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.

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.

On the Nonstationary Response of Stochastically Excited Secondary Systems

1987 ◽  
Vol 54 (3) ◽  
pp. 688-694 ◽  
Author(s):  
W. D. Iwan ◽  
K. S. Smith
Keyword(s):  
Closed Form Expression ◽  
Primary System ◽  
Mean Square ◽  
Stochastic Excitation ◽  
Secondary System ◽  
Form Expression ◽  
Combined System ◽  
Nonstationary Response ◽  
Secondary Systems ◽  
The Mean

The envelope response of a secondary system is derived for the case where the primary system is subjected to nonstationary stochastic excitation. An approximate closed form expression for the mean square envelope response is obtained for the case of transient response to stationary excitation when the primary and secondary systems are noninteracting. When the combined system is classically damped, the effect of the interaction is described by the introduction of an equivalent noninteracting system. The analytical results are compared with results of numerical simulations.

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.

The Random Vibration Response of a System Having Many Degrees of Freedom

1966 ◽  
Vol 17 (1) ◽  
pp. 21-30 ◽  
Author(s):  
J. D. Robson
Keyword(s):  
Density Matrix ◽  
Random Vibration ◽  
Degrees Of Freedom ◽  
Normal Modes ◽  
Random Excitation ◽  
Mean Square ◽  
Spectral Density Matrix ◽  
Mean Square Response ◽  
Cross Correlations ◽  
Generalised Coordinates

SummaryThe paper treats the general problem of the response to multiple random excitation of a system having n degrees of freedom. Analysis is developed which connects the spectral density matrix of a set of generalised coordinates with that of corresponding generalised forces, and makes explicit the contributions of the various normal modes. The case of two degrees of freedom is considered in detail. The importance of cross-correlations between modes is shown by determining their effects on spectra and on mean-square 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.

Maximum mean square response and critical orientation under bi-directional seismic excitation

2021 ◽  
Vol 233 ◽  
pp. 111881
Author(s):  
Athanasios Tsourekas ◽  
Asimina Athanatopoulou ◽  
Konstantinos Kostinakis
Keyword(s):  
Seismic Excitation ◽  
Mean Square ◽  
Critical Orientation ◽  
Mean Square Response

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.

Mean-Square Response of a Second-Order System to Nonstationary, Random Excitation

1970 ◽  
Vol 37 (3) ◽  
pp. 612-616 ◽  
Author(s):  
L. L. Bucciarelli ◽  
C. Kuo
Keyword(s):  
Narrow Band ◽  
Random Excitation ◽  
Second Order ◽  
Envelope Function ◽  
Order System ◽  
Mean Square ◽  
Forcing Function ◽  
Mean Square Response ◽  
Noise Function ◽  
The Mean

The mean-square response of a lightly damped, second-order system to a type of non-stationary random excitation is determined. The forcing function on the system is taken in the form of a product of a well-defined, slowly varying envelope function and a noise function. The latter is assumed to be white or correlated as a narrow band process. Taking advantage of the slow variation of the envelope function and the small damping of the system, relatively simple integrals are obtained which approximate the mean-square response. Upper bounds on the mean-square response are also obtained.

Stochastic Response and Stability Analysis of Two-Point Mooring System

2011 ◽  
Author(s):  
A. K. Banik ◽  
T. K. Datta
Keyword(s):  
Stability Analysis ◽  
Probability Density Function ◽  
Probability Density ◽  
Mooring System ◽  
Mean Square ◽  
Stochastic Response ◽  
Sea State ◽  
Mean Square Response ◽  
Linear Damping ◽  
The Mean

The stochastic response and stability of a two-point mooring system are investigated for random sea state represented by the P-M sea spectrum. The two point mooring system is modeled as a SDOF system having only stiffness nonlinearity; drag nonlinearity is represented by an equivalent linear damping. Since no parametric excitation exists and only the linear damping is assumed to be present in the system, only a local stability analysis is sufficient for the system. This is performed using a perturbation technique and the Infante’s method. The analysis requires the mean square response of the system, which may be obtained in various ways. In the present study, the method using van-der-Pol transformation and F-P-K equation is used to obtain the probability density function of the response under the random wave forces. From the moment of the probability density function, the mean square response is obtained. Stability of the system is represented by an inequality condition expressed as a function of some important parameters. A two point mooring system is analysed as an illustrative example for a water depth of 141.5 m and a sea state represented by PM spectrum with 16 m significant height. It is shown that for certain combinations of parameter values, stability of two point mooring system may not be achieved.

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