DYNAMICS OF A GEOMETRICALLY AND PHYSICALLY NONLINEAR SENSITIVE ELEMENT OF A NANOELECTROMECHANICAL SENSOR IN THE FORM OF AN INHOMOGENEOUS NANOBEAM IN THE TEMPERATURE AND NOISE FIELDS

Abstract

The research relevance. Nanoelectromechanical systems, being highly sensitive sensors with small dimensions and reliable in operation, are increasingly used in the oil and gas industry for monitoring various processes in oil production, from exploration to enhanced oil recovery, as well as in well drilling, cleaning, fractionation and processing before decommissioning. One application example of nanoelectromechanical systems is seismic exploration. The use of nanoelectromechanical systems offers improved performance in addition to significant cost and time savings for a wide range of oil and gas industry technologies. With continuous monitoring capabilities, these technologies can become the foundation of smart deposits. The main aim of the researchis a construction of a mathematical model that most closely describes the sensitive element nonlinear dynamics of a nanoelectromechanical sensor under an alternating load action. For this, it is necessary to take into account the most common kinematic hypotheses, scale effects using the modified couple stress theory of elasticity, the nonlinear relationship between stresses and strains, the material inhomogeneity, noise and thermal fields. And also to examine the complex nonlinear oscillations nature and identify patterns of transition from harmonic to chaotic. Objects: geometrically and physically nonlinear nanobeam, described by the kinematic model of the first approximation, which is affected by a uniformly distributed alternating transverse load with a harmonic component, the temperature field and additive external noise. Methods: variation methods, a second-order finite difference method for reducing the system of nonlinear partial differential equations to the Cauchy problem, the Newmark method for solving the Cauchy problem, the Birger method of variable elasticity parameters for solving a physically non-linear problem, the variation iteration method for obtaining an analytical solution of the two-dimensional heat equation. Results. The variation iterations method is used to obtain an analytical solution of thermal conductivity. An oscillations mathematical model for the sensitive element of the nanoelectromechanical sensor in the form of a size-dependent beam, on which a uniformly distributed transverse load with a harmonic component acts, is constructed. In addition to the variable load, the influence of the temperature field and additive external noise exposure were taken into account. The geometric nonlinearity is accepted according to Theodore von Karmantheory (the relationship between deformations and displacements). To take into account the physical nonlinearity of the beam material, the deformation plasticity theory and the method of variable elasticity parameters are used. The motion equations of a mechanical system element, as well as the corresponding boundary and initial conditions, are derived from the Ostrogradsky–Hamilton principle based on a modified moment theory taking into account the Euler–Bernoulli hypothesis. It was revealed that the temperature and noise fields reduce the load at which the transition to the chaotic state of the system occurs. The transition from harmonic to chaotic oscillations occurs according to Ruelle–Takens–Newhouse scenario.

Keywords

• euler–bernoulli nanobeam
• nanoelectromechanical system
• accelerometer for measuring borehole parameters
• temperature and noise fields
• modified couple stress theory of elasticity
• finite difference and newmark methods
• chaotic oscillations of a nanoelectromechanical system