scholarly journals Nonlinear Dynamics of Electrostatic Comb-drive with Variable Gap Under Harmonic Excitation

2021 ◽  
Author(s):  
Alexey V. Lukin ◽  
Dmitry Indeitsev ◽  
Ivan Popov ◽  
Nadezhda Mozhgova
Keyword(s):  
Nonlinear Dynamics ◽  
Frequency Response ◽  
Resonant Mode ◽  
Harmonic Excitation ◽  
Extensive Study ◽  
Force Response ◽  
Comb Drive ◽  
Elastic Suspension ◽  
Stationary Electrode ◽  
Mode Characteristics

Abstract This paper provides an extensive study of the nonlinear dynamics of a variable gap electrostatic comb-drive. The amplitude- and phase-frequency response, as well as the amplitude- and phase-force response of the comb-drive were obtained and analyzed with and without taking into account the cubic nonlinearity of the suspension. A significant variation in the frequency and force response is demonstrated in the presence of nonlinearity of the elastic suspension. Using numerical methods of bifurcation theory, solutions are obtained that correspond to the resonance peak of the frequency response when the constant and variable components of the voltages change. The result obtained makes it possible to determine the range of excitation voltage values that provide the required vibration amplitude in the resonant mode. The influence of the second stationary electrode on the dynamics of the system is estimated. The significant influence of this factor on the resonant-mode characteristics is revealed.

Nonlinear Dynamics of a Dielectric Elastomer Membrane Under Compressive Loading

2020 ◽  
Author(s):  
Robert L. Lowe ◽  
Christopher G. Cooley
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Frequency Response ◽  
Compressive Loading ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Dielectric Elastomer ◽  
Large Strains ◽  
Membrane Stretch ◽  
Wide Range

Abstract This paper investigates the nonlinear dynamics of square dielectric elastomer membranes under time-dependent, through-thickness compressive loading. The dielectric elastomer is modeled as an isotropic ideal dielectric, with mechanical stiffening at large strains captured using the Gent hyperelastic constitutive model. The equation of motion for the in-plane membrane stretch is derived using Hamilton’s principle. The static response of the membrane is first investigated, with equilibrium stretches calculated numerically for a wide range of compressive pre-loads and applied voltages. Snap-through instabilities are observed, with the critical snap-through voltage decreasing with increasing compressive pre-load. The dynamic response of the membrane is then investigated under forced harmonic excitation. Frequency response plots characterizing the steady-state vibration reveal primary, subharmonic, and superharmonic resonances. Near these resonances, two stable vibration states are possible, corresponding to upper and lower branches in the frequency response. Significant and practically meaningful differences in the dynamic response are observed when the system vibrates at a fixed frequency about the upper and lower branches, a feature not discussed in previous research.

A parametric analysis of the nonlinear dynamics of bistable vibration-based piezoelectric energy harvesters

2020 ◽  
pp. 1045389X2096318
Author(s):  
Luã Guedes Costa ◽  
Luciana Loureiro da Silva Monteiro ◽  
Pedro Manuel Calas Lopes Pacheco ◽  
Marcelo Amorim Savi
Keyword(s):  
Nonlinear Dynamics ◽  
Energy Harvesting ◽  
Parametric Analysis ◽  
Electromechanical Coupling ◽  
Performance Enhancement ◽  
Piezoelectric Materials ◽  
Electrical Power ◽  
Harmonic Excitation ◽  
Piezoelectric Energy ◽  
Harvesting Systems

Piezoelectric materials exhibit electromechanical coupling properties and have been gained importance over the last few decades due to their broad range of applications. Vibration-based energy harvesting systems have been proposed using the direct piezoelectric effect by converting mechanical into electrical energy. Although the great relevance of these systems, performance enhancement strategies are essential to improve the applicability of these system and have been studied substantially. This work addresses a numerical investigation of the influence of cubic polynomial nonlinearities in energy harvesting systems considering a bistable structure subjected to harmonic excitation. A deep parametric analysis is carried out employing nonlinear dynamics tools. Results show complex dynamical behaviors associated with the trigger of inter-well motion. Electrical power output and efficiency are monitored in order to evaluate the configurations associated with best system performances.

Resonant mode characteristics of a cajón drum and its effect on sound directivity

2016 ◽  
Vol 139 (4) ◽  
pp. 2203-2203
Author(s):  
Michael H. Denison ◽  
K. J. Bodon ◽  
Kent L. Gee
Keyword(s):  
Resonant Mode ◽  
Mode Characteristics

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.

Nonlinear Dynamics of Interconnected Structures: An Application to DNA Dynamics

2005 ◽  
Author(s):  
Amit Shukla
Keyword(s):  
Nonlinear Dynamics ◽  
Base Pair ◽  
Harmonic Excitation ◽  
Dna Dynamics ◽  
Base Pairs ◽  
Dna Base ◽  
Dna Base Pairs ◽  
Genetic Features ◽  
Nonlinear Potential ◽  
Single Base Pair

Nonlinear dynamics of DNA base-pairs is essential in many of the genetic features and functions of the molecule. The motion of the base-pair is influenced by the nonlinear potential between the two nucleotides as well as the adjacent base-pairs. In this paper nonlinear dynamics of the base-pairs is investigated. A single degree-of-freedom model for the base-pair dynamics as proposed by Peyrard-Bishop-Dauxois is analyzed. First a single base-pair dynamics is investigated using perturbation method. Then a three base-pair model is numerically investigated to understand the nonlinear response of the system to a harmonic excitation. Finally, it is also shown that the effect of interconnection can be minimized by selecting the environment surrounding the DNA molecule.

Stability Analysis of a Linearized MEMS

2004 ◽  
Author(s):  
A. Khazaei ◽  
M. Rastgaar Aagaah ◽  
M. Mahinfalah ◽  
N. Mahmoudian ◽  
G. Nakhaie Jazar
Keyword(s):  
Nonlinear Dynamics ◽  
Stability Analysis ◽  
Frequency Response ◽  
Dynamic Behavior ◽  
Stability Theory ◽  
Perturbation Methods ◽  
Time Varying ◽  
Design And Optimization ◽  
System Parameters ◽  
The Stability

This paper presents the stability theory and dynamic behavior of a micro-mechanical parametric-effect resonator. The device is a MEMS time-varying capacitor. The nonlinear dynamics of the MEMS are investigated analytically, and numerically. Applying perturbation methods, and deriving an analytical equation to describe the frequency response of the system enables the designer to study the effect of changes in the system parameters that can be used for design and optimization of the system.

scholarly journals Nonlinear Dynamics of a Planar Hinged-Supported Beam with One End Lumped Mass and Longitudinal Elastic Support

2018 ◽  
Vol 241 ◽  
pp. 01016 ◽  
Author(s):  
Lukasz Kloda ◽  
Stefano Lenci ◽  
Jerzy Warminski
Keyword(s):  
Nonlinear Dynamics ◽  
Finite Element Method ◽  
Frequency Response ◽  
Spring Stiffness ◽  
Lumped Mass ◽  
Response Curves ◽  
Simply Supported ◽  
Softening Behaviour ◽  
Damped Oscillations ◽  
Linear Spring

Nonlinear forced-damped oscillations of a non-slender hinged simply supported beam with mass and spring attached to one end are investigated by mean of a finite element method. The frequency response curves are constructed numerically and the variability of hardening/softening behaviour of frequency response curves due to the lumped mass and axial linear spring stiffness is investigated. Resonant and sub resonant motion of beam midpoint as well as jumps between solution branches are highlighted.

Transient Properties of Truck Tires on Real Road Surfaces

1987 ◽  
Vol 15 (3) ◽  
pp. 188-197
Author(s):  
R. Weber ◽  
M. Münster
Keyword(s):  
Frequency Response ◽  
Phase Angle ◽  
Lateral Force ◽  
Force Response ◽  
Heavy Duty ◽  
Time Rate ◽  
Heavy Duty Truck ◽  
Truck Tire ◽  
Truck Tires ◽  
Road Surfaces

Abstract The cornering, or lateral force response of heavy-duty truck tires, has been evaluated on real road surfaces at speeds of 10–60 km/h. The special mobile truck tire dynamometer has a two-test-tire carriage mounted just ahead of the rear support tires of an articulated truck (tractor) trailer. Equal slip angles may be applied simultaneously to both test tires. The frequency response was evaluated by typical phase angle methods. The phase angle (lag of lateral force behind instantaneous angle) increased with frequency (time rate of application of angle) and decreased with increasing speed.

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