5 edition of **Optimal control theory for the damping of vibrations of simple elastic systems.** found in the catalog.

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Published
**1972** by Springer in Berlin .

Written in English

**Edition Notes**

Series | Lecture notes in mathematics, 253, Lecture notes in mathematics (Berlin) -- 253. |

ID Numbers | |
---|---|

Open Library | OL15273417M |

ISBN 10 | 354005734X |

New designs, especially those that use newer, composite materials, may need to use different types of bonding agents, which makes the pieces stronger but also eliminates one of the methods of damping. There is a wide range of current applications, but Sorbothane can also be fully custom made to your own specifications as needed. For this construction, the mathematic bilinear model of elastic-hysteresis loop was theoretically developed. The Direct Updated Method is used in optimization procedure and the results show that the optimum values of the absorber parameters depend upon various factors, namely: the position of the applied force, the location where the absorbers are attached, the position at which the beam response should be minimized, and also the beam characteristics such as boundary conditions, rotatory inertia, shear deformation, structural damping, and cross sectional geometry.

Sorbothane is used in a number of these situations for the very fact that it is adaptable, customizable and better able to handle temperature fluctuations than other types of more rigid materials. The pressure on the contact surfaces was selected as the parameter for the control of the properties of the all-metal multilayer vibration insulators with structural damping. In such case, the differential equation that describes the free movement of a single-degree-of-freedom system becomes: where h is the hysteretic damping coefficient and i denotes the imaginary unit ; the presence of i is required to synchronize the damping force to the velocity xi being in phase with the velocity. In this regard, the authors of this article had an idea to create the design of all-metal vibration insulators with controlled elastic-hysteretic characteristics.

However, it can be improved. Elastic damping materials return to their original shape after absorbing shock or vibration. Elastic-damping element has a rectangular cross-section Fig. On the opposite end of the beam the force is applied.

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It was found that the multilayer structures with an instant slippage and the uniform pressure between the layers have the best damping properties. A wide range of models can be found in specialized literature, but one of them should be referred here: the so called "hysteretic damping model" or "structural damping model".

Sorbothane restores that ability without changing the strength or design of the machine and without impacting user safety. The uniformity of compression of layers in the package is provided by specially profiled elastic rings, which serve as the supports of the vibration insulator too.

The physical quantity that is oscillating varies greatly, and could be the swaying of a tall building in the wind, or the speed of an electric motorbut a normalised, or non-dimensionalised approach can be convenient in describing common aspects of behavior.

Each use is unique, but that does not mean that the same material cannot be used in multiple types of situations. If the material is always the source of breakdown or failure, it is time to consider replacing it.

The variety of case studies is expected to stimulate a holistic view of sound and vibration and related fields and to appeal to a broad spectrum of engineers such as the ones in the mechanical, aeronautical, aerospace, civil and electrical communities.

Damping not based on energy loss can be important in other oscillating systems such as those that occur in biological systems and bikes.

The authors noted that the slippage of the layers occurs immediately in two-layer beam when a certain force on the end of beam is reached.

The obtained results can be useful for design of effective parametrically controlled systems of vibration protection for any field of technology.

An elastic-damping element is working on bending mainly. It is flexible and can be made to be as thick or thin as is needed for the exact use at hand.

The optimum tuning and damping ratios of the absorbers, each tuned to the mode of concern, are determined numerically by sloving a min-max problem. Issue Section: Research Optimal control theory for the damping of vibrations of simple elastic systems.

book Topics:. Advanced Search A procedure in designing optimal Dynamic Vibration Absorbers DVA for a structurally damped beam system subjected to an arbitrary distributed harmonic force excitation, is presented. Goodman and J. The resulting curves giving the non-dimensional absorber parameters can he used for practical applications, and some interesting conclusions can be drown from the study of them.

Although requiring complex analysis to solve the equation, this model reproduces the real behaviour of many vibrating structures more closely Optimal control theory for the damping of vibrations of simple elastic systems. book the viscous model. The interaction between absorbers is also accounted for in the analysis.

It prevents vibrational creep, the action of a machine moving out of place due to the vibrations during operation.

The beam rigidly fixed at one end. It can withstand a wide range of temperatures or fluctuations in temperatures without hardening, melting or getting sticky. In [] an extensive analysis of the opportunities of the different energy dissipation systems with the structural damping e.

In the similar way, as in the first design, electrostriction items controlled by electrical voltage can be located under the clamps. In such case, the differential equation that describes the free movement of a single-degree-of-freedom system becomes: where h is the hysteretic damping coefficient and i denotes the imaginary unit ; the presence of i is required to synchronize the damping force to the velocity xi being in phase with the velocity.

Klamp []. Sorbothane is a unique material and may be the best solution to many types of situations where vibration damping is a must. Because it can also flow, it is able to be used in smaller, more delicate operations than other, firmer material would be.

Purely elastic materials do not dissipate energy heat when a load is applied, then removed; however, a viscoelastic substance does. One of the variants of the design of the all-metal vibration insulator with perception spatial load is illustrated on Fig.

They give off the energy absorbed as heat. The design of the controllable vibration insulator with perception spatial load [3, 27] 2. Alternative models Viscous damping models, although widely used, are not the only damping models.

Many systems exhibit oscillatory behavior when they are disturbed from their position of static equilibrium.Optimal control of elastic joints with variable damping. optimal control theory we show that it is possible to significantly and optimally exceed the motor maximum velocity by appropriate.

Introducing the control laws, including the quadratic, nonlinear and optimal feedback control laws, into the BLS, it is found that the eddy-current damper can be used to suppress flexible and shear vibrations simultaneously, and the system is globally asymptotically stable. Numerical results are provided to validate the theoretical galisend.com by: 9.

However, a similar type of parametrically controlled all-metal vibration insulators is little studied. In this research, the possibility of control of elastic-hysteretic characteristics of multilayer vibration insulators from metal is proved on the basis of the theory of similarity and theory of structural galisend.com: Alexander S.

Gvozdev, Vladimir S. Melentjev.Pdf 18, · Optimal Control Theory for the Damping of Vibrations of Simple Elastic Systems pp | Cite as Classification of the boundary conditions in optimal control theory of beams and thin plates AuthorsAuthor: Vadim Komkov.The purpose of optimal tuning of a damped vibration absorber is to minimize the steady-state amplitude of the primary mass over the entire range of driving frequency.

According to Fig.the minimum amplitude can be achieved when the ordinates of the fixed points A, B are the same.Aug 18, · Komkov V. () Introductory ebook. In: Optimal Control Theory for the Damping of Vibrations of Simple Elastic Systems.

Lecture Notes in Mathematics, vol