Transient Response of a SDOF System With an Inerter to Nonstationary Stochastic Excitation

2017 ◽  
Vol 84 (4) ◽  
Author(s):  
Sami F. Masri ◽  
John P. Caffrey
Keyword(s):  
Degrees Of Freedom ◽  
Analytical Study ◽  
Broad Band ◽  
Primary System ◽  
Stochastic Excitation ◽  
Mass Ratio ◽  
Vibration Damper ◽  
Tuning Parameters ◽  
Mass Damper ◽  
Mean Square Response

An analytical study is presented of the covariance kernels of a damped, linear, two-degrees-of-freedom (2DOF) system which resembles a primary system that is provided with an auxiliary mass damper (AMD), in addition to an “inerter” (a device that imparts additional inertia to the vibration damper, hence magnifying its effectiveness without a significant damper mass addition). The coupled 2DOF system is subjected to nonstationary stochastic excitation consisting of a modulated white noise. An exponential function, resembling the envelope of a typical earthquake, is considered. Results of the analysis are used to determine the dependence of the peak transient mean-square response of the system on the damper/inerter tuning parameters, and the shape of the deterministic intensity function. It is shown that, under favorable dynamic environments, a properly designed auxiliary damper, encompassing an inerter with a sizable mass ratio, can significantly attenuate the response of the primary system to broad band excitations; however, the dimensionless “rise-time” of the nonstationary excitation substantially reduces the effectiveness of such a class of devices (even when optimally tuned) in attenuating the peak dynamic response of the primary system.

Transient Response of MDOF Systems With Inerters to Nonstationary Stochastic Excitation

2017 ◽  
Vol 84 (10) ◽  
Author(s):  
Sami F. Masri ◽  
John P. Caffrey ◽  
Hui Li
Keyword(s):  
Degrees Of Freedom ◽  
Broad Band ◽  
Primary System ◽  
Mean Square ◽  
Stochastic Excitation ◽  
Mass Ratio ◽  
Tuning Parameters ◽  
Mdof Systems ◽  
Mean Square Response ◽  
Arbitrary Location

Explicit, closed-form, exact analytical expressions are derived for the covariance kernels of a multi degrees-of-freedom (MDOF) system with arbitrary amounts of viscous damping (not necessarily proportional-type), that is equipped with one or more auxiliary mass damper-inerters placed at arbitrary location(s) within the system. The “inerter” is a device that imparts additional inertia to the vibration damper, hence magnifying its effectiveness without a significant damper mass addition. The MDOF system is subjected to nonstationary stochastic excitation consisting of modulated white noise. Results of the analysis are used to determine the dependence of the time-varying mean-square response of the primary MDOF system on the key system parameters such as primary system damping, auxiliary damper mass ratio, location of the damper-inerter, inerter mass ratio, inerter node choices, tuning of the coupling between the damper-inerter and the primary system, and the excitation envelope function. Results of the analysis are used to determine the dependence of the peak transient mean-square response of the system on the damper/inerter tuning parameters, and the shape of the deterministic intensity function. It is shown that, under favorable dynamic environments, a properly designed auxiliary damper, encompassing an inerter with a sizable mass ratio, can significantly attenuate the response of the primary system to broad band excitations; however, the dimensionless “rise-time” of the nonstationary excitation substantially reduces the effectiveness of such a class of devices (even when optimally tuned) in attenuating the peak dynamic response of the primary system.

A Closed-Form Optimal Tuning of Mass Dampers for One Degree-of-Freedom Systems Under Rotating Unbalance Forcing

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
T. Argentini ◽  
M. Belloli ◽  
P. Borghesani
Keyword(s):  
Analytical Study ◽  
Mass Parameter ◽  
Primary System ◽  
Practical Applications ◽  
Tuning Parameters ◽  
Optimal Tuning ◽  
State Response ◽  
Optimal Damping ◽  
Mass Damper ◽  
Tuned Damper

This paper is focused on the study of a vibrating system forced by a rotating unbalance and coupled to a tuned mass damper (TMD). The analysis of the dynamic response of the entire system is used to define the parameters of such device in order to achieve optimal damping properties. The inertial forcing due to the rotating unbalance depends quadratically on the forcing frequency and it leads to optimal tuning parameters that differ from classical values obtained for pure harmonic forcing. Analytical results demonstrate that frequency and damping ratios, as a function of the mass parameter, should be higher than classical optimal parameters. The analytical study is carried out for the undamped primary system, and numerically investigated for the damped primary system. We show that, for practical applications, proper TMD tuning allows to achieve a reduction in the steady-state response of about 20% with respect to the response achieved with a classically tuned damper.

Performance of Particle Dampers Under Random Excitation

1996 ◽  
Vol 118 (4) ◽  
pp. 614-621 ◽  
Author(s):  
A. Papalou ◽  
S. F. Masri
Keyword(s):  
Wide Band ◽  
Small Mass ◽  
Random Excitation ◽  
Primary System ◽  
Mass Ratio ◽  
Impact Damper ◽  
Mean Square Response ◽  
Small Model ◽  
Particle Dampers ◽  
Auxiliary Mass

An experimental and analytical study is made of the performance of particle dampers under wide-band random excitation. A small model, provided with a nonlinear auxiliary mass damper, was used to investigate the major system parameters that influence the performance of particle dampers: total auxiliary mass ratio, particle size, container dimension, and the intensity and direction of the excitation. It is shown that properly designed particle dampers, even with a relatively small mass ratio, can considerably reduce the response of lightly damped structures. An approximate analytical solution, which is based on the concept of an equivalent single unit-impact damper, is presented. It is shown that the approximate solution can provide an adequate estimate of the root-mean-square response of the randomly excited primary system when provided with a particle damper that is operating in the vicinity of its optimum range of parameters.

Effectiveness of Location and Number of Multiple Tuned Mass Damper for Seismic Structures

2020 ◽  
Vol 9 (6) ◽  
pp. 780-783
Keyword(s):  
Seismic Response ◽  
Software Tool ◽  
Tuned Mass Damper ◽  
Structure Study ◽  
Structural Performance ◽  
Mass Ratio ◽  
Tuned Mass Dampers ◽  
Maximum Reduction ◽  
Mass Damper ◽  
Earthquake Data

Tuned mass dampers (TMD) are one of the most reliable devices to control the vibration of the structure. The optimum mass ratio required for a single tuned mass damper (STMD) is evaluated corresponding to the fundamental natural frequency of the structure. The effect of STMD and Multiple tuned mass dampers (MTMD) on a G+20 storey structure are studied to demonstrate the damper’s effectiveness in seismic application. The location and number of tuned mass dampers are studied to give best structural performance in maximum reduction of seismic response for El Centro earthquake data. The analysis results from SAP 2000 software tool shows damper weighing 2.5% of the total weight of the structure effectively reduce the response of the structure. Study shows that introduction of 4-MTMD at top storey can effectively reduce the response by 10% more in comparison to single tuned mass damper. The use of MTMD of same mass ratio that of STMD is more effective in seismic response.

scholarly journals High-performance magneto-rheological clutches for direct-drive actuation: Design and development

2021 ◽  
pp. 1045389X2110069
Author(s):  
Sergey Pisetskiy ◽  
Mehrdad Kermani
Keyword(s):  
High Performance ◽  
Degrees Of Freedom ◽  
Dynamic Range ◽  
Complete Analysis ◽  
Mass Ratio ◽  
Direct Drive ◽  
Element Analysis ◽  
Prototype Development ◽  
Magneto Rheological ◽  
Hall Sensors

This paper presents an improved design, complete analysis, and prototype development of high torque-to-mass ratio Magneto-Rheological (MR) clutches. The proposed MR clutches are intended as the main actuation mechanism of a robotic manipulator with five degrees of freedom. Multiple steps to increase the toque-to-mass ratio of the clutch are evaluated and implemented in one design. First, we focus on the Hall sensors’ configuration. Our proposed MR clutches feature embedded Hall sensors for the indirect torque measurement. A new arrangement of the sensors with no effect on the magnetic reluctance of the clutch is presented. Second, we improve the magnetization of the MR clutch. We utilize a new hybrid design that features a combination of an electromagnetic coil and a permanent magnet for improved torque-to-mass ratio. Third, the gap size reduction in the hybrid MR clutch is introduced and the effect of such reduction on maximum torque and the dynamic range of MR clutch is investigated. Finally, the design for a pair of MR clutches with a shared magnetic core for antagonistic actuation of the robot joint is presented and experimentally validated. The details of each approach are discussed and the results of the finite element analysis are used to highlight the required engineering steps and to demonstrate the improvements achieved. Using the proposed design, several prototypes of the MR clutch with various torque capacities ranging from 15 to 200 N·m are developed, assembled, and tested. The experimental results demonstrate the performance of the proposed design and validate the accuracy of the analysis used for the development.

scholarly journals Analysis study the used of Tuned Mass Damper (TMD) on an existing train bridge due to high speed train with moving mass load approach

2019 ◽  
Vol 258 ◽  
pp. 05005 ◽  
Author(s):  
Wivia Octarena Nugroho ◽  
Dina Rubiana Widarda ◽  
Oryza Herdha Dwyana
Keyword(s):  
High Speed ◽  
Tuned Mass Damper ◽  
Dynamic Responses ◽  
Mass Ratio ◽  
High Speed Train ◽  
Maximum Deformation ◽  
Mass Load ◽  
Mass Damper ◽  
Existing Bridges ◽  
Comfort Criteria

As the need of the train speed increased, the existing bridges need to be evaluated, especially in dynamic responses, which are deformation and acceleration. In this study, Cisomang Bridge is modeled and analyzed due to the high-speed train SJ X2 in varying speeds, 50 km/h, 100 km/h, 150 km/h, and 200 km/h. The used of tuned mass damper also will be varied on its setting and placing. The tuned mass dampers setting be varied based on the first or second natural frequency and the placing of tuned mass damper be varied based on maximum deformation of the first or second mode. Moreover, the tuned mass damper ratio will be varied 1% and 1.6%. For all speed variations, dynamic responses of structure without TMD still fulfil the Indonesian Government Criterion based on PM 60 - 2012 but do not meet requirement of comfort criteria based on DIN-Fachbericht 101. Furthermore, only for the speed train 50km/h dynamic responses of structure fulfil safety criteria based on Eurocode EN 1990:2002, whereas the other speed variations do not meet that requirement. In the use of TMD 1% mass ratio, the structure fulfils the safety criteria for all speed variations. In the use of TMD 1.6% mass ratio, all the structure fulfils the safety and comfort criteria except 100 km/h speed which only fulfils the safety criteria.

The Numerical Simulation of Two-Degrees-of-Freedom Vortex-Induced Vibrations of Circular Cylinder with High Mass-Ratio

2013 ◽  
Vol 284-287 ◽  
pp. 557-561
Author(s):  
Jie Li Fan ◽  
Wei Ping Huang
Keyword(s):  
Circular Cylinder ◽  
Drag Force ◽  
Frequency Ratio ◽  
Lift Force ◽  
Degrees Of Freedom ◽  
Cross Flow ◽  
High Mass ◽  
Mass Ratio ◽  
Main Frequency ◽  
Line Amplitude

The two-degrees-of-freedom VIV of the circular cylinder with high mass-ratio is numerically simulated with the software ANSYS/CFX. The VIV characteristic is analyzed in the different conditions (Ur=3, 5, 6, 8, 10). When Ur is 5, 6, 8 and 10, the conclusion which is different from the cylinder with low mass-ratio can be obtained. When Ur is 3, the frequency of in-line VIV is twice of that of cross-flow VIV which is equal to the frequency ratio between drag force and lift force, and the in-line amplitude is much smaller than the cross-flow amplitude. The motion trace is the crescent. When Ur is 5 and 6, the frequency ratio between the drag force and lift force is still 2, but the main frequency of in-line VIV is mainly the same as that of cross-flow VIV and the secondary frequency of in-line VIV is equal to the frequency of the drag force. The in-line amplitude is still very small compared with the cross-flow amplitude. When Ur is up to 8 and 10, the frequency of in-line VIV is the same as the main frequency of cross-flow VIV which is close to the inherent frequency of the cylinder and is different from the frequency of drag force or lift force. But the secondary frequency of cross-flow VIV is equal to the frequency of the lift force. The amplitude ratio of the VIV between in-line and cross-flow direction is about 0.5. When Ur is 5, 6, 8 and 10, the motion trace is mainly the oval.

The Two-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation

2005 ◽  
Vol 128 (1) ◽  
pp. 56-65 ◽  
Author(s):  
Lei Zuo ◽  
Samir A. Nayfeh
Keyword(s):  
Vibration Suppression ◽  
Single Mode ◽  
Tuned Mass Damper ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Primary System ◽  
H Infinity ◽  
Mass Damper ◽  
Mode Vibration ◽  
Two Degree Of Freedom

Whenever a tuned-mass damper is attached to a primary system, motion of the absorber body in more than one degree of freedom (DOF) relative to the primary system can be used to attenuate vibration of the primary system. In this paper, we propose that more than one mode of vibration of an absorber body relative to a primary system be tuned to suppress single-mode vibration of a primary system. We cast the problem of optimization of the multi-degree-of-freedom connection between the absorber body and primary structure as a decentralized control problem and develop optimization algorithms based on the H2 and H-infinity norms to minimize the response to random and harmonic excitations, respectively. We find that a two-DOF absorber can attain better performance than the optimal SDOF absorber, even for the case where the rotary inertia of the absorber tends to zero. With properly chosen connection locations, the two-DOF absorber achieves better vibration suppression than two separate absorbers of optimized mass distribution. A two-DOF absorber with a negative damper in one of its two connections to the primary system yields significantly better performance than absorbers with only positive dampers.

scholarly journals An unconventional rubber torsional vibration damper with two degrees of freedom

2017 ◽  
Vol 13 ◽  
pp. 136-141
Author(s):  
Václav Píštěk ◽  
Pavel Kučera ◽  
Olena Nozhenko ◽  
Kostiantyn Kravchenko ◽  
David Svída
Keyword(s):  
Torsional Vibration ◽  
Degrees Of Freedom ◽  
Vibration Damper ◽  
Two Degrees Of Freedom

scholarly journals Kolmogorov Unstable Stellar Oscillations

1983 ◽  
Vol 66 ◽  
pp. 297-321
Author(s):  
J. Perdang
Keyword(s):  
Numerical Analysis ◽  
Internal Resonance ◽  
Degrees Of Freedom ◽  
High Surface ◽  
Broad Band ◽  
Resonance Effects ◽  
Stellar Oscillations ◽  
Noise Type ◽  
Non Linear ◽  
Equipartition Of Energy

AbstractWe survey the mathematics of non-linear Hamiltonian oscillations with emphasis being laid on the more recently discovered Kolmogorov instability. In the context of radial adiabatic oscillations of stars this formalism predicts a Kolmogorov instability even at low oscillation energies, provided that sufficiently high linear asymptotic modes have been excited.Numerical analysis confirms the occurrence of this instability. It is found to show up already among the lowest order modes, although high surface amplitudes are then required (ǀδrǀ/R ~ 0.5 for an unstable fundamental mode – first harmonic coupling). On the basis of numerical evidence we conjecture that in the Kolmogorov unstable regime the enhanced coupling due to internal resonance effects leads to an equipartition of energy over all interacting degrees of freedom. We also indicate that the power spectrum of such oscillations is expected to display two components: A very broad band of overlapping pseudo-linear frequency peaks spread out over the asymptotic range, and a strictly non-linear 1/f-noise type component close to the frequency origin.It is finally argued that the Kolmogorov instability is likely to occur among non-linearly coupled non-radial stellar modes at a surface amplitude much lower than in the radial case. This lends support to the view that this instability might be operative among the solar oscillations.

Sign in / Sign up

Export Citation Format

Share Document