A Study of Pressure-Dependent Squeeze Film Stiffness as a Resonance Modulator Using Static and Dynamic Measurements

We report on the resonant frequency modulation of inertial microelectromechanical systems (MEMS) structures due to squeeze film stiffness over a range of working pressures. Squeeze film effects have been studied extensively, but mostly in the context of damping and Q-factor determination of dynamic MEMS structures, typically suspended over a fixed substrate with a very thin air gap. Here, we show with experimental measurements and analytical calculations how the pressure-dependent air springs (squeeze film stiffness) change the resonant frequency of an inertial MEMS structure by as much as five times. For capturing the isolated effect of the squeeze film stiffness, we first determine the static stiffness of our structure with atomic force microscope probing and then study the effect of the air spring by measuring the dynamic response of the structure, thus finding the resonant frequencies while varying the air pressure from 1 to 905 mbar. We also verify our results by analytical and Finite Element Method calculations. Our findings show that the pressure-dependent squeeze film stiffness can affect a rather huge range of frequency modulation (>400%) and, therefore, can be used as a design parameter for exploiting this effect in MEMS devices. 2014-0310]

Physical constraints, fundamental limits, and optimal locus of operating points for an inverted pendulum based actuated dynamic walker

The inverted pendulum is a popular model for describing bipedal dynamic walking. The operating point of the walker can be specified by the combination of initial mid-stance velocity (v(0)) and step angle (phi(m)) chosen for a given walk. In this paper, using basic mechanics, a framework of physical constraints that limit the choice of operating points is proposed. The constraint lines thus obtained delimit the allowable region of operation of the walker in the v(0)-phi(m) plane. A given average forward velocity v(x,) (avg) can be achieved by several combinations of v(0) and phi(m). Only one of these combinations results in the minimum mechanical power consumption and can be considered the optimum operating point for the given v(x, avg). This paper proposes a method for obtaining this optimal operating point based on tangency of the power and velocity contours. Putting together all such operating points for various v(x, avg,) a family of optimum operating points, called the optimal locus, is obtained. For the energy loss and internal energy models chosen, the optimal locus obtained has a largely constant step angle with increasing speed but tapers off at non-dimensional speeds close to unity.

On the Equivalence of Acoustic Impedance and Squeeze Film Impedance in Micromechanical Resonators

In this work, we address the issue of modeling squeeze film damping in nontrivial geometries that are not amenable to analytical solutions. The design and analysis of microelectromechanical systems (MEMS) resonators, especially those that use platelike two-dimensional structures, require structural dynamic response over the entire range of frequencies of interest. This response calculation typically involves the analysis of squeeze film effects and acoustic radiation losses. The acoustic analysis of vibrating plates is a very well understood problem that is routinely carried out using the equivalent electrical circuits that employ lumped parameters (LP) for acoustic impedance. Here, we present a method to use the same circuit with the same elements to account for the squeeze film effects as well by establishing an equivalence between the parameters of the two domains through a rescaled equivalent relationship between the acoustic impedance and the squeeze film impedance. Our analysis is based on a simple observation that the squeeze film impedance rescaled by a factor of jx, where x is the frequency of oscillation, qualitatively mimics the acoustic impedance over a large frequency range. We present a method to curvefit the numerically simulated stiffness and damping coefficients which are obtained using finite element analysis (FEA) analysis. A significant advantage of the proposed method is that it is applicable to any trivial/nontrivial geometry. It requires very limited finite element method (FEM) runs within the frequency range of interest, hence reducing the computational cost, yet modeling the behavior in the entire range accurately. We demonstrate the method using one trivial and one nontrivial geometry.

Efficient coupled polynomial interpolation scheme for out-of-plane free vibration analysis of curved beams

The performance of two curved beam finite element models based on coupled polynomial displacement fields is investigated for out-of-plane vibration of arches. These two-noded beam models employ curvilinear strain definitions and have three degrees of freedom per node namely, out-of-plane translation (v), out-of-plane bending rotation (theta(z)) and torsion rotation (theta(s)). The coupled polynomial interpolation fields are derived independently for Timoshenko and Euler-Bernoulli beam elements using the force-moment equilibrium equations. Numerical performance of these elements for constrained and unconstrained arches is compared with the conventional curved beam models which are based on independent polynomial fields. The formulation is shown to be free from any spurious constraints in the limit of `flexureless torsion' and `torsionless flexure' and hence devoid of flexure and torsion locking. The resulting stiffness and consistent mass matrices generated from the coupled displacement models show excellent convergence of natural frequencies in locking regimes. The accuracy of the shear flexibility added to the elements is also demonstrated. The coupled polynomial models are shown to perform consistently over a wide range of flexure-to-shear (EI/GA) and flexure-to-torsion (EI/GJ) stiffness ratios and are inherently devoid of flexure, torsion and shear locking phenomena. (C) 2015 Elsevier B.V. All rights reserved.

Seismic characterization and dynamic site response of a municipal solid waste landfill in Bangalore, India

Seismic design of landfills requires an understanding of the dynamic properties of municipal solid waste (MSW) and the dynamic site response of landfill waste during seismic events. The dynamic response of the Mavallipura landfill situated in Bangalore, India, is investigated using field measurements, laboratory studies and recorded ground motions from the intraplate region. The dynamic shear modulus values for the MSW were established on the basis of field measurements of shear wave velocities. Cyclic triaxial testing was performed on reconstituted MSW samples and the shear modulus reduction and damping characteristics of MSW were studied. Ten ground motions were selected based on regional seismicity and site response parameters have been obtained considering one-dimensional non-linear analysis in the DEEPSOIL program. The surface spectral response varied from 0.6 to 2g and persisted only for a period of 1s for most of the ground motions. The maximum peak ground acceleration (PGA) obtained was 0.5g and the minimum and maximum amplifications are 1.35 and 4.05. Amplification of the base acceleration was observed at the top surface of the landfill underlined by a composite soil layer and bedrock for all ground motions. Dynamic seismic properties with amplification and site response parameters for MSW landfill in Bangalore, India, are presented in this paper. This study shows that MSW has less shear stiffness and more amplification due to loose filling and damping, which need to be accounted for seismic design of MSW landfills in India.

The time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems

Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.

The time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems

Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.

Seismic characterization and dynamic site response of a municipal solid waste landfill in Bangalore, India

Seismic design of landfills requires an understanding of the dynamic properties of municipal solid waste (MSW) and the dynamic site response of landfill waste during seismic events. The dynamic response of the Mavallipura landfill situated in Bangalore, India, is investigated using field measurements, laboratory studies and recorded ground motions from the intraplate region. The dynamic shear modulus values for the MSW were established on the basis of field measurements of shear wave velocities. Cyclic triaxial testing was performed on reconstituted MSW samples and the shear modulus reduction and damping characteristics of MSW were studied. Ten ground motions were selected based on regional seismicity and site response parameters have been obtained considering one-dimensional non-linear analysis in the DEEPSOIL program. The surface spectral response varied from 0.6 to 2g and persisted only for a period of 1s for most of the ground motions. The maximum peak ground acceleration (PGA) obtained was 0.5g and the minimum and maximum amplifications are 1.35 and 4.05. Amplification of the base acceleration was observed at the top surface of the landfill underlined by a composite soil layer and bedrock for all ground motions. Dynamic seismic properties with amplification and site response parameters for MSW landfill in Bangalore, India, are presented in this paper. This study shows that MSW has less shear stiffness and more amplification due to loose filling and damping, which need to be accounted for seismic design of MSW landfills in India.

Identification of nonlinear dynamic systems: Time-frequency filtering and skeleton curves

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

Chaotic dynamic analysis of viscoelastic plates

The dynamic buckling of viscoelastic plates with large deflection is investigated in this paper by using chaotic and fractal theory. The material behavior is given in terms of the Boltzmann superposition principle. in order to obtain accurate computation results, the nonlinear integro-differential dynamic equation is changed into an autonomic four-dimensional dynamical system. The numerical time integrations of equations are performed by using the fourth-order Runge-Kutta method. And the Lyapunov exponent spectrum, the fractal dimension of strange attractors and the time evolution of deflection are obtained. The influence of geometry nonlinearity and viscoelastic parameter on the dynamic buckling of viscoelastic plates is discussed.

Reduction Approaches for Vibration Control of Repetitive Structures

The reduction approaches are presented for vibration control of symmetric, cyclic periodic and linking structures. The condensation of generalized coordinates, the locations of sensors and actuators, and the relation between system inputs and control forces are assumed to be set in a symmetric way so that the control system posses the same repetition as the structure considered. By employing proper transformations of condensed generalized coordinates and the system inputs, the vibration control of an entire system can be implemented by carrying out the control of a number of sub-structures, and thus the dimension of the control problem can be significantly reduced.

Dynamic Characteristics of Spherically Converging Detonation Waves

The spherically converging detonation wave was numerically investigated by solving the one-dimensional multi-component Euler equations in spherical coordinates with a dispersion-controlled dissipative scheme. Finite rate and detailed chemical reaction models were used and numerical solutions were obtained for both a spherical by converging detonation in a stoichiometric hydrogen-oxygen mixture and a spherically focusing shock in air. The results showed that the post-shock pressure approximately arises to the same amplitude in vicinity of the focal point for the two cases, but the post-shock temperature level mainly depends on chemical reactions and molecular dissociations of a gas mixture. While the chemical reaction heat plays an important role in the early stage of detonation wave propagation, gas dissociations dramatically affect the post-shock flow states near the focal point. The maximum pressure and temperature, non-dimensionalized by their initial value, are approximately scaled to the propagation radius over the initial detonation diameter. The post-shock pressure is proportional to the initial pressure of the detonable mixture, and the post-shock temperature is also increased with the initial pressure, but in a much lower rate than that of the post-shock pressure.

Comparison of the Dynamic Response of a Saturated Soil Between Two Models

By comparing the dynamic responses of saturated soil to Biot's and Yamamoto's models, the properties of the two models have be pointed out. First of all, an analysis has been made for energy loss of each model from the basic equations. Then the damping of elastic waves in coarse sand and fine sand with loading frequency and soil's parameters have been calculated and the representation of viscous friction and Coulomb friction in the two models has been concluded. Finally, the variations of loading wave damping and stress phase angles with water depth and soil's parameters have been obtained as loading waves range in ocean waves.