Nonlinear dynamics of microelectromechanical system resonators in the form of rectangular-plan spherical shells taking into account geometrical and physical non-linearity
The relevance. Due to the fact that mineral exploration is a high-tech process, the development of methods of constructing new mathematical models, most closely taking into account the true elements of microelectromechanical systems, is important. Microelectromechanical system is a promising instrum...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | Russian |
| Published: |
Tomsk Polytechnic University
2017-12-01
|
| Series: | Известия Томского политехнического университета: Инжиниринг георесурсов |
| Subjects: | |
| Online Access: | http://izvestiya.tpu.ru/archive/article/view/1950 |
| Summary: | The relevance. Due to the fact that mineral exploration is a high-tech process, the development of methods of constructing new mathematical models, most closely taking into account the true elements of microelectromechanical systems, is important. Microelectromechanical system is a promising instrument of modern Microsystems technology, intensively and dynamically developing scientific and technical direction. The systems are characterized by the unique small weight and size, low power consumption, capable of functioning in harshenvironments and the cost, which is several times lower than that of their traditional analogues. The main aim of the study is to construct the mathematical model, which would reflect more complete the real operation of microelectromechanical systems devices. To do this, one should consider large displacements, stress-strain nonlinear dependence, impact load, temperature field. To design the numerical methods that will allow us to consider a distributed mechanical structure as a system with infinite number degrees of freedom; to analyze the nature of complex nonlinear oscillations of the developed mathematical models; to identify the areas of unstable solution of the considered elements of microelectromechanical systems devices, associated with chaotic oscillations. The methods: variational methods, methods of mathematical physics, computational methods to reduce the equations to the Cauchy problem - the method of finite differences of the 2nd order of accuracy; solution of the Cauchy problem by the methods of Runge-Kutta; methods of qualitative study of nonlinear dynamics: Fourier transform, wavelet analysis, Poincare section, phase portrait. The results and conclusions. It is established that the transients depend on the geometrical and physical parameters of the shell, the frequency of the driving oscillations and other parameters, i. e. there is no a unified scenario of transition from harmonic oscillations to chaotic ones. The character of oscillations depends substantially on the intensity of deformation. The authors have revealed that the most common scenario is the Ruelle-Takens one. For some values of curvature the modifications of this script were obtained. |
|---|---|
| ISSN: | 2500-1019 2413-1830 |