### Vibrational mechanics : nonlinear dynamic effects, general approach, applications

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This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Views Reads 9. Downloads Given that the goal is to bring together the two communities, such self contained appendix is very helpful. In the informal introduction eight basic problems at the interface of dynamics and control are formulated, which are later developed throughout the book.

- Vibrational Mechanics: Nonlinear Dynamic Effects, General Approach, Applications!
- COMMON LISP : the language.
- High frequency forcing on nonlinear systems - IOPscience?
- Lessons of Disaster: Policy Change after Catastrophic Events (American Governance and Public Policy series);

The problems are formulated somewhat implicitly. It takes some effort to realize what they are. The book contains many examples which are helpful in mastering the material. There is even a special section on applications chapters Many examples go all the way from abstract notions to getting the actual numbers obtained either numerically or analytically.

For readers familiar with dynamical systems theory it would be interesting to see such classical examples as Saddle-Node and Pitchfork bifurcations, Lorentz , and Bogdanov-Takens systems presented in the context of control systems.

## Mechanical Vibration: Where Do We Stand?

In Summary, this book provides a fresh look at classical dynamics problems and is a source of new problems for dynamics community. Also, the systematic use of dynamical systems theory as applied to control systems should be interesting to control theorists. Dynamical Systems Magazine July, Mathematical interaction between the richer and developing countries.

July, Mathematical interaction between the richer and developing countries. We remark that the study of non-ideal vibrating systems, that is, those where the excitation is influenced by the response of the system, is still considered to be a major challenge in theoretical and practical engineering research.

## Steady-state dynamics of a non-ideal rotor with internal damping and gyroscopic effects

When the excitation is not influenced by the response, it is said to be an ideal excitation or an ideal source of energy. On the other hand, when the excitation is influenced by the response of the system, it is said to be non-ideal. Thus, depending on the excitation, one refers to vibrating systems as ideal or non-ideal. The behavior of ideal vibrating systems is well known in current literature, but there are few published results on non-ideal ones.

Generally, non-ideal vibrating systems are those for which the power supply is limited. The behavior of the vibrating systems departs from the ideal case as power supply becomes more limited.

### 5 editions of this work

For non-ideal dynamical systems, one must add an equation that describes how the energy source supplies the energy to the equations that govern the corresponding ideal dynamical system. Thus, as a first characteristic, the non-ideal vibrating system has one more degree of freedom than its ideal counterpart. The first kind of non-ideal problem arising in current literature is the so-called Sommerfeld effect, discovered in see Sommerfeld, , discussed in a book by Kononenko, , and entirely devoted to the subject.

Recently, a review of different theories concerning this subject, was presented in Balthazar et al, , Balthazar et al.

## Vibrational Mechanics: Nonlinear Dynamic Effects, General Approach, Applications

Self-synchronization of shafts is a well-known nonlinear phenomenon, whereby two or more unbalanced shafts on a common movable structure may rotate synchronously due to interaction via structural vibrations only, even in the absence of any direct kinematics coupling. The phenomenon has been extensively studied by asymptotic methods to predict possible multiple steady-state rotational motions and to evaluate their stability, mostly with application to the design of vibrators with a reduced number of driving motors. Certain cases of undesirable shaft self-synchronization in engineering have also been studied, but only steady-state motions were analyzed.

- Some references.
- High frequency forcing on nonlinear systems - IOPscience.
- High frequency forcing on nonlinear systems.
- Designing Cathodic Protection Systems for Marine Structures and Vehicles (ASTM Special Technical Publication, 1370).
- anenzihacharm.ml | Vibrational Mechanics | | Iliya I. Blekhman | Boeken?

Results of numerical simulation of transient self-synchronization of rotating shafts, one potential application being gas turbine engines with multiple shafts, was studied by Dimentberg, In this paper, two unbalanced dc motors are used to demonstrate the self-synchronization that may occur when the shafts rotation speeds become temporarily close to one another depending on the torque, considered as the control variable, and of a support with nonlinear stiffness. This paper is an extension of the following previous works: Palacios, that studied a portal frame with nonlinear characteristic of elasticity under one non-ideal excitation; Balthazar et al.

A first announcement of this work was done by Palacios et al, Consider a nonlinear mechanical system consisting of two unbalanced rotors driven by two dc motors with limited power supplies and mounted on an elastic support with nonlinear stiffening and damping.

Figure 1 illustrates such a system.