The damping in MEMS inertial sensors both at high and low pressure levels

Except for MEMS working in a ultra high vacuum, the main cause of damping is the air surrounding the system. When the working pressure is equal to the atmospheric one (from now on called “high pressure,” i.e., 10⁵ Pa), the mean free path of an air molecule is much smaller than typical MEMS dimensions. Thus, air can be considered as a viscous fluid and two phenomena occur: flow damping and squeeze film damping. These two phenomena can be evaluated through a simplified Navier–Stokes equation. In a medium vacuum (from now on called “low pressure”), i.e., the “packaging” pressure, the air cannot be considered as a viscous fluid any more since the mean free path of an air molecule is of the same order of magnitude of typical MEMS dimensions. Thus, the molecular fluid theory must be used to estimate the damping. To predict the damping of a MEMS device both at high and low pressure levels, a multiphysics code was used. The proposed approach was validated through comparison with experimental data.     

Nonlinear modeling of hysteretic systems with double hysteretic loops using position and acceleration information

This paper presents two new dynamic hysteresis models obtained from the Bouc–Wen model by incorporating position and acceleration information. On the one hand, the model employing position information is rate-independent and it is able to reproduce some kind of double hysteretic loops unable to be reproduced with the original Bouc–Wen model. On the other hand, the model employing acceleration information is insensitive to linear time-scale variations. Moreover, a classification of the BIBO-stable models has been derived for both position and acceleration cases. Double hysteretic loops have been experimentally reported in shape-memory alloys, reinforced concrete structures, wood structures and lightweight steel shear wall structures. The proposed hysteretic models represent a prominent use in the field of structural dynamics and earthquake engineering because they can capture the nonlinear dynamics of the materials and structures presented earlier when they are subjected to dynamic loads as earthquake excitations.     

A Recipe for Building the Torsional-Rigidity Bounds of Shafts Containing Multiply Coated Fibers with Imperfect Interfaces

This work is concerned with deriving the upper and lower bounds for the torsional rigidity of cylindrical shafts with arbitrary cross-section containing a number of multiply coated fibers with imperfect interfaces along the interfaces. Each multicoated fiber may have different constituents with different area fractions. In the formulation, we first extend our previous formulation, based on classical energy principles in elasticity, to construct torsional rigidity bounds for shafts containing simply coated fibers with two different kinds of imperfect interface. Next, based on the present results for shafts containing simply coated fibers and our previous findings for shafts containing homogeneous fibers with imperfectly bonded interfaces, we propose a concept of replacement fiber with an effective shear rigidity to replace the effect of fiber with imperfect bonding interface. In addition, we propose an equivalent shear rigidity to simulate the effect of a simply coated fiber. This replacement procedure allows us to construct the bounds, through a recursive procedure, for the torsional rigidity of shafts containing multiply coated fibers with possibly imperfect interfaces.     

A three-scale FE approach to reliability analysis of MEMS sensors subject to impacts

In this paper the effects of accidental impacts on polysilicon MEMS sensors are investigated within the framework of a three-scale finite element approach. By allowing for the very small ratio (on the order of 10⁻⁴) between the inertia of the MEMS and the inertia of the whole device, macro-scale analyses at the package length-scale are run to obtain the loading conditions at the sensor anchor points. These loading conditions are successively adopted in meso-scale analyses at the MEMS length-scale to detect where the stress level tends to be amplified by sensor layout. To foresee failure of polysilicon in these domains, as caused by the propagation of inter- as well as trans-granular cracks up to percolation, representative crystal topologies are handled in micro-scale analyses. In case of a uni-axial MEMS accelerometer falling from a reference drop height, results show that the crystal structure within the failing sensor detail can have a remarkable effect on the failure mode and on the time to failure. Conversely, through comparison with simulations where the MEMS is assumed to fall anchored to the naked die, it is assessed that packaging only slightly modifies failure details, without significantly reducing the shock loading on the sensor. F. Fachin is currently with: Technology Laboratory for Advanced Materials and Structures, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307 (USA). F. Cacchione is currently with: ABB SACE, Viale dell’Industria 18, Vittuone, 20010 (Italy).     

Performance comparison among some nonlinear filters for a low cost SINS/GPS integrated solution

The Kalman filter is a familiar minimum mean square estimator for linear systems. In practice, the filter is frequently employed for nonlinear problems. This paper investigates into the application of the Kalman filter’s nonlinear variants, namely the extended Kalman filter (EKF), the unscented Kalman filter (UKF) and the second order central difference filter (CDF2). A low cost strapdown inertial navigation system (SINS) integrated with the global position system (GPS) is the performance evaluation platform for the three nonlinear data synthesis techniques. Here, the discrete-time nonlinear error equations for the SINS are implemented. Test results of a field experiment are presented and performance comparison is made for the aforesaid nonlinear estimation techniques.     

A new chaotic system with fractional order and its projective synchronization

Based on Rikitake system, a new chaotic system is discussed. Some basic dynamical properties, such as equilibrium points, Lyapunov exponents, fractal dimension, Poincaré map, bifurcation diagrams and chaotic dynamical behaviors of the new chaotic system are studied, either numerically or analytically. The obtained results show clearly that the system discussed is a new chaotic system. By utilizing the fractional calculus theory and computer simulations, it is found that chaos exists in the new fractional-order three-dimensional system with order less than 3. The lowest order to yield chaos in this system is 2.733. The results are validated by the existence of one positive Lyapunov exponent and some phase diagrams. Further, based on the stability theory of the fractional-order system, projective synchronization of the new fractional-order chaotic system through designing the suitable nonlinear controller is investigated. The proposed method is rather simple and need not compute the conditional Lyapunov exponents. Numerical results are performed to verify the effectiveness of the presented synchronization scheme.     

A multibody-based dynamic simulation method for electrostatic actuators

A numerical simulation method is developed to analyze the dynamic responses of electrostatic actuators, which are electromechanically-coupled systems. The developed method can be used to determine the dynamic responses of cantilever-type switches, which are an example of typical MEMS (Micro-Electro-Mechanical System) devices driven by an electrostatic force. We propose the approach that adopts a point charge to deal with electric field effects between electrodes. This approach may be considered as a lumped parameter model for the electrostatic interactions. An advantage of this model may be the easy incorporation of the electrostatic effects between electrodes into a multibody dynamics analysis algorithm. The resulting equations contain the variables for position, velocity, and electric charge to describe the motion of the masses and the charges on the electrodes in a system. By solving these equations simultaneously, the dynamic response of an electrostatically-driven system can be correctly simulated. In order to realize this approach, we implement the procedures into RecurDyn, the multibody dynamics software developed by the authors. The developed numerical simulation tool was evaluated by applying it to cantilever-type electrostatic switches in many different driving conditions. The results suggest that the developed tool may be useful for predicting behaviors of electrostatic actuators in testing as well as in design.     

A symbolic algorithm for the automatic computation of multitone-input harmonic balance equations for nonlinear systems

A symbolic algorithm is developed for the automatic generation of harmonic balance equations for multitone input for a class of nonlinear differential systems with polynomial nonlinearities. Generalized expressions are derived for the construction of balance equations for a defined multitone signal form. Procedures are described for determining combinations for a given output frequency from the desired set obtained from box truncated spectra and their permutations to automate symbolic algorithm. An application of method is demonstrated using the well-known Duffing–Van der Pol equation. Then the obtained analytical results are compared with numerical simulations to show the accuracy of the approach. The computation times for both the numerical solutions of equations versus the number of frequency components and the symbolic generation of the equations versus the power of nonlinearity are also investigated.     

A stage-structured single species model with pulse input in a polluted environment

In this paper, we study a stage-structured single species model with pulse input in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain the globally attractive condition for the species-extinction periodic solution of the investigated system. By the use of the theory of impulsive delayed differential equation, we also obtain sufficient condition of the permanence of the investigated system. Our results reveal that long mature period of the population in polluted environment can cause it to go extinct. Supported by National Natural Science Foundation of China (10647005), and the Nomarch Foundation of Guizhou Province.     

Approximate stationary solution and stochastic stability for a class of differential equations with parametric colored noise

This paper aims to study a class of differential equations with parametric Gaussian colored noise. We present the general framework to get the solvability conditions of the approximate stationary probability density function, which is determined by the Fokker-Planck-Kolmogorov (FPK) equations. These equations are derived using the stochastic averaging method and the operator theory with the perturbation technique. An illustrative example is proposed to demonstrate the procedure of our proposed method. The analytical expression of approximate stationary probability density function is obtained. Numerical simulation is carried out to verify the analytical results and excellent agreement can be easily found. The FPK equation for the probability density function of order ε ⁰ is used to examine the almost-sure stability for the amplitude process. Finally, the stability in probability of the amplitude process is investigated by Lin and Cai’s method.     

Multiple scales analysis for double Hopf bifurcation with?1:3?resonance

The dynamical behavior of a general n-dimensional delay differential equation (DDE) around a 1:3 resonant double Hopf bifurcation point is analyzed. The method of multiple scales is used to obtain complex bifurcation equations. By expressing complex amplitudes in a mixed polar-Cartesian representation, the complex bifurcation equations are again obtained in real form. As an illustration, a system of two coupled van der Pol oscillators is considered and a set of parameter values for which a 1:3 resonant double Hopf bifurcation occurs is established. The dynamical behavior around the resonant double Hopf bifurcation point is analyzed in terms of three control parameters. The validity of analytical results is shown by their consistency with numerical simulations.     

A numerical model for static and free vibration analysis of elastic composite beams with end shear restraint

The end shear restraint, which is an un-classical type of end support, has a significant effect on the behavior of elastic composite beams. The principal aim of this paper is to present a numerical model for studying the effect of end shear restraint on static and free vibration behavior of elastic composite beams with various end conditions. The elastic composite beam, considered in this study, is composed of an upper concrete slab and a lower steel beam, connected at the interface by shear transmitting studs. This type of beam is widely used in constructions especially for highway bridges. The three types of end conditions considered in this study are simple, fixed and free supports. The numerical model is based on the combination of transfer matrix and analog beam methods. The field transfer matrices for the element of the elastic composite beam are derived. The present model is applied to the beam systems with and without end shear restraint and the static response and natural frequencies are calculated. the effect of shear stiffness between the upper slab and lower beam is also demonstrated.     

Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions

Euler’s celebrated buckling formula gives the critical load N for the buckling of a slender cylindrical column with radius B and length L as

Mathematic modeling and characteristic analysis for dynamic system with asymmetrical hysteresis in vibratory compaction

We investigate dynamic characteristics of vibratory compaction system with asymmetrical hysteresis. An asymmetrical model derived from Bouc-Wen differential equation is employed to describe hysteretic behavior of vibration engineering. A practical polynomial expression for hysteretic restoring force is deduced to be substituted into standard equation of the system, assuming that the non-linearity of the restoring force is weak. An asymptotic method, which combines Krylov-Bogolyubov-Mitropolsky (KBM) method with harmonic balance (HB) method, is applied to analyze steady-state responses of the asymmetrical hysteretic system subjected to harmonic excitation. Dynamic responses, such as the restoring force time histories and frequency responses of the system for the first order approximate, are obtained. Furthermore, numerical solution obtained using Runge-Kutta method as well as results of experiments (asphalt compaction on the Beijing-Fuzhou highway) are compared with the asymptotic solution. These results investigated that asymmetrical hysteretic model and the methods applied in this paper are quite appropriate for engineering applications.     

Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters

In this paper, the stability analysis problem is considered for a class of stochastic neural networks with mixed time-delays and Markovian jumping parameters. The mixed delays include discrete and distributed time-delays, and the jumping parameters are generated from a continuous-time discrete-state homogeneous Markov process. The aim of this paper is to establish some criteria under which the delayed stochastic neural networks are exponentially stable in the mean square. By constructing suitable Lyapunov functionals, several stability conditions are derived on the basis of inequality techniques and the stochastic analysis. An example is also provided in the end of this paper to demonstrate the usefulness of the proposed criteria.     

A new pedestrian-following model for aircraft boarding and numerical tests

The purpose of this paper is to develop a new pedestrian-following model based on the properties of the aircraft boarding process. The passengers’ motion trail, the number of interfaces, the total aircraft boarding time, the wasted time that is resulted by the interfaces and the effective aircraft boarding time are investigated in detail. The numerical results illustrate that the new model can qualitatively describe some dynamic properties of the aircraft boarding process.     

A Universal Expression for Bounds on the Torsional Rigidity of Cylindrical Shafts Containing Fibers with Arbitrary Transverse Cross-Sections

We derive upper and lower bounds for the torsional rigidity of host shafts containing a number of cylindrical fibers. The transverse cross-sections of the host shaft and the fibers are simply connected, but could be arbitrary in shape. Utilizing the fact that the torsion solution of a homogeneous host shaft with simply connected cross-section can be known, we propose a method to construct statically and kinematically admissible fields interior to the matrix and to the fibers. Previous developments on bounding the torsional rigidity of composite shaft so far are confined to circular fibers. Here we try to simulate fibers with non-circular cross-section and incorporate the interactions of the cross-sectional shapes of the host shaft and the fibers at the same time. Proceeding from extremal principles of elasticity, together with propositions of some domain integration procedures, we provide a universal expression for bounds on the torsional rigidity of the composite shaft. The exact expressions depend on the constituent information of the fibers and the host shaft, which could offer useful information to tailor the shape and the arrangement of the constituents to achieve an optimal value.     

A revisit to synchronization of Lurie systems with time-delay feedback control

This paper revisits the problem of synchronization for general Lurie systems with time-delay feedback control. Differently from most of existing results, the more restrictively slope restrictions on the nonlinearities of Lurie systems are considered in view of the fact that the slope restrictions may improve synchronization conditions compared with the sector ones. The Kalman–Yakubovich–Popov (KYP) lemma and the Schur complement formula are applied to get novel and less conservative synchronization criteria, which have the forms of linear matrix inequalities (LMIs). Numerical examples are presented to illustrate the efficiency of the proposed results.     

A nonlinear numerical simulation of a lab centrifuge with internal damping

This paper is about numerical simulations of dissipation processes in rotor shaft joints of rotor systems. Based on measurement results a nonlinear simulation model of a lab centrifuge is stated. The effects of internal damping in combination with nonlinear stiffness and friction in the rotor shaft joint of the lab centrifuge are worked out. It is shown that the nonlinearities cause the amplitudes to rest limited once increased amplitudes due to internal damping appear. One focus is the derivation of suitable force laws describing the mechanisms of the components within the connection.     

A comparative experimental study on the use of three denoising methods for bearing defect detection

In the conditional maintenance of mechanical components by vibratory analysis, one distinguishes two types of analyses which are necessary for obtaining a reliable diagnosis. The first analysis lies in the detection of potential defects; there are currently various succeeded methods based on the treatment of the vibratory signals allowing the localization of a defect. One can quote among these methods the analysis of spectrum (with constant resolution (RC) or percentage of bands constant (PCB)), the analysis of envelope, the analysis cepstrale, the analysis time-frequencies or the analysis time-scales (wavelet). The second analysis is interested in the determination and the evaluation of severity of a defect detected to estimate the influence of this defect on the operation of a mechanism. The scalar indicators which make it possible to estimate the gravity of a defect are indicators known as total which are based on the statistical analysis of a temporal signal. However, the signals resulting from accelerometer sensors are the results of a mixture of sources of vibrations, sources being able to be allotted to one or more defects and are generally polluted by noise. This work presents the three principal methods of denoising and the study of their influence on the scalar parameters (kurtosis, factor peak, value rms) and this within the framework of the detection of defects of the chippings types of bearings.