Studying thin film damping in a micro-beam resonator based on non-classical theories

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.

Effects of air damping on quality factors of different probes in tapping mode atomic force microscopy

The AFM probe in tapping mode is a continuous process of energy dissipation,from moving away from to intermittent contact with the sample surfaces.At present,studies regarding the energy dissipation mechanism of this continuous process have only been reported sporadically,and there are no systematic explanations or experimental verifications of the energy dissipation mechanism in each stage of the continuous process.The quality factors can be used to characterize the energy dissipation in TM-AFM systems.In this study,the vibration model of the microcantilever beam was established,coupling the vibration and damping effects of the microcantilever beam.The quality factor of the vibrating microcantilever beam under damping was derived,and the air viscous damping when the probe is away from the sample and the air squeeze film damping when the probe is close to the sample were calculated.In addition,the mechanism of the damping effects of different shapes of probes at different tip–sample distances was analyzed.The accuracy of the theoretical simplified model was verified using both experimental and simulation methods.A clearer understanding of the kinetic characteristics and damping mechanism of the TM-AFM was achieved by examining the air damping dissipation mechanism of AFM probes in the tapping mode,which was very important for improving both the quality factor and the imaging quality of the TM-AFM system.This study’s research findings also provided theoretical references and experimental methods for the future study of the energy dissipation mechanism of micro-nano-electromechanical systems.

A Generalized Reynolds' Equation For Squeeze-Film Air Damping in MEMS

A differential equation that is generally effective for squeeze film air damping of perforated plate and non perforated plate as well as in MEMS devices is developed.For perforated plate,the thickness and the dimensions of the plate are not limited.With boundary conditions,pressure distribution and the damping force on the plate can be found by solving the differential equation.Analytical expressions for damping pressure and damping force of a long strip holeplate are presented with a finite thickness and a finite width.To the extreme conditions of very thin plate and very thin hole,the results are reduced to the corresponding results of the conventional Reynolds' equation.Thus, the effectiveness of the generalized differential equation is justified.Therefore,the generalized Reynolds' equation will be a useful tool of design for damping structures in MEMS.

Damping characteristics analysis of squeeze film damper with metal rubber

A squeeze film damper (SFD) with metal rubber (MR) ring installed on the end and the radial direction of rotor are implemented in this paper. Based on the hypothesis of π film, the description of the new SFD/MR flux and nonlinear oil film damping force is derived according to the Reynolds Eq. and Darcy’s law. It proves that the SFD/MR has better damping characteristics than the traditional SFD after comparatively analyzing characteristics of oil film between the traditional short SFD and the SFD/MR.

Broad-Band FMR Linewidth of Co_2MnSi Thin Films with Low Damping Factor:The Role of Two-Magnon Scattering

The low Gilbert damping factor, which is usually measured by ferromagnetic resonance, is crucial in spintronic applications. Two-magnon scattering occurs when the orthogonMity of the ferromagnetic resonance mode and other degenerate spin wave modes was broken by magnetic anisotropy, voids, second phase, surface defects, etc., which is important in analysis of ferromagnetic resonance linewidth. Direct fitting to linewidth with Gilbert damping is advisable only when the measured linewidth is a linear function of measuring frequency in a broad band measurement. We observe the nonlinear ferromagnetic resonance linewidth of Co2MnSi thin films with respect to measuring frequency in broad band measurement. Experimental data could be well fitted with the model including two-magnon scattering with no fixed parameters. The fitting results show that two-magnon scattering results in the nonlinear linewidth behavior, and the Gilbert damping factor is much smaller than reported ones, indicating that our Co2MnSi films are more suitable for the applications of spin transfer torque.

Structural and Magnetic Properties of Co2MnSi Thin Film with a Low Damping Constant

Co2MnSi thin films are made by magnetron sputtering onto MgO （001） substrates. The crystalline quality is improved by increasing depositing temperature and/or annealing temperature. The sample deposited at 550℃ and subsequently annealed at 550℃ （sample I） exhibits a pseudo-epitaxial growth with partially ordered L21 phase. Sample I shows a four-fold magnetic anisotropy, in addition to a relatively weak uniaxial anisotropy. The Gilbert damping factor of sample I is smaller than 0.001, much smaller than reported ones. The possible reasons responsible for the small Gilbert damping factor are discussed, including weak spin-orbit coupling, small density of states at Fermi level, and so on.

Multi-relaxation-time lattice Boltzmann simulation of slide damping in micro-scale shear-driven rarefied gas flow

To investigate the slide film damping in the micro-scale shear-driven rarefied gas flows, an effective multi-relaxation-time lattice Boltzmann method(MRT-LBM) is proposed. Through the Knudsen boundary layer model, the effects of wall and rarefaction are considered in the correction of relaxation time. The results of gas velocity distributions are compared among the MRT, Monte Carlo model(DSMC) and high-order LBM, and the effects of the tangential momentum accommodation coefficient on the gas velocity distributions are also compared between the MRT and the high-order LBM. It is indicated that the amendatory MRT-LBM can unlock the dilemma of simulation of micro-scale non-equilibrium. Finally, the effects of the Knudsen number, the Stokes number, and the gap between the plates on the damping are researched. The results show that by decreasing the Knudsen number or increasing the Stokes number, the slide film damping increases in the transition regime;however, as the size of the gap increases, the slide film damping decreases substantially.