ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

The study of the vibrating systems when the external excitation it is influenced by the response of the system, has been considered a major challenge in theoretical and practical engineering research. When motors are attached to structures that need excitation power levels similar to the power capacity of those motors, interesting non-linear phenomena may happen, such as: Modal saturation-energy transfer between modes and Sommeferld effect. On one hand, it is also well know that those Micro-electro-mechanical systems (MEMS) are one of the new and modern challenges in the engineering sciences field, owing to its interdisciplinary nature of research and extremely small feature size, which are now produced cheaply and in very small packages, in the micro domain. The research is going on, by using macro model as a possible outlook in this area. We mention the study of the characteristics of the parameters need to be studied in more detail to guarantee the reliability of the (MEMS). On the other hand, the atomic force microscope (AFM) system has become a useful instrument to measure the intermolecular forces, with atomic-resolution, since its discovery in 1986. The nonlinear dynamic (AFM), consists itself of a vibrating micro cantilever, with a nanoscale tip, which interacts with a sample surface via short- and long-range intermolecular forces. Amplitude-modulation (AFM) involves amplitude oscillations between 1 and 100 nm. It is known that, micro cantilevers possess several distinct eigenmodes and the tip-sample interaction forces are Highly nonlinear. The adopted cantilever-sample mode interaction was mathematically modeled as a number of single spring-mass (mass: being the tip of the cantilever). The cantilever interacts with the sample via a tip, which is mounted on the cantilever.