Internal Resonance Analysis for Electromechanical Integrated Toroidal Drive

2010 ◽  
Vol 5 (4) ◽  
Author(s):  
Xiuhong Hao Lizhong Xu
Keyword(s):  
Free Vibration ◽  
Internal Resonance ◽  
Energy Exchange ◽  
Forced Response ◽  
Drive System ◽  
Design Stage ◽  
Internal Resonances ◽  
Resonance Analysis ◽  
Electromechanical Integrated ◽  
Electromechanical Coupled

In this paper, the electromechanical coupled nonlinear equations for the electromechanical integrated toroidal drive are proposed. Using the equations, the free vibration and forced response under internal resonance are investigated. The effects of the drive parameters on the resonance are investigated. Three different resonance types exist for the different drive parameters. They are the normal resonance, internal resonance, and jump vibration between the normal and internal resonances. Compared with the normal resonance without internal resonance, the internal resonance has a large amplitude and the energy exchange occurs between the vibrations of the different components. The resonance types of the drive system are dependent on the electromechanical parameters of the drive system. In the design stage, one can select properly the electromechanical parameters of the drive system to remove the internal resonance and the jump vibration.

Forced Response of Electromechanical Integrated Electrostatic Harmonic Drive to Voltage Excitation

2007 ◽  
Author(s):  
Lizhong Xu ◽  
Cuirong Zhu ◽  
Lei Qin ◽  
Yanling Zao
Keyword(s):  
Forced Response ◽  
Drive System ◽  
Harmonic Drive ◽  
Frequency Responses ◽  
Electromechanical Integrated ◽  
Generalized Force ◽  
Electric Field Force ◽  
Exciting Voltage ◽  
Generalized Coordinate ◽  
Electromechanical Coupled

In this paper, a micro electromechanical integrated electrostatic harmonic drive system is presented. The operating principle of the MEMS is introduced. The exciting electric field force under exciting voltage is given. Based on the electromechanical coupled dynamic equations of the drive system, by generalized force and generalized coordinate, the forced response of the drive system to voltage excitation are obtained. The forced frequency responses of the drive system to voltage excitation are investigated. Changes of the frequency response along with the system parameters are given as well.

scholarly journals Nonlinear Forced Response of Electromechanical Integrated Toroidal Drive to Coupled Excitation

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Lizhong Xu ◽  
Fen Wang
Keyword(s):  
Natural Frequencies ◽  
Forced Response ◽  
Drive System ◽  
Mesh Stiffness ◽  
Electric Excitation ◽  
Time Period ◽  
Electromechanical Integrated ◽  
Exciting Frequency ◽  
Mesh Parameter ◽  
Forced Responses

The electric excitation and the parameter excitation from mesh stiffness fluctuation are analyzed. The forced response equations of the drive system to the coupled excitations are presented. For the exciting frequencies far from and near natural frequencies, the forced responses of the drive system to the coupled excitations are investigated. Results show that the nonlinear forced responses of the drive system to the coupled excitations change periodically and unsteadily; the time period of the nonlinear forced responses depends on the frequencies of the electric excitation, the mesh parameter excitation, and the nonlinear natural frequencies of the drive system; in order to improve the dynamics performance of the drive system, the frequencies of the electric excitations should not be taken as integral multiple of the mesh parameter exciting frequency.

Nonlinear Free Vibration for Electromechanical Integrated Toroidal Drive

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Lizhong Xu ◽  
Fen Wang ◽  
Xiuhong Hao
Keyword(s):  
Operating Performance ◽  
Free Vibrations ◽  
Drive System ◽  
Vibration Frequencies ◽  
Mesh Stiffness ◽  
Nonlinear Free Vibration ◽  
System Parameters ◽  
Noise Radiation ◽  
Electromechanical Integrated ◽  
Electromechanical Coupled

Electromechanical integrated toroidal drive is an electromechanical coupled dynamics system. Here, the electromagnetic nonlinearity occurs which has important effects on the operating performance of the drive system. In this paper, the electromagnetic mesh stiffness is presented and nonlinear electromechanical coupled dynamic equations are deduced. Using the perturbation method, the nonlinear free vibrations of the drive system are investigated. Changes of the nonlinear vibration frequencies along with the system parameters are given. Results show that the electromagnetic nonlinearity has obvious effects on the vibration frequencies of the drive system. The results are useful in maximizing the power density of the drive system and reducing noise radiation.

LATERAL-FLEXURAL AND TORSIONAL VIBRATIONS OF FLEXIBLE RING FOR ELECTROMECHANICAL INTEGRATED ELECTROSTATIC HARMONIC ACTUATOR

2009 ◽  
Vol 09 (03) ◽  
pp. 391-409
Author(s):  
LIZHONG XU ◽  
YAOWU LI
Keyword(s):  
Natural Frequency ◽  
Dynamic Equation ◽  
Forced Response ◽  
Dynamic Responses ◽  
Torsional Vibrations ◽  
Vibration Modes ◽  
System Parameters ◽  
Electromechanical Integrated ◽  
Flexible Ring ◽  
Electromechanical Coupled

This paper presents an electromechanical coupled dynamic equation for the lateral-flexural and torsional vibrations of a flexible ring for an electromechanical integrated electrostatic harmonic actuator as well as the equation of the forced response of the electromechanical integrated electrostatic harmonic actuator to voltage excitation. By solving these equations, the natural frequency and vibration modes of the flexible ring for the actuator are investigated. Changes in the natural frequency with respect to the main system parameters are also examined and the dynamic responses of the actuator to voltage excitation obtained.

Non-Linear Vibration Behaviour of an Axial Compressor Rotor Blade

2015 ◽  
Author(s):  
Caetano Peng ◽  
Tomokazu Miyakozawa ◽  
Thomas Schroeter ◽  
Jan Schnitzler ◽  
Ian Lyndon
Keyword(s):  
Internal Resonance ◽  
Natural Frequencies ◽  
Forced Response ◽  
Contact Friction ◽  
Vibration Modes ◽  
Linear Temperature Dependence ◽  
Internal Resonances ◽  
Blade Vibration ◽  
Modal Response ◽  
Non Linear

There has been some concern that the blades in the real engine operating environment may not always behave in a linear manner. The non-linearity can arise from friction contact surfaces (i.e. blade dovetails and discs), non-linear material properties (i.e. Young’s modulus, non-linear temperature dependence of modulus), component manufacturing variability, and component design geometry. The vibration forcing itself can also cause multi-modal responses when applied as multi-mode excitation. The present study aims at investigating the effects of static contact friction loads on the blade vibration responses. Moreover, some natural frequencies of the blade investigated here are commensurable and thus leading to internal resonance in the system and nonlinear interactions between involved modes. This investigation shows that some blade vibration modes are more sensitive to the blade root friction loads than others. This sensitivity is associated with modeshape localisations. The other source of non-linear behavior is related to internal resonances. This particular blade geometry affects the blade stiffness in such a way that some natural frequencies are commensurable. For instance, there is an internal resonance between the first and second torsion modes. The modal frequency of second torsion is twice the first torsion frequency. Both the non-linearity effects associated with contact friction loads and internal resonances seem to result from the interactions of two or more natural vibration modes. There is a dominant modal response among the interacting modes. Fast Fourier Transforms (FFT) of response histories also reveals the contribution of individual modes in the multi-modal response. This paper attempts to address this non-linear blade behaviour by conducting both experimental tests and numerical simulations using an in-house forced response code.

Internal Resonance of Plane Waves in Nonlinear Lattices

2019 ◽  
Author(s):  
Matthew D. Fronk ◽  
Michael J. Leamy
Keyword(s):  
Internal Resonance ◽  
Energy Exchange ◽  
New Technology ◽  
Signal Transmission ◽  
Equations Of Motion ◽  
Plane Waves ◽  
Local Analysis ◽  
Internal Resonances ◽  
Single Wave ◽  
Direct Numerical Integration

Abstract Recent studies have employed perturbation techniques to derive amplitude-dependent band structures in nonlinear periodic materials. The associated applications include amplitude-dependent filters, waveguides, and diodes. However, for a range of frequencies and wavenumbers, perturbation-based dispersion corrections for a single wave break-down due to internal resonance between the primary wave and its nonlinearity-induced higher-harmonics. This work presents a perturbation analysis of one-dimensional plane waves in lattices with internal resonances. The exchange of energy between propagating modes within the same branch of the lattice’s band structure is considered, and the stability of the energy exchange is assessed through a local analysis. Direct numerical integration of the lattice equations of motion validates the analytical expressions for energy exchange. These findings can be used to resolve discontinuities in band diagrams that do not account for internal resonances and may inspire new technology that enables long-range coherent signal transmission in nonlinear media.

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 Tuning nonlinear damping in graphene nanoresonators by parametric–direct internal resonance

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ata Keşkekler ◽  
Oriel Shoshani ◽  
Martin Lee ◽  
Herre S. J. van der Zant ◽  
Peter G. Steeneken ◽  
...  
Keyword(s):  
Parametric Resonance ◽  
Internal Resonance ◽  
Microscopic Theory ◽  
Fold Increase ◽  
Nonlinear Damping ◽  
Supporting Evidence ◽  
Nonlinear Dissipation ◽  
Modal Interactions ◽  
Solid State Physics ◽  
Internal Resonances

AbstractMechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. To date, no experimental evidence of this enhancement has been realized. In this letter, we experimentally show that nanoresonators driven into parametric-direct internal resonance provide supporting evidence for the microscopic theory of nonlinear dissipation. By regulating the drive level, we tune the parametric resonance of a graphene nanodrum over a range of 40–70 MHz to reach successive two-to-one internal resonances, leading to a nearly two-fold increase of the nonlinear damping. Our study opens up a route towards utilizing modal interactions and parametric resonance to realize resonators with engineered nonlinear dissipation over wide frequency range.

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