Auxiliary Mass Damper Research Articles

An efficient reliability-based design of TMD & MTMD in nonlinear structures under uncertainty

One of the methods to improve the performance of tuned mass dampers is to combine the primary and auxiliary mass dampers in series, known as multiple tuned mass dampers. The mechanical properties of these dampers influence the seismic behavior of structures equipped with tuned mass dampers. Generally, the determination of TMD parameters to achieve optimal seismic behavior is defined in the framework of optimization problems. In structures with nonlinear behavior, there are several sources of uncertainty in the structure, which emphasizes the importance of using the reliability-based design optimization method. For this purpose, two strategies based on the meta-heuristic optimization and reliability-based design optimization method are used for the optimal design of TMD and MTMD. In the RBDO method, the optimal design is performed based on the objective function established on the target reliability of the structure. Furthermore, a hybrid metaheuristic method was developed based on BOA and CSS algorithms to increase search-ability. The results show the efficiency of the HBC algorithm in solving engineering design problems. Also, reliability analysis and sensitivity analysis are conducted on passive controlled structures to display the effect of uncertainty in mechanical parameters of the system and their importance in the reliability of the system. Also, the optimum design of TMD and MTMD was evaluated based on the target reliability using the efficient RBDO method. The results show that the RBDO strategy has an excellent ability to design TMD and MTMD with a good performance in reducing seismic responses.

Response of a multi-degree-of-freedom system with a pounding vibration neutralizer to harmonic and random excitation

Exact steady-state solutions are obtained for the motion of a multi-degree-of-freedom system (MDOF) that is provided, at an arbitrary location within the primary structure, with a highly-nonlinear auxiliary mass damper which resembles a conventional linear 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 composite nonlinear MDOF system under harmonic excitation is undergoing steady-state motion with two symmetric impacts per period of the excitation, an exact, closed-form solution is obtained for the motion of the MDOF as well as the nonlinear damper. This solution is subsequently used to develop an approximate analytical procedure to estimate the stationary response of the pounding DVN when subjected to random excitation with white spectral density and Gaussian probability distribution. Since the vibration control effectiveness of auxiliary mass dampers, whether linear or not, deteriorates considerably when dealing with transient dynamic loads, an extensive investigation is provided for assessing the influence and interaction effects of the major nonlinear system parameters, so as to provide useful guidelines for quantifying the tradeoffs in selecting a suitable strategy to enhance the mitigation capabilities of the subject class of dampers, under stationary as well as nonstationary deterministic and random dynamic environments.

Assessment of semi-active friction dampers in auxiliary mass dampers’ suspension

Because of the efficiency of semi-active friction dampers to dissipate mechanical energy, their use have been extensively proposed for a variety of mechanical systems to reduce vibration amplitudes. A considerably simple model for a semi-active friction damper can be obtained with the use of an elastic element coupled to a vibratory system through a variable friction joint. Another approach against excessive vibrations in mechanical structures is the addition of auxiliary mass systems by means of elastic elements and viscous dampers—the auxiliary mass damper (AMD). However, their performance is susceptible to changes in the frequency or form of the excitation force. Therefore, to improve their robustness, it is necessary to design adaptive systems, i.e., adjustable devices that can be used efficiently over a large frequency range. In this work, a semi-active friction damper was used in the auxiliary mass damper’s suspension to tune it by altering the normal force in the friction joint while it dissipates the mechanical energy from the primary vibratory structure. This AMD was named tunable auxiliary mass damper. Furthermore, assemblies using semi-active friction dampers and tunable auxiliary mass dampers were numerically simulated in order to evaluate their effectiveness in the vibration attenuation. Numerical experiments in a multiple-degree-of-freedom vibratory structure were performed and efficiencies of the proposed assemblies were evaluated by means of a performance parameter obtained from their frequency responses. Moreover, their robustness was assessed by imposing several types of excitation forces. Numerical responses that use seismic records as base excitations were obtained for comparison with results in the literature through performance indexes normally used for seismic damage prevention studies. The obtained results presented a promising performance for the selected assemblies that use different positions for friction devices.

Response of Pounding Dynamic Vibration Neutralizer Under Harmonic and Random Excitation

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.

Analysis of systems with nonlinear auxiliary mass dampers by means of a special selection of linear generating functions

Nonlinear vibration isolation systems have a wider range of effective damping than linear ones. However, their analysis with an arbitrary load is quite laborious. In the article the method of special selection of linear generating systems for analyzing nonlinear systems proposed by professor Chernov Yu T is used. The linear generating system is chosen in such a way that the difference between the solutions of the linear and nonlinear systems in the first approximation for the first harmonic is minimal. Such an approach makes it possible to reduce the complexity of constructing the amplitude-frequency characteristics of nonlinear systems. In this paper, the amplitude-frequency characteristics were constructed to evaluate the efficiency of nonlinear auxiliary mass dampers at different frequencies of the external load. Tuned mass damper (TMD) was chosen as the type of auxiliary mass damper. The article looks at numerical examples of two systems with nonlinear TMD as a three degrees of freedom system. In the first numerical example, a stand with an equipment installed on it was analyzed. The TMD is installed on the stand. In the second numerical example the equipment is installed on a pedestal. The equipment is equipped with a nonlinear TMD. In both examples, there is cubic reaction-displacement relationship in the link that attaches the TMD. The amplitude-frequency characteristics for both systems are constructed for different variants: with a nonlinear, linear TMD and without a damper. The linear TMD was tuned to the first natural frequency of oscillations of the system without a damper. A comparative analysis of the options is given. The efficiency of using nonlinear TMD is determined from the numerical examples. There is a three times reduction in displacements in the nonlinear system as compared to the linear system.

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

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.

Nonlinear Controllers for Active Composite Tuned Mass Dampers

This paper considers nonlinear control of buildings utilizing composite tuned mass dampers subject to earthquake. Basically composite tuned mass dampers are tuned mass dampers having two dampers connected in series, where auxiliary mass dampers as satellite damper is attached on the first dampers. The properties of composite tuned mass dampers are optimized before they are used in the structures. Active control systems are then applied to the composite tuned mass dampers. Because the magnitude of control force is not unlimited, the maximum energy to be supplied to the building should be bounded within the actuator's capacity. Several combinations of active control locations are investigated, i.e., two controllers at both dampers, one controller at first damper only, and one controller at the second damper only. Continuous bounded control algorithms utilizing continuous function are used as the control algorithms in this paper. From the numerical simulations, it is found that the best result is obtained when both control forces are applied to the mass dampers. In the case that only one actuator is used, better performance is achieved when the control force is applied at the first (bottom) damper.

On the assessment of a tunable auxiliary mass damper with a friction damper in its suspension: numerical study

Auxiliary Mass Damper‘s (AMD) performance is susceptible to changes in the frequency or in the excitation force’s nature. Therefore, to improve the robustness of the AMD it’s necessary to design new systems which are tunable and that could be used over large frequency range. In this work a friction damper, which is an association in series of a spring and a scratcher, is used to tune the AMD at the same time it dissipates the mechanical energy of the principal mass by changing the normal force on the scratcher. Three normal force control strategies, and two combinations of them, are studied: i) The normal force is assumed constant; ii) The normal force is obtained from the solution of the equation of motion assuming null displacement for the principal mass; iii) The normal force is obtained based on the vibratory system’s state variables condition, guarantying that the direction of the friction force promotes the movement of the principal mass toward its static equilibrium position. The effectiveness of the proposed tunable AMD, where the adaptability is obtained by controlling the normal force on the smart friction damper, is evaluated based on mass and frequency ratios variations for each strategy.

Characterization of an Eigenfrequency Adaptable Machine Tool Carriage

Current machine tools feature fixed eigenfrequencies which are often excited by high performance cutting operations leading to unfavorable process conditions or poor workpiece quality, for example, due to chatter. Approaches to resolve this problem either constitute in changes of the process conditions, adaptable auxiliary mass dampers or vast and expensive changes within the machine tool structure. All of these approaches are either expensive, lead to a lower cutting ability or do not address the underlying problem.A novel approach to avoid chatter is described in this paper. It deals with a frequency adaptable machine tool carriage made out of hollow carbon fiber reinforced plastic (CFRP) profiles. This light structure enables chambers to be filled separately. This allows a tuning of the eigenfrequencies by pumping fluid into the chambers of the carriage reducing the eigenfrequencies. The CFRP structure has a high “added mass to component mass” ratio due to the high stiffness in relation to the density of the CFRP. Thus shifting the eigenfrequencies on a larger scale in comparison to the carriages of the same kind but made out of steel or cast iron.Within this paper, the approach as well as measurement results of the prototypical realization will be presented. The paper will address measurements of sloshing, the influence of added fluid mass regarding different filling levels and the influence of the control behavior of the feed axis. The paper shall conclude with a comparison of the measurements to a similar machine tool carriage made out of steel. In the end, an outlook on upcoming research topics and activities shall be given.

Active vibration control by a smart auxiliary mass damper equipped with a fiber Bragg grating sensor

This paper presents the results of a key activity of a large research project (MESEMA) in the aeronautics field, funded by the European Community under the Sixth Framework Programme, namely the modeling and control of a magnetostrictive actuator to be used for broadband vibration and noise control. The developed auxiliary mass damper was designed in order to meet the demanding requirements of the application at hand, especially in terms of weight reduction and force capability. The specifications were successfully satisfied using a resonant intertial actuator concept based on a nonlinear mechanism for amplifying the seismic mass displacement. The nonlinearities of the actuator highly affect the problem of its adoption within the active feedback control system devoted to vibration and noise reduction of the controlled structure. In order to overcome the limitation and negative effects of these nonlinearities within the main control system, the actuator was equipped with an optical sensor based on a fiber Bragg grating (FBG). The FBG was used within a low-level control loop based on a model-following control algorithm, aimed at imposing a desired linear behavior to the actuator itself. The controlled actuator was used to design an optimal vibration controller. Experimental results show the effectiveness of the approach both for the low-level and the high-level control loops.

Performance of Particle Dampers Under Random Excitation

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.

Modeling and control of an electrorheological device for structural control applications

This paper presents some of the results of an experimental and analytical study of a controllable electrorheological (ER) device configured to induce an adjustable amount of dynamic shear force in response to an applied voltage. Maps of the force-deformation characteristics of the aluminosilicate based ER material are developed over a relatively wide frequency range, and approximating analytical expressions are obtained for the force-deformation-frequency-voltage characteristics of the material. Subsequently, an evaluation is made of the efficiency of using online control of an electrorheological actuator to emulate the operation of an optimally tuned auxiliary mass damper attached to a primary system subjected to arbitrary dynamic environments. It is shown through numerical simulation studies that the proposed parameter control algorithm provides an efficient means for the online control of the primary system under a wide range of excitations. An experimental study is presented in which an ER device is used, in conjunction with a small laboratory building model, as a semiactive element in an online structural control approach using pulse control techniques.

Control of intelligent nonlinear adaptive systems under earthquake excitation

AbstractA semi‐active control procedure which utilizes a class of nonlinear auxiliary mass dampers with adaptive parameters is presented. Among the major features of this approach is its simplicity, robustness, and lack of need of a mathematical model of the structure whose motion is to be controlled. Numerical simulation results as well as experimental studies with a simple laboratory test structure (reported in a cited reference) demonstrate the feasibility of the proposed approach.

Modeling the oscillatory dynamic behaviour of electrorheological materials in shear

Electrorheological (ER) materials consisting of alumino-silicate in fluorinated liquids are experimentally studied with the objective of developing mathematical models of the observed dynamic behaviour. Experiments investigating the oscillatory behaviour of ER materials in shear are carried out over a frequency range of 1-45 Hz. Mathematical models are developed by three approaches: first, a global equivalent linear system approach; second, a parametric identification in which a mechanical model is developed; and third, a non-parametric method which approximates the experimentally measured non-linear restoring force. Models of ER material behaviour would greatly aid designers to better evaluate the appropriateness of these materials for a specific application. One such practical application of interest explored is in the area of vibration control. An auxiliary mass damper using an ER device is found to be capable of reducing the steady-state response of a system by an additional 30% when compared to an optimal linear viscous damper.

Active Parameter Control of Nonlinear Vibrating Structures

A simple, yet efficient method is presented for the on-line vibration control of nonlinear, multidegree-of-freedom systems responding to arbitrary dynamic environments. The procedure uses nonlinear auxiliary mass dampers with adjustable motion-limiting stops located at selected positions throughout a given nonlinear system. A mathematical model of the system to be controlled is not needed for implementing the control algorithm. The degree of the primary structure oscillation near each vibration damper determines the damper’s actively-controlled gap size and activation time. By using control energy to adjust the damper parameters instead of directly attenuating the motion of the primary system, a significant improvement is achieved in the total amount of energy expended to accomplish a given level of vibration control. In a related paper, the direct method of Lyapunov is used to establish that the response of the controlled nonlinear primary structure is Lagrange stable. Numerical simulation studies of several example systems, as well as an experimental study with a mechanical model, demonstrate the feasibility, reliability, and robustness of the proposed semi-active control method.

Response and damping of a rectangular cantilever plate with vibrating beam dampers

In this work the use of beams as auxiliary mass dampers for cantilever plates is considered. Because the cantilever plate problem, which is of strong industrial interest, does not lend itself to a Lévy-type solution, the procedure developed by Ritz is used. Structural damping is incorporated into the main and auxiliary systems by treating them as having a complex elastic modulus. With appropriate selection of the parameters, the fundamental resonance of the plate is split into two new ones with considerably suppressed responses. In order to verify the analysis, an experimental investigation was carried out and the results obtained were compared with the theory developed.

Random Excitation of a Nonlinear Vibration Neutralizer

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.

Forced Vibration of Class of Nonlinear Dissipative Beams

An “exact” solution employing a Galerkin-type approach is presented for the steady-state motion of a class of dissipative Bernoulli-Euler beams provided with nonlinear auxiliary mass dampers. The beams are viscously damped and the excitation is furnished in the form of distributed, or concentrated loads, or both, that vary sinusoidally. The nonlinear damper may be applied to any point in the system. Experimental studies with a mechanical model corroborate the theoretical results. Results of the analysis are applied to cantilever and simply-supported beams subjected to base excitation, uniform load, and discrete force excitation at various points along the beams. The effects of all system parameters and mass ratio are determined. It is found that the damper under consideration is an efficient device for reducing the vibration of continuous systems, particularly cantilevered structures.

Stochastic excitation of a simple system with impact damper

AbstractAn approximate analytical solution is obtained for the stationary response of a highly nonlinear auxiliary mass damper (impact damper) attached to a single‐degree‐of‐freedom oscillator that is subjected to an excitation with white power spectral density and Gaussian probability distribution. Experimental measurements with an electronic analogue computer verify the analytical findings both qualitatively and quantitatively. Results are given for the mean‐squared level and the power spectral density of the response. The effects of various damper parameters on the response of the primary system are determined. The impact damper under consideration is shown to be substantially more effective than the conventional dynamic vibration neutralizer in controlling the response of stochastically excited primary systems.