Mass dampers

Find the differential equation relating the displaeements X[ t) and Xo t) for the spring-mass-damper system shown in Figure 2.5. What would be the effeet of negleeting the mass ... 

Fig. 2.6 Free-body diagram for spring-mass-damper system.

Henee a spring-mass-damper system is a seeond-order system. If the mass is zero then... 

Find the value of the eritieal damping eoeffieient Q spring-mass-damper system shown in Figure 3.17. 

A spring-mass-damper system has a mass of 20 kg, a spring of stiffness 8000 N/m and a damper with a damping eoeffieient of 80Ns/m. The system is exeited by a eonstant amplitude harmonie foreing funetion of the form... 

Fig. 8.1 Spring-mass-damper system and free-body diagram.

For the spring-mass-damper system given in Example 8.1, Figure 8.1, the state equations are shown in equation (8.13)... 

Flarmonic Excitation of a SDOF System In this section, we will see the behavior of the spring mass damper model when we add a harmonic force in the form below (Fig. 3). 

Restriction of achievable feed bandwidth and performance capability of machines High stiffness and damping with low mass required Active vibration suppression by semi-active and active ancillary systems (e.g., adaptive mass damper, adaptive friction damper)... 

Fig. 9. a) Cathedral furnace where the seismic isolation can be easily applied, b) Distillation column and adjacent steel frame in which is possible to realize dissipative bracings in the steel frame, dissipative coupling between column and frame, and Timed Mass Damper, linking the equipment placed at several levels of the frame with the same frame using proper isolators. 

Hoang N., Fujino Y., Wamitchai P., 2008. Optimal tuned mass damper for seismic ap>plication and practical design formulas. Engineering Structures 30,707-715. 

There are essentially three parts to the sensor. One is the mechanical part, the second is the piezoelectric transformation, and the last one is the electronics necessary to produce the amplification. The oscillating mass is a second-order mass, damper, stiffness system. Let us consider now the models of each of these sections with the aim at putting them together as a multidisciplinary mechatronics model. 

Without a tuned mass damper, the top floors of very tall buildings can sway back-and-forth 30 centimeters or more in a strong wind, let alone an earthquake. 

He proposed an example that uses this flow chart to design a 70 m footbridge. He found that dynamics was the dimensioning criterion. If one wants a first natural frequency larger than 5 Hz, one needs to reduce the stress level to an unacceptable level. Therefore one can use a Tuned Mass Damper to attenuate the accelerations in... 

A very important gain in volume can be achieved if one uses tuned mass dampers. An example, with parametric analysis, shows clearly that one needs to consider a design for stiffness approach when dynamic loads are important. 

A complex structural system, such as frame structures representing buildings, bridges or mechanical systems, can be assembled from components which are formulated as reciprocal structures. Reciprocal structures are those structures characterized by convex potential and dissipation functions (Stern, 1965). In this section, the concept of reciprocal structures is explained using simple spring-mass-damper-slider models shown in Figure 1. Mixed Lagrangian and Dissipation functions of such systems are derived for various structural components. 

A multi-objective robust criterion for tuned mass dampers optimal design... 

ABSTRACT This work proposes a robust optimization criterion of mechanical parameters in the design of linear Tuned Mass Dampers (TMD) located at the top of a main structural system subject to random base accelerations. The dynamic input is modelled as a stationary filtered white noise random process. The aim is to properly consider non-uniform spectral contents that happen in many real physical vibration phenomena. The main structural system is described as a single linear degree of freedom, and it is assumed that uncertainty affects the system model. The problem parameters treated are described as random uncorrelated variables known only by the estimation of their means and variances. Robustness is formulated as a multi-objective optimization problem in which both the mean and variance of a conventional objective function (OF) are minimized simultaneously. Optimal Pareto fronts are obtained and results show a significant improvement in performance stability compared to a standard conventional solution. 

A Tuned Mass Damper (TMD) is one of the simplest and the most rehable passive device for vibration control in a wide range of applications, and for this reason many optimization criteria have been proposed for this specific device. Essentially, a TMD consists in an additional mass connected to a main system by a spring and a damper. The main system, excited by a base acceleration, is modelled as a stochastic stationary coloured noise and introducing the global space state vector ... 

Marano, G.C., Greco, R., Trentadue, F. Chiaia, B. 2007. Constrained reliability-based optimization of linear tuned mass dampers for seismic control . International Journal of Solids and Structures, accepted for publication. 

As in most technical fields, actuators are increasingly designed with the help of computers. The actuator and its surrounding are simulated as a mathematical model by means of commercially available software. Such models are fundamental for the simulation of the system response characteristic in each specific case. In this way, it is possible to find out about all the important properties of the system even before the actuator is built, and the actuators relevant parameters can be optimized to achieve the desired values. This designing strategy is exemplified below with an auxiliary mass damper which is able to withdraw kinetic energy from a host vibrating system. 

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