Application of a Weakly Nonlinear Absorber to Suppress the Resonant Vibrations of a Forced Nonlinear Oscillator

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
J. C. Ji
Keyword(s):  
Natural Frequency ◽  
Nonlinear Oscillator ◽  
Vibration Suppression ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Integrated System ◽  
Frequency Interval ◽  
Weakly Nonlinear ◽  
Nonlinear Absorber ◽  
Forced Nonlinear Oscillator

A weakly nonlinear vibration absorber is used to suppress the primary resonance vibrations of a single degree-of-freedom weakly nonlinear oscillator with periodic excitation, where the two linearized natural frequencies of the integrated system are not under any internal resonance conditions. The values of the absorber parameters are significantly lower than those of the forced nonlinear oscillator, as such the nonlinear absorber can be regarded as a perturbation to the nonlinear primary oscillator. The characteristics of the nonlinear primary oscillator change only slightly in terms of its new linearized natural frequency and the frequency interval of primary resonances after the nonlinear absorber is added. The method of multiple scales is employed to obtain the averaged equations that determine the amplitudes and phases of the first-order approximate solutions. Selection criteria are developed for the absorber linear stiffness (linearized natural frequency) and nonlinear stiffness in order to achieve better performance in vibration suppression. Illustrative examples are given to show the effectiveness of the nonlinear absorber in suppressing nonlinear vibrations of the forced oscillator under primary resonance conditions.

Voltage Response of Primary Resonance of Electrostatically Actuated MEMS Clamped Circular Plate Resonators

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides
Keyword(s):  
Natural Frequency ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Micro Electro Mechanical System ◽  
Voltage Response ◽  
Voltage Amplitude ◽  
Amplitude Response ◽  
Weakly Nonlinear ◽  
Electrostatically Actuated ◽  
Sensing Applications

This paper investigates the voltage–amplitude response of soft alternating current (AC) electrostatically actuated micro-electro-mechanical system (MEMS) clamped circular plates for sensing applications. The case of soft AC voltage of frequency near half natural frequency of the plate is considered. Soft AC produces small to very small amplitudes away from resonance zones. Nearness to half natural frequency results in primary resonance of the system, which is investigated using the method of multiple scales (MMS) and numerical simulations using reduced order model (ROM) of seven terms (modes of vibration). The system is assumed to be weakly nonlinear. Pull-in instability of the voltage–amplitude response and the effects of detuning frequency and damping on the response are reported.

Primary Resonance Voltage Response of Electrostatically Actuated M/NEMS Circular Plate Resonators

2014 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides
Keyword(s):  
Casimir Force ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Excitation Frequency ◽  
Primary Resonance ◽  
Voltage Response ◽  
Circular Plates ◽  
Amplitude Response ◽  
Weakly Nonlinear ◽  
Electrostatically Actuated

This paper investigates the voltage-amplitude response of soft AC electrostatically actuated M/NEMS clamped circular plates. AC frequency is near half natural frequency of the plate. This results in primary resonance. The system is analytically modeled using the Method of Multiple Scales (MMS). The system is assumed weakly nonlinear. The behavior of the system including pull-in instability as the AC voltage is swept up and down while the excitation frequency is constant is reported. The effects of detuning frequency, damping, Casimir force, and van der Waals force are reported as well.

Influence of van der Waals Forces on Electrostatically Actuated MEMS/NEMS Circular Plates

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Iris Alvarado
Keyword(s):  
Circular Plate ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Circular Plates ◽  
Weakly Nonlinear ◽  
Electrostatically Actuated ◽  
Ground Plate ◽  
Scale Surface ◽  
Two Bodies

This paper deals with electrostatically actuated micro and nano-electromechanical (MEMS/NEMS) circular plates. The system under investigation consists of two bodies, a deformable and conductive circular plate placed above a fixed, rigid and conductive ground plate. The deformable circular plate is electrostatically actuated by applying an AC voltage between the two plates. Nonlinear parametric resonance and pull-in occur at certain frequencies and relatively large AC voltage, respectively. Such phenomena are useful for applications such as sensors, actuators, switches, micro-pumps, micro-tweezers, chemical and mass sensing, and micro-mirrors. A mathematical model of clamped circular MEMS/NEMS electrostatically actuated plates has been developed. Since the model is in the micro- and nano-scale, surface forces, van der Waals and/or Casimir, acting on the plate are included. A perturbation method, the Method of Multiple Scales (MMS), is used for investigating the case of weakly nonlinear MEMS/NEMS circular plates. Two time scales, fast and slow, are considered in this work. The amplitude-frequency and phase-frequency response of the plate in the case of primary resonance are obtained and discussed.

Vibration Suppression of a Saturation Control System Using Delayed Feedback Control

2012 ◽  
Vol 226-228 ◽  
pp. 82-86
Author(s):  
Yan Ying Zhao
Keyword(s):  
Feedback Control ◽  
Analytical Solutions ◽  
Vibration Suppression ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Single Mode ◽  
Original System ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Saturation Control

In the present paper, the delayed feedback control is applied to suppress the amplitude of the vibration of a beam. The method of multiple scales is employed to obtain the analytical solutions when the primary resonance and 1:2 internal resonance occur simultaneously. The predictions from analytical solutions agree with the numerical simulations well. The analytical results show that the amplitude of the beam of the saturation control is much larger than its amplitude of the single-mode motion. The effects of the delayed feedback control on amplitude of the beam are investigated when the original system is in the saturation control. There is a tunable range of the delay could be used to suppress the amplitude of the beam for a fixed value of the gain. The amplitude of the beam can be suppressed from 0.20 to 0.10 when the gain and the delay are chosen appropriate values.

Dynamic Analysis of Composite Laminated Circular Plate with Circular Delamination

2016 ◽  
Vol 32 (6) ◽  
pp. 683-692 ◽  
Author(s):  
D.-L. Chen
Keyword(s):  
Differential Equations ◽  
Bessel Function ◽  
Natural Frequency ◽  
Circular Plate ◽  
Nonlinear Dynamic ◽  
Multiple Scales ◽  
Dynamic Equilibrium ◽  
Primary Resonance ◽  
Equilibrium Equations ◽  
Generalized Displacements

AbstractIn this paper, the effect of delamination on free vibration and primary resonance behaviors of composite circular plate with circular delamination is investigated. Through Reissner Variational Principle, the nonlinear dynamic equilibrium equations, the generalized displacements continuity conditions and the generalized forces equilibrium conditions across delamination front and consistent boundary conditions of delaminated circular plate are obtained. In the work, by introducing Bessel Function and Modified Bessel Function and using Galerkin discretization method, the nonlinear dynamic partial differential equations of delaminated circular plate are transferred into a set of nonlinear ordinary differential equations. Then by using semi-analytic method and multiple scales method, the effects of delamination radius and delamination depth in the thickness-wise on the natural frequency and primary resonance behaviors of delaminated circular plate are presented. The Results show that delamination has considerable effects on the natural frequency and its primary resonance behaviors of delaminated plate.

scholarly journals Influence of Time Delay on Controlling the Non-Linear Oscillations of a Rotating Blade

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 85
Author(s):  
Yasser Salah Hamed ◽  
Ali Kandil
Keyword(s):  
Time Delay ◽  
Natural Frequency ◽  
Multiple Scales ◽  
Control Process ◽  
Control Force ◽  
Specific Level ◽  
Loop Control ◽  
Positive Displacement ◽  
Non Linear ◽  
Linear Vibrations

Time delay is an obstacle in the way of actively controlling non-linear vibrations. In this paper, a rotating blade’s non-linear oscillations are reduced via a time-delayed non-linear saturation controller (NSC). This controller is excited by a positive displacement signal measured from the sensors on the blade, and its output is the suitable control force applied onto the actuators on the blade driving it to the desired minimum vibratory level. Based on the saturation phenomenon, the blade vibrations can be saturated at a specific level while the rest of the energy is transferred to the controller. This can be done by adjusting the controller natural frequency to be one half of the blade natural frequency. The whole behavior is governed by a system of first-order differential equations gained by the method of multiple scales. Different responses are included to show the influences of time delay on the closed-loop control process. Also, a good agreement can be noticed between the analytical curves and the numerically simulated ones.

Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths

2017 ◽  
Vol 9 (6) ◽  
pp. 1485-1505
Author(s):  
Lingchang Meng ◽  
Fengming Li
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Composite Laminated Plate ◽  
Vibration Localization ◽  
Composite Laminated Plates ◽  
Localization Phenomenon ◽  
Harmonic Resonance

AbstractThe nonlinear transverse vibrations of ordered and disordered two-dimensional (2D) two-span composite laminated plates are studied. Based on the von Karman's large deformation theory, the equations of motion of each-span composite laminated plate are formulated using Hamilton's principle, and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin's method. The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales. The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out. The effects of the disorder ratio and ply angle on the two different resonances are analyzed. From the numerical results, it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon, and with the increase of the disorder ratio, the vibration localization phenomenon will become more obvious. Moreover, the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration, and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.

The Static and Dynamic Behavior of MEMS Arches Under Electrostatic Actuation

2009 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis ◽  
Fadi M. Alsaleem ◽  
Ronald Miles ◽  
Weili Cui
Keyword(s):  
Multiple Scales ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Primary Resonance ◽  
Reduced Order Model ◽  
Harmonic Load ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Model Equations

In this paper, we investigate theoretically and experimentally the static and dynamic behaviors of electrostatically actuated clamped-clamped micromachined arches when excited by a DC load superimposed to an AC harmonic load. A Galerkin based reduced-order model is used to discretize the distributed-parameter model of the considered shallow arch. The natural frequencies of the arch are calculated for various values of DC voltages and initial rises of the arch. The forced vibration response of the arch to a combined DC and AC harmonic load is determined when excited near its fundamental natural frequency. For small DC and AC loads, a perturbation technique (the method of multiple scales) is also used. For large DC and AC, the reduced-order model equations are integrated numerically with time to get the arch dynamic response. The results show various nonlinear scenarios of transitions to snap-through and dynamic pull-in. The effect of rise is shown to have significant effect on the dynamical behavior of the MEMS arch. Experimental work is conducted to test polysilicon curved microbeam when excited by DC and AC loads. Experimental results on primary resonance and dynamic pull-in are shown and compared with the theoretical results.

Choosing Damping Parameters for the Inertial Orientation System

2021 ◽  
pp. 113-128
Author(s):  
V.P. Podchezertsev ◽  
S.V. Topilskaya
Keyword(s):  
Natural Frequency ◽  
Vibration Suppression ◽  
Outer Space ◽  
Protection System ◽  
Dynamic Vibration ◽  
Shock Absorbers ◽  
Vibration Protection ◽  
Orientation System ◽  
Vibration Impact ◽  
Vibration Dampers

The article discusses criteria for selecting the vibration protection for the spacecraft inertial orientation system. The considered vibration protection system allows providing acceptable amplitude acceleration for the gyroscopic device sensitive elements under vibration impact on the device body during the spacecraft launching and high angular stability of the position of the sensitive elements relative to the inertial coordinate system during a long period of operation (15 years) in orbit. The proposed vibration protection system consists of shock absorbers (springs) with stable high elastic characteristics under all factors of operation in the outer space and dynamic vibration dampers. The article presents a method for determining the parameters of dynamic vibration dampers taking into account the characteristics of the shock absorber, critical for the damping system of an inertial device. The proposed method for adjusting dynamic vibration dampers consists in suppressing vibrations at the natural frequency f1 of the shock absorption system and providing acceptable values of the gain coefficients of the structure resonant vibration amplitudes near the natural frequency f1. Certain characteristics of the damping system allow realizing the permissible vibration amplification coefficients at resonance, without significantly affecting the level of vibration suppression in the natural frequency zone of the vibration protection object

The Influence Region Analysis for the Delayed Resonator Vibration Absorber

2001 ◽  
Author(s):  
Giulio Grillo ◽  
Nejat Olgac
Keyword(s):  
Vibration Suppression ◽  
Vibration Absorber ◽  
Primary System ◽  
Frequency Interval ◽  
Vibration Absorption ◽  
Region Analysis ◽  
The Common ◽  
Resonator Vibration ◽  
Three Degree Of Freedom ◽  
Tuned Vibration Absorber

Abstract This paper presents an influence region analysis for an actively tuned vibration absorber, the Delayed Resonator (DR). DR is shown to respond to tonal excitations with time varying frequencies [1–3]. The vibration suppression is most effective at the point of attachment of the absorber to the primary structure. In this study we show that proper feedback control on the absorber can yield successful vibration suppression at points away from this point of attachment. The form and the size of such “influence region” strongly depend on the structural properties of the absorber and the primary system. There are a number of questions addressed in this paper: a) Stability of vibration absorption, considering that a single absorber is used to suppress oscillations at different locations. b) Possible common operating frequency intervals in which the suppression can be switched from one point on the structure to the others. A three-degree-of-freedom system is taken for as example case. One single DR absorber is demonstrated to suppress the oscillations at one of the three masses at a given time. Instead of an “influence region” a set of “influence points” is introduced. An analysis method is presented to find the common frequency interval in which the DR absorber operates at all three influence points.

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