In this paper, a mathematical model is presented for studying thin film damping of the surrounding fluid in an in-plane oscillating micro-beam resonator. The proposed model for this study is made up of a clamped-clamp...In this paper, a mathematical model is presented for studying thin film damping of the surrounding fluid in an in-plane oscillating micro-beam resonator. The proposed model for this study is made up of a clamped-clamped micro-beam bound between two fixed layers. The microgap between the micro-beam and fixed layers is filled with air. As classical theories are not properly capable of predicting the size dependence behaviors of the micro-beam,and also behavior of micro-scale fluid media, hence in the presented model, equation of motion governing longitudinal displacement of the micro-beam has been extracted based on non-local elasticity theory. Furthermore, the fluid field has been modeled based on micro-polar theory. These coupled equations have been simplified using Newton-Laplace and continuity equations. After transforming to non-dimensional form and linearizing, the equations have been discretized and solved simultaneously using a Galerkin-based reduced order model. Considering slip boundary conditions and applying a complex frequency approach, the equivalent damping ratio and quality factor of the micro-beam resonator have been obtained. The obtained values for the quality factor have been compared to those based on classical theories. We have shown that applying non-classical theories underestimate the values of the quality factor obtained based on classical theo-ries. The effects of geometrical parameters of the micro-beam and micro-scale fluid field on the quality factor of the resonator have also been investigated.展开更多
Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, ...Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, the assumption of the continuum fluid theory is no longer justified and the use of micro-polar fluid theory is indispensable. In this paper a mathematical model was presented in order to predict the viscous fluid damping in a laterally oscillating finger of a micro-resonator considering micro-polar fluid theory. The coupled governing partial differential equations of motion for the vibration of the finger and the micro-polar fluid field have been derived. Considering spin and no-spin boundary conditions, the related shape functions for the fluid field were presented. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions and have been discretized using a Galerkin-based reduced order model. The effects of physical properties of the micro-polar fluid and geometrical parameters of the oscillating structure on the damping ratio of the system have been investigated.展开更多
文摘In this paper, a mathematical model is presented for studying thin film damping of the surrounding fluid in an in-plane oscillating micro-beam resonator. The proposed model for this study is made up of a clamped-clamped micro-beam bound between two fixed layers. The microgap between the micro-beam and fixed layers is filled with air. As classical theories are not properly capable of predicting the size dependence behaviors of the micro-beam,and also behavior of micro-scale fluid media, hence in the presented model, equation of motion governing longitudinal displacement of the micro-beam has been extracted based on non-local elasticity theory. Furthermore, the fluid field has been modeled based on micro-polar theory. These coupled equations have been simplified using Newton-Laplace and continuity equations. After transforming to non-dimensional form and linearizing, the equations have been discretized and solved simultaneously using a Galerkin-based reduced order model. Considering slip boundary conditions and applying a complex frequency approach, the equivalent damping ratio and quality factor of the micro-beam resonator have been obtained. The obtained values for the quality factor have been compared to those based on classical theories. We have shown that applying non-classical theories underestimate the values of the quality factor obtained based on classical theo-ries. The effects of geometrical parameters of the micro-beam and micro-scale fluid field on the quality factor of the resonator have also been investigated.
文摘Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, the assumption of the continuum fluid theory is no longer justified and the use of micro-polar fluid theory is indispensable. In this paper a mathematical model was presented in order to predict the viscous fluid damping in a laterally oscillating finger of a micro-resonator considering micro-polar fluid theory. The coupled governing partial differential equations of motion for the vibration of the finger and the micro-polar fluid field have been derived. Considering spin and no-spin boundary conditions, the related shape functions for the fluid field were presented. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions and have been discretized using a Galerkin-based reduced order model. The effects of physical properties of the micro-polar fluid and geometrical parameters of the oscillating structure on the damping ratio of the system have been investigated.
