No description available.

Acoustic liners employing the Helmholtz resonator concept are commonly used in the intake duct of modern jet engines to reduce radiated noise. In response to reports of core failures, the possibility of acoustic loading as the source of these liner failures is investigated. Experimental data are used as input to a model for non-rigid cavity walls and the induced stresses analysed. An alternative, more robust, liner design utilizing viscous damping is proposed, and an analytical model developed and numerically validated against published data. A study of the key parameters leads to an improved configuration, the attenuating properties of which are compared to a typical liner.

A numerical method is used to predict flow fields and forces for squeeze film dampers (SFDs). A two dimensional SFD is modeled with different amplitudes and frequencies of the journal orbiting inside the wall. In addition to the typical circular centered orbit (CCO) motion prescribed in most studies, orbits can vary greatly from circular to linear. The study is divided into two distinctive models including single phase flow model and two phase flow model. The single phase flow model cases including three amplitudes, i.e. 0.002, 0.001, and 0.0005 inches, and three frequencies, i.e. 10, 50, and 200 Hz, of journal motions are conducted to portray flow fields and forces and ultimately determine their relationships. The numerical prediction shows that the journal amplitude and frequency affect flow and consequently force in the SFD. The force is directly proportional to frequency and motion amplitude. Owing to the presence of cavitation in the practical SFD, the two phase flow model is also presented with the journal amplitude of 0.0002 and three frequencies of 10, 50, and 100 Hz, respectively. The ambient pressure condition was set up for numerical processing ranging from 0.001 Mpa to 100 Mpa. The results indicate that the operating pressure has an integral role in suppressing the presence of the cavitation. The caviation disappears if the operating pressure is high enough above the vapor pressure of the lubricant.

Squeeze film dampers (SFDs) provide viscous damping to attenuate excessive vibrations and enhance system stability in turbomachinery. SFDs are of special importance in aircraft engines which use rolling element support bearings that, by themselves, do not provide enough damping to ensure safe operation. A modular test rig capable of simulating actual operating conditions in aircraft jet engines is used to test two centrally grooved, end sealed, SFDs. Both SFDs have diameter D and nominal radial clearance c and consist of two parallel squeeze film lands separated by a deep circumferential groove of length LG and depth dG. A short length damper with film land lengths L and a long damper with land lengths 2L are tested. Piston rings seal the damper lands. An ISO VG2 lubricant is supplied to the SFD via three radial holes that discharge lubricant into the central groove. The lubricant passes through the damper lands and across the piston ring seals to finally exit the damper at ambient pressure. Circular orbit tests of amplitude ~0.5c and for static eccentricities varying from 0 to ~0.36c are conducted on the two sealed dampers. The instrumental variable filter method (IVFM) serves to identify the SFD dynamic force coefficients. The parameter identification range is 50Hz to 210Hz for the short damper and 110Hz to 250Hz for the long damper. Large amplitude dynamic pressures measured in the central groove demonstrate that the central groove does not divide the damper in two separate film lands, but the lubricant in the groove interacts with the squeeze film lands, hence contributing significantly to the SFD forced response. Dynamic pressures in the film lands and in the central groove reveal that both dampers operate free of air ingestion or cavitation for the tested static eccentricities and amplitudes of motion. Comparisons to test results for the same SFD configurations but with open ends demonstrate the effectiveness of the end seals on increasing the direct damping coefficients. For the sealed ends short length damper, the added mass coefficients are ~2 times larger and the damping coefficients are ~3.8 times larger than the respective coefficients of the open ends long damper. For the sealed ends long damper, the damping coefficients are ~2.8 times, and the added mass coefficients are ~3.1 times larger than coefficients from the open ends configuration. The identified SFD direct stiffness coefficients are nearly zero except at the maximum static eccentricity for the long damper. Predictions from a novel computational model that include the effects of the central groove, the lubricant feed holes and the end seals are in excellent agreement with results from the short length damper. For the long damper, the predicted damping coefficients are in good agreement with the test results, while the added mass coefficients are under predicted by ~25 percent. Experimental results from the two sealed SFD configurations lead to a better understanding of the effects of end seals as well as central feed groves on the SFD forced performance. The results presented in this thesis will help improve the effectiveness of SFDs aircraft jet engines.

This paper is going to emphasize on the air squeeze film damping effect on micro-mechanical resonant beam in MEMS. In general, the low energy density of electrode force will cause high-voltage power supply to drive the electro- micro resonators; reducing the distance between the electrode and resonant beam can be the most efficient way to solve this problem. But bringing different exciting frequency of system and environmental pressure to the air squeeze film effect might cause it changes form similarly to the damping qualities, and this will also change the dynamic characteristics of micro resonator. The dynamic model for double clamped micro-mechanical resonant beam is proposed by using Lagrange¡¦s equation in this study. The corresponding eigenvalue problems of resonant beam are formulated and solved by employing the hypothetical mode method. Under the presumption of viscous damping model, we may obtain a damping factor which includes the parameters of size, temperature and air pressure when energy transfer model is employed to simulate the squeeze film damping effect of two immediate objects. Eventually, the damping ratio and the dynamic characteristics of resonant microbeam are derived by means of exploring the frequency response function of system. Besides, the frequency change of micro-mechanical resonant beam due to an axial force is also considered in the thesis.

Squeeze film dampers are used in the high speed turbo machinery industry and aerospace industries as a means to reduce vibration amplitude, to provide damping, to improve dynamic stability of the rotor bearing system and to isolate structural components. The effects of cavitation included in previous studies were not effective. The effect of different design parameters were not studied thoroughly as experimental investigation of squeeze film dampers is very expensive. Few of them used numerical investigation but the methods they used are either time consuming or complicated. The present study investigated the feasibility of applying a steady state solver, which is computationally less expensive, for analyzing flow field inside the squeeze film dampers. The behavior of dynamic pressure profiles at different operating conditions, and the effect of a central groove on dynamic pressure profiles were also studied. Simulation results of a 3D case which is similar to the one experimentally studied by Delgado were used to establish if the moving reference frame (MRF) model in Fluent 12.1 can be used. A steady state solver in an absolute frame of reference was used to produce whirling motion of the rotor in this study. The inlet pressure of 31kpa and the whirling speed of 50 and 100Hz were used as boundary conditions. The mixture model with three percent dissolved air in lubricant is used to model multiphase flow. Singhal cavitation model is used to model cavitation. The simulations (50,000 iterations) were run until steady state solutions were reached. The results closely agreed with those obtained experimentally by San Andrés and Delgado. Numerical simulations of three-dimensional cases with an additional central groove on the squeeze film land were also performed to predict the effect of central groove on dynamic pressure profiles. Addition central groove reduces the pressures and forces generated by squeeze film damper.

Fluid damping arising from squeeze film flow of air or some inert gas trapped between an oscillating micro mechanical structure, such as a beam or a plate, and a fixed substrate often dominates the other energy dissipation mechanisms in silicon based MEM devices. As a consequence, it has maximum effect on the resonant response or dynamic response of the device. Unfortunately, modelling of the squeeze film flow in most MEMS devices is quite complex because of several factors unique to MEMS structures. In this thesis, we set out to study the effect of these factors on squeeze film flow. First we list these factors and study each of them in the context of a particular application, using experimental measurements, extensive numerical simulations, and analytical modelling for all chosen factors. We consider five important factors. The most important factor perhaps is the effect of rarefaction that is dominant when a device is vacuum packed with low to moderate vacuum, typical for MEMS packaging. The second problem is to investigate and model the effect of perforations which are usually provided for efficient etching of the sacrificial layer during fabrication of the suspended structures. The third problem is to consider the effect of non-uniform deflection of the structure such as those in MEMS cantilever beams and model its effect on the squeeze film. The fourth effect studied is the influence of different boundary conditions such as simple, fully open and partially closed boundaries around the vibrating structure on the characteristics of the squeeze film flow. The fifth problem undertaken is to analyze the effect of high operating frequencies on the squeeze film damping. In the first problem, the rarefaction effect is studied by performing experiments under varying pressures. Depending on the ambient pressure or the size of the gap between the vibrating and the fixed structure, the fluid flow may fall in any of the flow regimes, ranging from continuum flow to molecular flow, and giving a wide range of dissipation. The relevant fluid flow characteristics are determined by the Knudsen number, which is the ratio of the mean free path of the gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably big for molecular flow. Here, we study the effect of fluid pressure on the squeeze film damping by carrying out experiments on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects and switches. We vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow, transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different air pressures ranging from 760 torr to 0.001 torr. The variation of this pressure over six orders of magnitude ensures the required rarefaction to range over all flow conditions. Finally, we get the variation of the quality factor with pressure. The result indicates that the quality factor, Q, follows a power law, Q P-r, with different values of the exponent r in different flow regimes. To numerically model the effect of rarefaction, we propose the use of effective viscosity in Navier-Stokes equation. This concept is validated with analytical results for a simple case. It is then compared with the experimental results presented in this thesis. The study shows that the effective viscosity concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h0/L < 0.01). However, as this ratio increases, the range of validity decreases. Next, a semianalytical approach is presented to model the rarefaction effect in double-gimballed MEMS torsion mirror. In this device, the air gap thickness is 80 µm which is comparable to the lateral dimension 400 µm of the oscillating plate and thus giving the air-gap to length ratio of 0.2. As the ratio 0.2 is much greater than 0.01, the conventional Reynolds equation cannot be used to compute the squeeze film damping. Consequently, we find the effective length of an equivalent simple mirror corresponding to the motion about the two axes of the mirror such that the Reynolds equation still holds. After finding the effective length, we model the rarefaction effect by incorporating effective viscosity which is based on different models including the one proposed in this paper. Then we compare the analytical solution with the experimental result and find that the proposed model not only captures the rarefaction effect in the slip, transition and molecular regimes but also couples well with the non-fluid damping in the intrinsic regime. For the second problem, several analytical models exist for evaluating squeeze film damping in rigid rectangular perforated MEMS structures. These models vary in their treatment of losses through perforations and squeezed film, in their assumptions of compressibility, rarefaction and inertia, and their treatment of various second order corrections. We present a model that improves upon previously reported models by incorporating more accurate losses through holes proposed by Veijola and treating boundary cells and interior cells differently as proposed by Mohite et al. The proposed model is governed by a modified Reynolds equation that includes compressibility and rarefaction effect. This equation is linearized and transformed to the standard two-dimensional diffusion equation using a simple mapping function. The analytical solution is then obtained using Green’s function. The solution thus obtained adds an additional term Γ to the damping and spring force expressions derived by Blech for compressible squeeze flow through non-perforated plates. This additional term contains several parameters related to perforations and rarefaction. Setting Γ = 0, one recovers Blech’s formulas. We benchmark all the models against experimental results obtained for a typical perforated MEMS structure with geometric parameters (e.g., perforation geometry, air gap, plate thickness) that fall well within the acceptable range of parameters for these models (with the sole exception of Blech’s model that does not include perforations but is included for historical reasons). We compare the results and discuss the sources of errors. We show that the proposed model gives the best result by predicting the damping constant within 10% of the experimental value. The approximate limit of maximum frequencies under which the formulas give reasonable results is also discussed. In the third problem, we study the effect of elastic modeshape during vibration on the squeeze film flow. We present an analytical model that gives the values of squeeze film damping and spring coefficients for MEMS cantilever resonators taking into account the effect of flexural modes of the resonator. We use the exact modeshapes of a 2D cantilever plate to solve for pressure in the squeeze film and then derive the equivalent damping and spring coefficient relations from the back force calculations. The relations thus obtained can be used for any flexural mode of vibration of the resonators. We validate the analytical formulas by comparing the results with numerical simulations carried out using coupled finite element analysis in ANSYS, as well as experimentally measured values from MEMS cantilever resonators of various sizes and vibrating in different modes. The analytically predicted values of damping are, in the worst case, within less than 10% of the values obtained experimentally or numerically. We also compare the results with previously reported analytical formulas based on approximate flexural modeshapes and show that the proposed model gives much better estimates of the squeeze film damping. From the analytical model presented here, we find that the squeeze film damping drops by 84% from the first mode to the second mode in a cantilever resonator, thus improving the quality factor by a factor of six to seven. This result has significant implications in using cantilever resonators for mass detection where a significant increase in quality factor is obtained only by using vacuum. In the fourth and fifth problem, the effects of partially blocked boundary condition and high operating frequencies on squeeze films are studied in a MEMS torsion mirror with different boundary conditions. For the structures with narrow air-gap, Reynolds equation is used for calculating squeeze film damping, generally with zero pressure boundary conditions on the side walls. This procedure, however, fails to give satisfactory results for structures under two important conditions: (a) for an air-gap thickness comparable to the lateral dimensions of the micro structure, and (b) for non-trivial pressure boundary conditions such as fully open boundaries on an extended substrate or partially blocked boundaries that provide side clearance to the fluid flow. Several formulas exist to account for simple boundary conditions. In practice, however, there are many micromechanical structures, such as torsional MEMS structures, that have non-trivial boundary conditions arising from partially blocked boundaries. The most common example is the double-gimballed MEMS torsion mirror of rectangular, circular, or hexagonal shape. Such boundaries usually have clearance parameters that can vary due to fabrication. These parameters, however, can also be used as design parameters if we understand their role on the dynamics of the structure. We take a MEMS torsion mirror as an example device that has large air-gap and partially blocked boundaries due to static frames. Next we model the same structure in ANSYS and carry out CFD (computational fluid dynamics) analysis to evaluate the stiffness constant K, the damping constant C, as well as the quality factor Q due to the squeeze film. We compare the computational results with experimental results and show that without taking care of the partially blocked boundaries properly in the computational model, we get unacceptably large errors. Subsequently, we use the CFD calculations to study the effect of two important boundary parameters, the side clearance c, and the flow length s, that specify the partial blocking. We show the sensitivity of K and C on these boundary design parameters. The results clearly show that the effect of these parameters on K and C is substantial, especially when the frequency of excitation becomes close to resonant frequency of the oscillating fluid and high enough for inertial and compressibility effects to be significant. Later, we present a compact model to capture the effect of side boundaries on the squeeze film damping in a simple rectangular torsional structure with two sides open and two sides closed. The analytical model matches well with the numerical results. However, the proposed analytical model is limited to low operating frequencies such that the inertial effect is negligible. The emphasis of this work has been towards developing a comprehensive understanding of different significant factors on the squeeze film damping in MEMS devices. We have proposed various ways of modelling these effects, both numerically as well as analytically, and shown the efficacy of these models by comparing their predictive results with experimental results. In particular, we think that the proposed analytical models can help MEMS device designers by providing quick estimates of damping while incorporating complex effects in the squeeze film flow. The contents of the thesis may also be of interest to researchers working in the area of microfluidics and nanofluidics.

With increasing rotor flexibility and shaft speeds, turbomachinery undergoes large dynamic loads and displacements. Squeeze film dampers (SFDs) are a type of fluid film bearing used in rotating machinery to attenuate rotor vibration, provide mechanical isolation, and/or to tune the placement of system critical speeds. Industry has a keen interest in designing SFDs that are small, lightweight, and mechanically simple. To achieve this, one must have a full understanding of how various design features affect the SFD forced performance. This thesis presents a comprehensive analysis, experimental and theoretical, of a short (L=25.4 mm) open ends SFD design incorporating three lubricant feed holes (without a circumferential feed groove). The damper radial clearance (c=127 μm), L/D ratio (0.2), and lubricant (ISO VG2) have similar dimensions and properties as in actual SFDs for aircraft engine applications. The work presents the identification of experimental force coefficients (K, C, M) from a 2-DOF system model for circular and elliptical orbit tests over the frequency range ω=10-250Hz. The whirl amplitudes range from r=0.05c-0.6c, while the static eccentricity ranges from eS=0-0.5c. Analysis of the measured film land pressures evidence that the deep end grooves (provisions for installation of end seals) contribute to the generation of dynamic pressures in an almost purely inertial fashion. Film land dynamic pressures show both viscous and inertial effects. Experimental pressure traces show the occurrence of significant air ingestion for orbits with amplitudes r>0.4c, and lubricant vapor cavitation when pressures drop to the lubricant saturation pressure (PSAT~0 bar). Identified force coefficients show the damper configuration offers direct damping coefficients that are more sensitive to increases in static eccentricity (eS) than to increases in amplitude of whirl (r). On the other hand, SFD inertia coefficients are more sensitive to increases in the amplitude of whirl than to increases in static eccentricity. For small amplitude motions, the added or virtual mass of the damper is as large as 27% of the bearing cartridge mass (MBC=15.15 kg). The identified force coefficients are shown to be insensitive to the orbit type (circular or elliptical) and the number of open feed holes (3, 2, or 1). Comparisons of damping coefficients between a damper employing a circumferential feed groove1 and the current damper employing feed holes (no groove), show that both dampers offer similar damping coefficients, irrespective of the orbit amplitude or static eccentricity. On the other hand, the grooved damper shows much larger inertia force coefficients, at least ~60% more. Predictions from a physics based model agree well with the experimental damping coefficients, however for large orbit motion, over predict inertia coefficients due to the model neglecting convective inertia effects. Credence is given to the validity of the linearized force coefficients by comparing the actual dissipated energy to the estimated dissipated energy derived from the identified force coefficients. The percent difference is below 25% for all test conditions, and in fact is shown to be less than 5% for certain combinations of orbit amplitude (r), static eccentricity (eS), and whirl frequency (ω).

The accuracy of rotordynamic analysis of aeroengine structures is typically limited by a trade-off between the capabilities and the computational cost of the squeeze-film damper (SFD) bearing model used. Identification techniques provide a means of efficiently implementing complex nonlinear bearing models in practical rotordynamic analysis; thus facilitating design optimisation of the SFD and the engine structure. This thesis considers both identification from advanced numerical models and identification from experimental tests. Identification from numerical models is essential at the design stage, where rapid simulation of the dynamic performance of a variety of designs is required. Experimental identification is useful to capture effects that are difficult to model (e.g. geometric imperfections). The main contributions of this thesis are: • The development of an identification technique using Chebyshev polynomial fits to identify the numerical solution of the incompressible Reynolds equation. The proposed method manipulates the Reynolds equation to allow efficient and accurate identification in the presence of cavitation, the feed-groove, feed-ports, end-plate seals and supply pressure. • The first-ever nonlinear dynamic analysis on a realistically sized twin-spool aeroengine model that fulfills the aim of taking into account the complexities of both structure and bearing model while allowing the analysis to be performed, in reasonable time frames, on a standard desktop computer. • The introduction and validation of a nonlinear SFD identification technique that uses neural networks trained from experimental data to reproduce the input-output function governing a real SFD. Numerical solution of the Reynolds equation, using a finite difference (FD) formulation with appropriate boundary conditions, is presented. This provides the base data for the identification of the SFD via Chebyshev interpolation. The identified 'FD-Chebyshev' model is initially validated against the base (FD) model by application to a simple rotor-bearing system. The superiority of vibration prediction using the FD-Chebyshev model over simplified analytical SFD models is demonstrated by comparison with published experimental results. An enhanced FD-Chebyshev scheme is then implemented within the whole-engine analysis of a realistically sized representative twin-spool aeroengine model provided by a leading manufacturer. Use of the novel Chebyshev polynomial technique is repeatedly demonstrated to reduce computation times by a factor of 10 or more when compared to the basis (FD) model, with virtually no effect on the accuracy. Focus is then shifted to an empirical identification technique. Details of the commissioning of an identification test rig and its associated data acquisition system are presented. Finally, the empirical neural networks identification process for the force function of an SFD is presented and thoroughly validated. When used within the rotordynamic analysis of the test rig, the trained neural networks is shown to be capable of predicting complex nonlinear phenomena with remarkable accuracy. The results show that the neural networks are able to capture the effects of features that are difficult to model or peculiar to a given SFD.

There are many ways in which the surrounding media, such as air between an oscillating MEMS structure and a fixed substrate, can affect the dynamic response of a MEMS transducer. Some of these effects involve dissipation while others involve energy transfer. Transverse oscillations of a planar structure can cause a lateral air flow in small gaps that results in pressure gradients. The forces due to the built–up pressure are always against the vibration of the structure and have characteristics of damper and stiffener. In this work, we study the squeeze film phenomenon due to the interaction between the air–film and the structure in the presence of restrictive flow boundary conditions. It is known that the squeeze film damping due to the air trapped between the oscillating MEMS structure and the fixed substrate often contributes to maximum energy dissipation. We carry out an analysis to estimate damping and stiffness in cases with restrictive flow boundaries in dynamic MEMS devices. While the studies reported in the present work address fluid flow damping with restrictive flow boundaries, the analysis of air-flow shows another important phenomenon of enhanced air-spring stiffness. This study is discussed separately in the context of spring stiffening behavior in MEMS devices exhibiting squeeze film phenomenon. First a theoretical framework for modeling squeeze film flow is established and this is followed with analytical and numerical solutions of problems involving squeeze film phenomenon. Modeling of squeeze film effects under different flow conditions is carried out using Reynold’s equation. The problem of squeeze film damping in MEMS transducers is more involved due to the complexities arising from different boundary conditions of the fluid flow. In particular, we focus our attention on estimation of damping in restricted flow boundaries such as only one side vented and no side vented passive boundary conditions. Damping coefficient for these cases are extracted when the fluid is subjected to an input velocity profile according to a specific mode shape at a given frequency of oscillation. We also explain the squeeze film flow in restricted boundaries by introducing the concept of passive and active boundary conditions and analyzing the pressure gradients which are related to the compressibility of the air in the cavity. Passive boundary conditions is imposed by specifying the free flow or no flow along one of the edges of the cavity, whereas, active boundary condition is imposed by the velocity profile being specified at the interface of the cavity with the oscillating structure. Some micromechanical structures, such as pressure sensors and ultrasound transducers use fully restricted or closed boundaries where the damping for such cases, even if small, is very important for the determination of the Q–factor of these devices. Our goal here is to understand damping due to flow in such constrained spaces. Using computational fluid dynamics (ANSYS–FLOTRAN), the case of fully restricted boundaries is studied in detail to study the effect of important parameters which determines the fluid damping, such as flow length of the cavity, air–gap height, frequency of oscillations and the operating pressure in the cavity. A simulation strategy is developed using macros programming which overcomes some of the limitations of the existing techniques and proves useful in imposing a non–uniform velocity and the extraction of damping coefficient corresponding to the flexibility of the structure in specific oscillation modes. Rarefaction effects are also accounted for in the FEM model by introducing the flow rate coefficient, or, alternatively using the concept of effective viscosity. The analysis carried out for the fully restricted case is motivated by the analytical modeling of squeeze film phenomenon for a wide range of different restricted boundaries, and analyzing the resulting pressure gradient patterns. We show that significant damping exists even in fully restricted boundaries due to lateral viscous flow. This is contrary to known reported results, which neglect damping in such cases. The result indicates that in fully restrictive fluid flow boundaries or in a closed cavity, air damping cannot be neglected at lower oscillation frequencies and large flow length to air-gap ratio if the active boundary has a non-uniform velocity profile. Analysis of air-flow in the case of restricted flow boundaries shows another important phenomenon of enhanced air-spring stiffness. It is found that fluid film stiffness has a nonlinear dependence on various parameters such as air-gap to length ratio, fluid flow boundary conditions and the frequency of oscillation. We carry out analysis to obtain the dynamic response of MEMS devices where it is significantly affected by the frequency dependent stiffness component of the squeeze film. We show these effects by introducing frequency dependent stiffness in the equation of motion, and taking examples of fluid boundary conditions with varying restriction on flow conditions. The stiffness interaction between the fluid and the structure is shown to depend critically on stiffness ratios, and the cut-off frequency. It is also inferred that for a given air–gap to flow length ratio, the spring behaviour of the air is independent of the flow boundary conditions at very high oscillation frequencies. Hence, we limit our focus on studying the effect of fluid stiffness in the regime where it is not fully compressible. For non-resonant devices, this study finds its utility in tuning the operating frequency range while for resonant devices it can be useful to predict the exact response. We show that it is possible to design or tune the operating frequency range or shift the resonance of the system by appropriate selection of the fluid flow boundary conditions. The emphasis of the present work has been toward studying the effect of squeeze film flow on dynamic response of MEMS structures with restrictive flow boundary conditions. Estimation of energy dissipation due to viscous flow cannot be ignored in the design of MEMS which comprise of restricted flow boundaries. We also remark that modeling of a system with squeeze film flow of the trapped air in terms of frequency independent parameters, viz. damping and stiffness coefficient, is unlikely to be very accurate and may be of limited utility in specific cases. Although the central interest in studying squeeze film phenomenon is on the damping characteristics because of their direct bearing on energy dissipation or Q–factor of a MEMS device, the elastic behaviour of the film also deserves attention while considering restrictive flow boundary conditions.