizing Internal Resonance of Liquid Sloshing in Nearly Square Tanks

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Passive Control ◽  
Harmonic Excitation ◽  
Liquid Sloshing ◽  
Maximum Efficiency ◽  
System Response ◽  
Response Curves ◽  
System Parameters ◽  
Theoretical Results

Passive control of vibrations in an elastic structure subjected to horizontal, harmonic excitation by utilizing a nearly square liquid tank is investigated. When the natural frequency ratio 1:1:1 is satisfied among the natural frequencies of the structure and the two predominant sloshing modes (1,0) and (0,1), the performance of a nearly square tank as a tuned liquid damper (TLD) is expected to be superior to rectangular TLDs due to internal resonance. In the theoretical analysis, Galerkin's method is used to determine the modal equations of motion for liquid sloshing considering the nonlinearity of sloshing. Then, van der Pol's method is used to obtain the expressions for the frequency response curves for the structure and sloshing modes. Frequency response curves and bifurcation set diagrams are shown to investigate the influences of the aspect ratio of the tank cross section and the tank installation angle on the system response. From the theoretical results, the optimal values of the system parameters can be determined in order to achieve maximum efficiency of vibration suppression for the structure. Hopf bifurcations occur and amplitude modulated motions (AMMs) may appear depending on the values of the system parameters. Experiments were also conducted, and the theoretical results agreed well with the experimental data.

Frequency Response Characteristics of a Revolute Impact Pair

1993 ◽  
Author(s):  
Y. Wang
Keyword(s):  
Frequency Response ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Analytical Techniques ◽  
Single Frequency ◽  
Nonlinear Frequency ◽  
Response Characteristics ◽  
State Response ◽  
Existence And Stability ◽  
Nonlinear Frequency Response

Abstract Clearances in mechanical joints have deteriorating effects on the dynamic behavior of a machine in increasing noise and vibration and reducing the performance. In order to properly characterize these effects and to develop analytical techniques for machine design, it is necessary to investigate the dynamics associated with basic models of impacting systems. In this paper, we develop a method of harmonic balance to study a revolute impact pair. We focus on the characteristics of nonlinear frequency response of the system for a single frequency excitation. These characteristics include multiply-valued steady state response, multiple jump resonances, and existence and stability of these solutions. The effectiveness of the harmonic balance method combined with the Fast Fourier Transform technique is shown through numerical examples.

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