**7. References**

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© 2012 Balthazar et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**On an Overview of Nonlinear and Chaotic** 

José Manoel Balthazar, Angelo Marcelo Tusset, Atila Madureira Bueno

It is known that in Brazil and in the whole world, the development of mathematical modeling techniques for the study of problems involving new technologies and the design of nonlinear structures is an emerging area in Engineering Science. To background to the general problems of non-linear dynamics, see the comprehensive monographs:

This chapter addresses this issue, involving the dynamical behavior of Electrical Mechanical Systems (EMS), that are systems responsible for electromechanical energy conversion. It is common knowledge that an electromechanical system can be classified in three different groups, according to scales dimensions: *i*) Macro-Systems >1mm, *ii*) Micro-Systems <1mm

The Macro-Systems are characterized by being visible without using microscope and they are present in our Day to Day activities. The Micro-Systems are generally constructed on silicon chips, and are employed in manufacturing integrated electronic circuits. The Nano-Systems can only be seen and manipulated with the use of the Atomic Force Microscope.

In this research field - MEMS and NEMS -, the researches are based on the fact that, in opposition to traditional macro-scale problems, the atomic forces effects and surface phenomena are preponderant over the forces of inertia and gravity. It is also known that the manufacture of these new products have been based on the binomial consuming time and an enormous amount of financial resources. Thus, it becomes necessary some investment in an interface, which addresses the design and manufacturing that, gives designers of

and reproduction in any medium, provided the original work is properly cited.

**Microscopy (AFM) Vibrating Problem** 

and Bento Rodrigues de Pontes Junior

http://dx.doi.org/10.5772/51834

**1. Introduction** 

Additional information is available at the end of the chapter

(Awrejcewicz, 1991) and (Awrejcewicz and Lamarque, 2003).

and >0.1μm, and *iii*) Nano-Systems <0.1 μm and >0.1nm.

**Behavior and Their Controls of an Atomic Force** 
