Izhak Bucher

Damping of a micro-resonator torsion mirror in rarefied gas ambient

Damping in resonating MEMS mirrors has a profound effect on the dynamical behavior. The validity of the existing theories is investigated in this work by theoretical and experimental means. The squeeze-film model with artificial viscosity and the molecular dynamics model are adapted for the case of a torsion mirror under a wide range of vacuum levels. The considered ambient pressure varies from atmospheric to a pressure under which structural damping prevails. High resolution experiments have been conducted on dedicated devices. Two independent experimental damping extraction methods have been employed for substantiating the validity of the measured parameters. Although the theoretical models agree favorably with the experimental data, it appears they provide slightly different predictions under different operating regimes.

Levitation force induced by pressure radiation in gas squeeze films

An analytical and numerical study on the levitation force induced by pressure radiation in gas squeeze films is investigated. The levitation phenomenon is known to occur when a planar object is placed at close proximity to a vibrating piston. The existing analytical approaches are based on either conventional acoustic radiation, where the fluid is assumed inviscid or on a variant of the Reynolds equation that incorporates viscous effects. Alas, these solutions are often in poor agreement with accurate numerical results and, at best, describe appropriately cases that include a limited range of object weights and vibration frequencies. In this work, two cases are addressed: the flow induced by vibrations perpendicular to a flat surface and that by flexural wave propagation parallel to the surface. For the first case, numerical and second-order analytical perturbation solutions are obtained and compared, proving them to be in good agreement. In addition, a novel, analytical expression for the levitation forc...

Model updating via weighted reference basis with connectivity constraints

Abstract The paper considers the problem of updating an analytical model from experimental data using the reference basis approach. In the general framework of the reference basis method, certain quantities, e.g., natural frequencies or modeshapes, are considered to be completely accurate and the others are updated by solving a constrained optimization problem. However, the underlying structure, known as connectivity, existing in the model is not preserved, and the method is not suited for parametric updating. In this paper, a method for introducing connectivity constraints into reference basis, while maintaining its advantages, is presented. It brings the reference basis method closer to a broad class of updating methods that use parametric updating. The notions of “connectivity cost” and “parameterization cost” are defined and used to obtain the best model for a given parameterization and to compare the outcomes of different parameterizations.

Coupled dynamics of a squeeze-film levitated mass and a vibrating piezoelectric disc: numerical analysis and experimental study

Abstract This work deals with the dynamics of a vibrating piezoelectric disc, which creates, under specific vibrating conditions, an air squeeze film that is able to levitate a freely suspended object. In such problems, the coupling effects between the various components affect the overall dynamical behaviour of the combined system. For complex systems, which combine elastic and electro-static effects together with compressible fluid effects, the coupled equations are often dealt with separately to avoid modelling and computational complexity. In this paper, the importance of handling such systems in a coupled manner is advocated by means of numerical and experimental examples. A coupled model is derived in this work making use of a concise numerical solver to allow for this investigation under several conditions. The piezoelectric part of the structure is modelled by finite elements while the squeeze film phenomenon is represented by means of finite-difference equations, to model a variant of the Reynolds equation. The numerical model was verified during each step in the development of the numerical algorithm and indeed showed good agreement with existing publications, but once the components were combined, it was found that several phenomena were misrepresented in the past due to the neglect of the coupling effects. Several physical insights are brought from the simulation and investigation of the numerical results. In the last part, the importance of coupled analysis is emphasized by introducing an experimental investigation of the dynamical behaviour while conducting a comparison with numerical simulation results. From this comparison, the limitations of state-of-the-art modelling procedures are clarified.

Noncontacting lateral transportation using gas squeeze film generated by flexural traveling waves—Numerical analysis

This paper presents the theory describing the dynamical behavior of a noncontacting lateral transportation of planer objects by means of a gas squeeze film created by traveling flexural waves of a driving surface. An oscillating motion in the normal direction between two surfaces can generate a gas film with an average pressure higher than the surrounding. This load-carrying phenomenon arises from the fact that a viscous flow cannot be instantaneously squeezed; therefore, fast vibrations give rise to a cushioning effect. Equilibrium is established through a balance between viscous flow forces and compressibility forces. When the oscillatory motion between two surfaces creates traveling waves, lateral viscous forces are generated in addition to the normal levitation forces. These forces are produced as a result of nonuniform pressure gradients in the lateral direction between the surfaces. The combination of normal and lateral forces could be used for transporting objects without any direct contact with the driving surface. The numerical algorithm in this work couples the squeeze film phenomenon, which is represented by means of finite difference equations, to model a variant of the Reynolds equation, together with the equations describing the dynamics of the floating object. Numerical simulations are presented and investigated to highlight noteworthy topics.

Estimating the ratio between travelling and standing vibration waves under non-stationary conditions

This paper presents a new method of spatially decomposing vibration patterns in real time into their travelling and standing parts. This method creates a localized parametric model describing the nature of the developed vibrations leading to a scalar measure of the travelling to standing waves ratio. Despite being rather simple compared with spatial Fourier transform that yields space-averaged results, the current method seems superior for a localized description. Due to its superior localization, the decomposition conveys important insight and valuable information for vibrating structures that can be used for identification, diagnosis and for control purposes of ultrasonic motors and rotating discs. Several features make the proposed method advantageous over existing schemes, in particular when the number of deployed sensors is small and confined to a small region. It is shown that the presented approach differs from the commonly used Fourier-based methods in several ways: (a) the proposed method does not require equally distributed sensors and does not require a spatially complete coverage of the analyzed domain nor does it require equally spaced sensing elements; (b) the algorithm makes neither use of the spatial wavelength nor requires its estimate to curve-fit the instantaneous spatial deformation patterns; (c) the method is most suitable for cases where a localized pattern needs to be estimated and is therefore robust to imperfections in the vibrating structure; (d) the presented formulation has a recursive form that is suitable for real-time implementations by a digital signal processor.

On the sensing and tuning of progressive structural vibration waves

Progressive flexural waves can be generated only in finite structures by fine tuning the excitation and the boundary conditions. The tuning process eliminates the reflected waves arising from discontinuities and edge effects. This work presents and expands two new methods for the identification and tuning of traveling waves. One is a parametric method based on fitting an ellipse to the complex spatial amplitude distribution. The other is a nonparametric method based on the Hubert transform providing a space-localized estimate. With these methods, an optimization-based tuning of transverse flexural waves in a one-dimensional structure, a vibrating beam, is developed. Existing methods are designed for a single frequency and are based on either combining two vibration modes or mechanical impedance matching. Such methods are limited to a designated excitation frequency determined by a specific configuration of the system. With the proposed methods, structural progressive waves can be generated for a wide range of frequencies under the same given system configuration and can be tuned in real time to accommodate changes in boundary conditions. An analytical study on the nature of the optimal excitation conditions has been carried out, revealing singular configurations. The experimental verification of the sensing and tuning methods is demonstrated on a dedicated laboratory prototype. The proposed methods are not confined to mechanical waves and present a comprehensive approach applicable for other physical wave phenomena.

Experimental Identification of Nonlinearities under Free and Forced Vibration using the Hilbert Transform

In this paper we discuss the experimental identification of a nonlinear vibrating mechanical system. The system under test incorporated several spring and damping related nonlinearities. Indeed, in this paper we use data from a real laboratory device thus increasing the confidence in the proposed methods that have been previously applied mostly to simulated data. A unique feature of the identified model is that it shows the dependency of the estimated parameters on the vibration amplitude. The provided measurements of free and forced vibration motion, together with the unique signal processing, based on the Hilbert transform analysis, yield an accurate estimation of nonlinear spring and friction parameters of the vibration model. The obtained natural frequencies and friction parameters are functions rather than scalars that describe the system’s behavior under different operating conditions. This paper complements previously published Hilbert transform analytical methods with experimental and numerical results.

Spatial and Temporal Excitation to Generate Traveling Waves in Structures

The problem in the creation of traveling waves is approached here from an unconventional angle. The formulation makes use of normal vibration modes, which are standing waves, to express both traveling waves and the required force distribution. It is shown that a localized force is required at any discontinuity along the structure to absorb reflected waves. This convention is demonstrated for one- and two-dimensional structures modeled as continua, and as discretized numerical approximation of the mass and stiffness matrices. Harmonic vibrations can be characterized as standing or traveling waves or as a combination of both. By applying forces that have been specially designed for the purpose, the vibratory response can become a pure traveling wave. The force distribution is important for the design of ultrasonic motors and in control applications, attempting to absorb and create outgoing and incoming waves.

Experimental crack identification using electrical impedance tomography

Abstract This paper addresses the problem of practical crack identification in electrically conducting specimens using only boundary measurements. The method is commonly referred to in the literature as Electrical Impedance Tomography (EIT). Crack identification is determined from the electrical impedance distribution, which amounts to solving an inverse problem, starting from boundary measurements. Whereas this kind of inverse problem has been extensively addressed in its theoretical and numerical aspects, there is a scarcity of experimental results aimed at examining the applicability of the method for real conditions. We present new experimental results, based on a simple identification methodology. The efficiency and limitations of this method are assessed through a series of numerical simulations and laboratory experiments on two-dimensional geometries. Following a preliminary numerical validation stage, actual crack detection is carried out on a discrete network of resistors, as an approximation to Laplaces equation. Next, experiments are carried out on a continuous conductive medium, containing one and two flaws. Our results show that EIT is a promising candidate for crack identification in real life conditions with a potential for multiple crack detection.