scholarly journals Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing System

2008 ◽  
Vol 15 (3-4) ◽  
pp. 355-368 ◽  
Author(s):  
Benjamın Vazquez-Gonzalez ◽  
Gerardo Silva-Navarro
Keyword(s):  
Frequency Response ◽  
Fixed Points ◽  
Multiple Scales ◽  
Coupled System ◽  
Vibration Absorber ◽  
Primary System ◽  
Duffing System ◽  
Approximate Frequency ◽  
The Stability ◽  
Cubic Stiffness

In this work we study the frequency and dynamic response of a damped Duffing system attached to a parametrically excited pendulum vibration absorber. The multiple scales method is applied to get the autoparametric resonance conditions and the results are compared with a similar application of a pendulum absorber for a linear primary system. The approximate frequency analysis reveals that the nonlinear dynamics of the externally excited system are suppressed by the pendulum absorber and, under this condition, the primary Duffing system yields a time response almost equivalent to that obtained for a linear primary system, although the absorber frequency response is drastically modified and affected by the cubic stiffness, thus modifying the jumps defined by the fixed points. In the absorber frequency response can be appreciated a good absorption capability for certain ranges of nonlinear stiffness and the internal coupling is maintained by the existing damping between the pendulum and the primary system. Moreover, the stability of the coupled system is also affected by some extra fixed points introduced by the cubic stiffness, which is illustrated with several amplitude-force responses. Some numerical simulations of the approximate frequency responses and dynamic behavior are performed to show the steady-state and transient responses.

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.

The Vibration Reduction Analysis of a Rotating Mechanism Deck System

2008 ◽  
Vol 24 (3) ◽  
pp. 253-266 ◽  
Author(s):  
Y.-R. Wang ◽  
T.-H. Chen
Keyword(s):  
Multiple Scales ◽  
Vibration Reduction ◽  
Coupled System ◽  
Cost Effective ◽  
Disk Drive ◽  
Theoretical Background ◽  
Vibration Absorber ◽  
Aeroelastic System ◽  
Lagrange’S Equation ◽  
Optical Disk Drive

AbstractIn this paper, an optimized position of a mass-spring-damper vibration absorber is proposed for a rotating mechanism device (such as optical disk drive or rotary-wing and deck coupled system). A nonlinear 3-D theoretical model for a deck is established by Lagrange's equation. A 2-bladed rotor and deck (foundation) coupled aeroelastic system with vibration reduction device is presented and studied as well. The analytical solution is obtained by the Multiple-scales method for the case of no vibration absorber. The numerical results in time and frequency domain and with/no absorber are acquired. This research provides a theoretical background for the preliminary vibration reduction design for industries. It is found that the existing disk drives vibration can be reduced by simply adding the absorber at the end corner isolator of the deck, but without changing the main configurations. This will not only save costs but also increase testing efficiency, achieving the most cost-effective vibration reduction result.

scholarly journals Experiment and Analysis of Active Vibration Suppression via an Absorber with a Tunable Delay

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yixia Sun
Keyword(s):  
Vibration Suppression ◽  
Transfer Functions ◽  
Experimental Studies ◽  
Coupled System ◽  
Gain Coefficient ◽  
Feedback Gain ◽  
Primary System ◽  
Active Vibration ◽  
The Stability ◽  
Proper Values

A time-delayed absorber is utilized to suppress the vibration of a primary system excited by a simple harmonic force. The inherent and intentional time delays in the feedback control loop are taken into consideration. The value of the former is fixed, while the value of the latter is tunable in the controller. To begin with, the mechanical model of the system is established and the acceleration transfer functions of the system are derived. Consequently, the stability analysis of the coupled system is carried out. Finally, the experimental studies on the performance of the time-delayed absorber are conducted. Both experimental and theoretical results show that the time-delayed absorber with proper values of feedback gain coefficient and intentional time delay greatly suppresses the vibration of the primary system. The numerical results validate the correctness of the experimental and theoretical ones.

Nonlinear Oscillations of Nonlinear Damping Gyros: Resonances, Hysteresis and Multistability

2020 ◽  
Vol 30 (14) ◽  
pp. 2050203
Author(s):  
C. H. Miwadinou ◽  
A. V. Monwanou ◽  
L. A. Hinvi ◽  
V. Kamdoum Tamba ◽  
A. A. Koukpémèdji ◽  
...  
Keyword(s):  
Fixed Points ◽  
Parametric Excitation ◽  
Multiple Scales ◽  
Nonlinear Oscillations ◽  
Approximate Equation ◽  
Nonlinear Damping ◽  
Phase Portraits ◽  
Exact Equation ◽  
Restoring Force ◽  
The Stability

This paper addresses the issues on the dynamics of nonlinear damping gyros subjected to a quintic nonlinear parametric excitation. The fixed points and their stability are analyzed for the autonomous gyros equation. The number of fixed points of the system varies from one to six. The approximate equation of gyros is considered by expanding the nonlinear restoring force and parametric excitation for the study of the dynamics of gyros. Amplitude and frequency of possible resonances are found by using the multiple scales method. Also obtained are the principal parametric resonance and orders 4 and 6 subharmonic resonances. The stability conditions for each of these resonances are also obtained. Chaotic oscillations, multistability, hysteresis, and coexisting attractors are found using the bifurcation diagrams, the Lyapunov exponents, the phase portraits, the Poincaré section and the time histories. The effects of the damping parameter, the angular spin velocity and the parametric nonlinear excitation are analyzed. Results obtained by using the approximate gyros equation are compared to the dynamics obtained with the exact equation of gyros. The analytical investigations are complemented by numerical simulations.

Optimal Design of an Inerter-Based Dynamic Vibration Absorber Connected to Ground

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Shaoyi Zhou ◽  
Claire Jean-Mistral ◽  
Simon Chesne
Keyword(s):  
Fixed Point ◽  
Optimal Design ◽  
Transient Response ◽  
Damping Ratio ◽  
Vibration Absorber ◽  
Practical Implementation ◽  
Primary System ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
The Stability

Abstract This paper addresses the optimal design of a novel nontraditional inerter-based dynamic vibration absorber (NTIDVA) installed on an undamped primary system of single degree-of-freedom under harmonic and transient excitations. Our NTIDVA is based on the traditional dynamic vibration absorber (TDVA) with the damper replaced by a grounded inerter-based mechanical network. Closed-form expressions of optimal parameters of NTIDVA are derived according to an extended version of fixed point theory developed in the literature and the stability maximization criterion. The transient response of the primary system is optimized when the coupled system becomes defective, namely having three pairs of coalesced conjugate poles, the proof of which is also spelt out in this paper. Moreover, the analogous relationship between NTIDVA and electromagnetic dynamic vibration absorber is highlighted, facilitating the practical implementation of the proposed absorber. Finally, numerical studies suggest that compared with TDVA, NTIDVA can decrease the peak vibration amplitude of the primary system and enlarge the frequency bandwidth of vibration suppression when optimized by the extended fixed point technique, while the stability maximization criterion shows an improved transient response in terms of larger modal damping ratio and accelerated attenuation rate.

An Investigation of an Impact Vibration Absorber

1967 ◽  
Vol 89 (4) ◽  
pp. 653-657 ◽  
Author(s):  
D. M. Egle
Keyword(s):  
Approximate Expression ◽  
Small Mass ◽  
Vibration Absorber ◽  
Primary System ◽  
Maximum Displacement ◽  
State Response ◽  
System A ◽  
The Stability ◽  
The Impact ◽  
Impact Vibration

The impact vibration absorber consists of a small mass, moving unidirectionally, impacting against the ends of a container which is rigidly attached to the primary vibrating system. A simplified theory for the forced steady-state response of a linear, single-degree-of-freedom system with an impact vibration absorber is presented. The assumption of two impacts per cycle at equal time intervals is known to lead to two possible solutions near the resonant frequency of the primary system. A criterion for determining the stability of the solutions is developed. An approximate expression for the maximum displacement of the primary system is given and the theory is compared to experimental results.

Frequency Response of Parametric Resonance of Double Wall Carbon Nanotube Under Electrostatic Actuation for Noncoaxial Vibration

2017 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ezequiel Juarez
Keyword(s):  
Carbon Nanotube ◽  
Frequency Response ◽  
Multiple Scales ◽  
Van Der Waals ◽  
First Order ◽  
Electrostatically Actuated ◽  
The Stability ◽  
Euler Bernoulli Beam ◽  
Steady State Solutions ◽  
High Length

In this paper, the Method of Multiple Scales is used to investigate the influences of dimensionless damping and voltage parameters on the amplitude-frequency response of an electrostatically actuated double-walled carbon nanotube. The forces responsible for the nonlinearities in the vibrational behavior are intertube van der Waals and electrostatic forces. Soft AC excitation and small viscous damping forces are assumed. Herein, the noncoaxial case is investigated at near-zero amplitude conditions in the free vibration, which eliminates the influence of the cubic van der Waals in the first-order solution. The DWCNT structure is modelled as a cantilever beam with Euler-Bernoulli beam assumptions since the DWCNT is characterized with high length-diameter ratio. The results shown assume steady-state solutions in the first-order MMS solution. The importance of the results in this paper are the effect of damping and detuning frequency on the stability of the DWCNT vibration.

Dynamic Analysis of Active Vibration Absorber by Time Delay Acceleration Feedback Using Higher Order Method of Multiple Scales

2017 ◽  
Author(s):  
S. Mohanty ◽  
S. K. Dwivedy
Keyword(s):  
Time Delay ◽  
Lead Zirconate Titanate ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vibration Absorber ◽  
Primary System ◽  
Order Method ◽  
Primary Mass ◽  
Acceleration Feedback ◽  
Active Vibration

In the present work, analysis of a nonlinear active vibration absorber is carried out by time delay acceleration feedback. The primary system consisting of spring, mass and damper is subjected to multi harmonic and parametric excitation. It is proposed to reduce the vibration of both the primary system and the absorber by attaching a lead zirconate titanate (PZT) stack actuator connected in series with a spring in absorber configuration which act as an active vibration absorber. Due to the external excitation on the primary mass strain is developed in the PZT sensor, which produces voltage and this voltage converted to a counter acting force by the PZT actuator to suppress the vibration of the primary system. Second order method of multiple scales (MMS) is used to obtain approximate solution of the system to study frequency responses for simultaneous primary resonance, principal parametric and 1:1 internal resonance conditions. The analysis is performed for the mass ratio of 0.01 between the absorber and the primary mass.

A Sensitivity Study on Optimum Delayed Feedback Vibration Absorber

1998 ◽  
Vol 122 (2) ◽  
pp. 314-321 ◽  
Author(s):  
Nader Jalili ◽  
Nejat Olgac
Keyword(s):  
Sensitivity Analysis ◽  
Wide Band ◽  
Sensitivity Study ◽  
Optimal Operation ◽  
Delayed Feedback ◽  
Vibration Absorber ◽  
Primary System ◽  
Vibration Absorption ◽  
The Stability ◽  
Stiffness And Damping

A sensitivity analysis is presented for a novel tuned vibration absorber. The active tuning of the absorber is achieved using partial state feedback with a controlled time delay. The final structure, which is named Delayed Feedback Vibration Absorber (DFVA), is optimized to yield minimum Mpeak of the primary system involved for a given wide band of excitation frequencies. The optimization is performed over the absorber’s structural properties and the feedback control parameters. An optimal tuning over optimally designed passive absorber is conducted first, and separately a collective optimization over both the absorber structure and the control is studied. The assurance of the stability of the time-delayed system, which forms a critical constraint on the optimization, is also discussed. Regardless of the nature of the optimal operation, the parametric variations in the structure can influence the vibration absorption performance significantly. This concern is addressed via a sensitivity analysis. Primarily, the variations on the absorber stiffness and damping properties are studied. The findings of this effort provide tools for determining the acceptable tolerance limits of the absorber properties. [S0022-0434(00)02202-4]

Reduced Order Model of Coaxial Vibrations of Electrostatically Actuated Double Wall Carbon Nanotubes: Frequency Response of Primary Resonance

2018 ◽  
Author(s):  
Ezequiel Juarez ◽  
Dumitru I. Caruntu
Keyword(s):  
Carbon Nanotubes ◽  
Frequency Response ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Approximate Solutions ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
The Stability ◽  
Euler Bernoulli Beam ◽  
Steady State Solutions

In this paper, the Reduced Order Method (ROM) and the Method of Multiple Scales (MMS) are used to investigate the influences of dimensionless damping and voltage parameters on the amplitude-frequency response of an electrostatically actuated double-walled carbon nanotube (DWCNT). The forces responsible for the nonlinearities in the vibrational behavior are intertube van der Waals and electrostatic forces. Soft AC excitation and small viscous damping forces are assumed. Herein, the coaxial case is investigated. In this mode of vibration, the outer and inner carbon nanotubes move synchronously (in-phase) with the same maximum tip deflection. The DWCNT structure is modelled as a cantilever beam with Euler-Bernoulli beam assumptions since the DWCNT is characterized with high length-diameter ratio. The results shown assume steady-state solutions in the first-order MMS solution. The analytical approximate solutions provided by MMS are validated numerically by two-term (2T) Time Reponses and AUTO-07P. The two methods in this paper are found to be in excellent agreement at lower amplitudes. Additionally, the two methods are assessed for their advantages and limitations. The importance of the results in this paper are the effect of damping and voltage on the stability of the DWCNT vibration.

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