Random Excitation of a Nonlinear Vibration Neutralizer

1978 ◽  
Vol 100 (4) ◽  
pp. 681-689 ◽  
Author(s):  
S. F. Masri ◽  
S. J. Stott
Keyword(s):  
Approximate Analytical Solution ◽  
Random Excitation ◽  
Analog Computer ◽  
Primary System ◽  
Experimental Measurements ◽  
Dynamic Vibration ◽  
Power Spectral ◽  
Highly Nonlinear ◽  
Mass Damper ◽  
Auxiliary Mass

An approximate analytical solution is obtained for the stationary response of a highly nonlinear auxiliary mass damper (a dynamic vibration neutralizer with motion-limiting stops) attached to an oscillator that is subjected to random excitation. Experimental measurements with an electronic analog computer and numerically simulated solutions generated by means of a digital computer verify the findings. Results are given for the power spectral density and root-mean-squared level of the response. The effects of various damper parameters on the response of the primary system are determined. The nonlinear damper under consideration is shown to be significantly more effective than the conventional dynamic vibration neutralizer in controlling the response of systems subjected to random excitation.

Theory of the Dynamic Vibration Neutralizer With Motion-Limiting Stops

1972 ◽  
Vol 39 (2) ◽  
pp. 563-568 ◽  
Author(s):  
S. F. Masri
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Experimental Studies ◽  
Analog Computer ◽  
Primary System ◽  
Asymptotically Stable ◽  
Mass System ◽  
Dynamic Vibration ◽  
Simulated Motion ◽  
Auxiliary Mass

The exact solution for the steady-state motion of a dynamic vibration neutralizer with motion-limiting stops attached to a sinusoidally excited primary system is derived analytically, and its asymptotically stable regions are determined. Simulated motion on a digital computer and experimental studies with an analog computer corroborate the predictions of the theory. Results of the analysis are applied to modified vibration neutralizers, Lanchester dampers, and impact dampers. It is shown that the incorporation of properly designed motion-limiting stops into the auxiliary mass system will enhance the performance of the foregoing dampers.

Response of Pounding Dynamic Vibration Neutralizer Under Harmonic and Random Excitation

2018 ◽  
Vol 86 (2) ◽  
Author(s):  
Sami F. Masri ◽  
John P. Caffrey
Keyword(s):  
Steady State ◽  
Relative Motion ◽  
Closed Form Solution ◽  
Harmonic Excitation ◽  
Random Excitation ◽  
Form Solution ◽  
Primary System ◽  
Tuning Parameters ◽  
Dynamic Vibration ◽  
Highly Nonlinear

Exact steady-state solutions are obtained for the motion of an single-degree-of-freedom (SDOF) system that is provided with a highly nonlinear auxiliary mass damper (AMD), which resembles a conventional dynamic vibration neutralizer (DVN), whose relative motion with respect to the primary system is constrained to remain within a specified gap, thus operating as a “pounding DVN.” This configuration of a conventional DVN with motion-limiting stops could be quite useful when a primary structure with a linear DVN is subjected to transient loads (e.g., earthquakes) that may cause excessive relative motion between the auxiliary and primary systems. Under the assumption that the motion of the nonlinear system under harmonic excitation is undergoing steady-state motion with two impacts per period of the excitation, an exact, closed-form solution is obtained for the system motion. This solution is subsequently used to develop an approximate analytical solution for the stationary response of the pounding DVN when subjected to random excitation with white spectral density and Gaussian probability distribution. Comparison between the analytically estimated rms response of the primary system and its corresponding response obtained via numerical simulation shows that the analytical estimates are quite accurate when the coupling (tuning parameters) between the primary system and the damper are weak, but only moderately accurate when the linear components of the tuning parameters are optimized. It is also shown that under nonstationary, the pounding DVN provides slightly degraded performance compared to the linear one but simultaneously limits the damper-free motion to specified design constraints.

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.

Design of non-traditional dynamic vibration absorber for damped linear structures

2013 ◽  
Vol 228 (1) ◽  
pp. 45-55 ◽  
Author(s):  
ND Anh ◽  
NX Nguyen
Keyword(s):  
Approximate Analytical Solution ◽  
High Reliability ◽  
Classical Model ◽  
Main Idea ◽  
Vibration Absorber ◽  
Primary System ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Approximate Analytical Solutions ◽  
Force Excitation

The Voigt-type of dynamic vibration absorber is a classical model and has attracted considerable attention in many years because of its simple design, high reliability and useful applications in the fields of civil and mechanical engineering. Recently, a non-traditional type of dynamic vibration absorber was proposed. Unlike the traditional damped absorber configuration, the non-traditional absorber has a linear viscous damper connecting the absorber mass directly to the ground instead of the main mass. There have been some studies on the design of the non-traditional dynamic vibration absorber in the case of undamped primary structures. Those studies have shown that the non-traditional dynamic vibration absorber has better performance than the traditional dynamic vibration absorber. However, when damping is present at the primary system, there are very few studies on the design of non-traditional dynamic vibration absorber. This article presents a simple approach to determine the approximate analytical solutions for the [Formula: see text] optimization of the non-traditional dynamic vibration absorber attached to the damped primary structure subjected to force excitation. The main idea of the study is based on the dual criterion suggested by Anh in order to replace approximately the original damped structure by an equivalent undamped structure. Then the approximate analytical solution of dynamic vibration absorber’s parameters is given by using known results for undamped structure obtained. The comparisons have been done to verify the effectiveness of the obtained results.

H 2 Optimization of the Three-Element Type Dynamic Vibration Absorbers

2002 ◽  
Vol 124 (4) ◽  
pp. 583-592 ◽  
Author(s):  
Toshihiko Asami ◽  
Osamu Nishihara
Keyword(s):  
Optimization Design ◽  
Random Excitation ◽  
Control Device ◽  
Algebraic Solution ◽  
Primary System ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Optimum Parameters ◽  
Element Type ◽  
H2 Optimization

The dynamic vibration absorber (DVA) is a passive vibration control device which is attached to a vibrating body (called a primary system) subjected to exciting force or motion. In this paper, we will discuss an optimization problem of the three-element type DVA on the basis of the H2 optimization criterion. The objective of the H2 optimization is to reduce the total vibration energy of the system for overall frequencies; the total area under the power spectrum response curve is minimized in this criterion. If the system is subjected to random excitation instead of sinusoidal excitation, then the H2 optimization is probably more desirable than the popular H∞ optimization. In the past decade there has been increasing interest in the three-element type DVA. However, most previous studies on this type of DVA were based on the H∞ optimization design, and no one has been able to find the algebraic solution as of yet. We found a closed-form exact solution for a special case where the primary system has no damping. Furthermore, the general case solution including the damped primary system is presented in the form of a numerical solution. The optimum parameters obtained here are compared to those of the conventional Voigt type DVA. They are also compared to other optimum parameters based on the H∞ criterion.

scholarly journals Propagation of Blast waves in a Non-Ideal Magnetogasdynamics

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 458 ◽  
Author(s):  
Astha Chauhan ◽  
Rajan Arora ◽  
Mohd Siddiqui
Keyword(s):  
Magnetic Field ◽  
Gas Dynamics ◽  
Approximate Analytical Solution ◽  
Ideal Gas ◽  
Specific Conductance ◽  
Blast Waves ◽  
Highly Nonlinear ◽  
Vast Literature ◽  
Flow Variables ◽  
The Magnetic Field

Blast waves are generated when an area grows abruptly with a supersonic speed, as in explosions. This problem is quite interesting, as a large amount of energy is released in the process. In contrast to the situation of imploding shocks in ideal gas, where a vast literature is available on the effect of magnetic fields, very little is known about blast waves propagating in a magnetic field. As this problem is highly nonlinear, there are very few techniques that may provide even an approximate analytical solution. We have considered a problem on planar and radially symmetric blast waves to find an approximate solution analytically using Sakurai’s technique. A magnetic field has been taken in the transverse direction. Gas particles are supposed to be propagating orthogonally to the magnetic field in a non-deal medium. We have further assumed that specific conductance of the medium is infinite. Using Sakurai’s approach, we have constructed the solution in a power series of ( C / U ) 2 , where C is the velocity of sound in an ideal gas and U is the velocity of shock front. A comparison of obtained results in the absence of a magnetic field within the published work of Sakurai has been made to generate the confidence in our results. Our results match well with the results reported by Sakurai for gas dynamics. The flow variables are computed behind the leading shock and are shown graphically. It is very interesting that the solution of the problem is obtained in closed form.

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.

Development of V-Shaped Hybrid Mass Damper and its Application to High-Rise Buildings

1995 ◽  
Author(s):  
Masanori Imazeki ◽  
Koji Tanida ◽  
Masao Mutaguchi ◽  
Yuji Koike ◽  
Tamotsu Murata ◽  
...  
Keyword(s):  
First Year ◽  
Building Structures ◽  
Large Space ◽  
Natural Period ◽  
High Rise ◽  
High Rise Building ◽  
System A ◽  
Mass Damper ◽  
Story Building ◽  
Auxiliary Mass

Abstract A hybrid mass damper system has been developed with a view to counteracting wind- and earthquake-excited vibrations of large high-rise building structures. In order to eliminate the large space needed to accommodate a pendulum-type mass damper adapted to the long period of high-rise building, mechanism has been devised for suspending the auxiliary mass on a V-shaped rail sliding on rollers. The base angle of the V-shaped rail is varied for adjusting the natural period of the mass damper system. A suboptimal algorithm based on the minimum norm method has been adopted for designing the auxiliary mass driving system. Three units of this damper system, each equipped with auxiliary mass weighing 110 tons, have been installed on a 52-story building. Satisfactory performance conforming in all practical aspects with design has been verified from vibration test on actual building after installation. As sequel, the functioning of the system during the first year of service is also reported.

Application of Dynamic Vibration Absorbers to Mass Measurement

1997 ◽  
Author(s):  
Takeshi Mizuno
Keyword(s):  
Measurement System ◽  
Mass Measurement ◽  
Vibration Absorber ◽  
Rotational Axis ◽  
Automatic Frequency ◽  
Dynamic Vibration Absorber ◽  
Measuring Device ◽  
Supporting Structure ◽  
Dynamic Vibration ◽  
Auxiliary Mass

Abstract A mass measurement system which uses a dynamic vibration absorber as measuring device is developed. It can measure mass even under weightless conditions like in space stations. In this system, an object to be measured is fixed to a rotating table (rotor) at a distance from the rotational axis. Since it makes the rotor unbalanced, a centrifugal force causes the supporting structure to vibrate during rotation. A dynamic vibration absorber attached to the structure is tuned or controlled to cancel the excitation force. When the structure does not vibrate, the amplitude of motion of the auxiliary mass equals the ratio of the amount of unbalance to the auxiliary mass. Therefore, the mass of the object is determined from the motion of the auxiliary mass. According to the measurement principles, the vibration of the supporting structure must be eliminated. A servocompensator with the performance of automatic frequency tracking is applied to reduce the vibration. Experimental results demonstrate that mass can be measured accurately with the developed measurement system.

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