- Mech. Eng. Dept. Urmia University, Urmia, IRAN
- +98-914-145-1407
Ghader Rezazadeh
Urmia University, Mechanical Engineering, Faculty Member
- Was born in March 21, in 1965. He received BS and Msc. degree in mechanical engineering from Isfahan Technical Univer... moreWas born in March 21, in 1965. He received BS and Msc. degree in mechanical engineering from Isfahan Technical University, IRAN, in 1991 and Ph. D. degree in applied mechanics from Bauman Moscow State Technical University in 1997. He joined the faculty of engineering of Urmia University, Urmia, IRAN, where he is a professor in the Mechanical Engineering Department. His current research interests are in the areas of static and dynamic behavior of MEMS/NEMS Structures.(Was born in March 21, in 1965. He received BS and Msc. degree in mechanical engineering from Isfahan Technical University, IRAN, in 1991 and Ph. D. degree in applied mechanics from Bauman Moscow State Technical University in 1997. He joined the faculty of engineering of Urmia University, Urmia, IRAN, where he is a professor in the Mechanical Engineering Department. His current research interests are in the areas of static and dynamic behavior of MEMS/NEMS Structures.)edit
Experiments on micro- and nano-mechanical systems (M/NEMS) have shown that their behavior under bending loads departs in many cases from the classical predictions using Euler-Bernoulli theory and... more
Experiments on micro- and nano-mechanical systems (M/NEMS) have shown that their behavior under bending loads departs in many cases from the classical predictions using Euler-Bernoulli theory and Hooke's law. This anomalous response has usually been seen as a dependence of the material properties on the size of the structure, in particular thickness. A theoretical model that allows for quantitative understanding and prediction of this size effect is important for the design of M/NEMS. In this paper, we summarize and analyze the five theories that can be found in the literature: Grain Boundary Theory (GBT), Surface Stress Theory (SST), Residual Stress Theory (RST), Couple Stress Theory (CST) and Surface Elasticity Theory (SET). By comparing these theories with experimental data we propose a simplified model combination of CST and SET that properly fits all considered cases, therefore delivering a simple (two parameters) model that can be used to predict the mechanical properties at the nanoscale.
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ABSTRACT In this paper, squeeze film damping in a micro-beam resonator based on micro-polar theory has been investigated. The proposed model for this study consists of a clamped-clamped micro-beam bounded between two fixed layers. The gap... more
ABSTRACT In this paper, squeeze film damping in a micro-beam resonator based on micro-polar theory has been investigated. The proposed model for this study consists of a clamped-clamped micro-beam bounded between two fixed layers. The gap between the microbeam and layers is filled with air. As fluid behaves differently in micro scale than macro, the micro-scale fluid field in the gap has been modeled based on micro-polar theory. Equation of motion governing transverse deflection of the micro- beam based on modified couple stress theory and also non-linear Reynolds equation of the fluid field based on micropolar theory have been nondimensionalized, linearized and solved simultaneously in order to calculate the quality factor of the resonator. The effect of micropolar parameters of air on the quality factor has been investigated. The quality factor of the of the micro-beam resonator for different values of non-dimensionalized length scale of the beam, squeeze number and also non-dimensionalized pressure has been calculated and compared to the obtained values of quality factor based on classical theory.
ABSTRACT Thermoelastic damping (TED) is a fundamental dissipation mechanism in micro/nano-scale resonators. Therefore, it is crucial to minimize this dissipation in design of these resonators. The problem has been formulated by the... more
ABSTRACT Thermoelastic damping (TED) is a fundamental dissipation mechanism in micro/nano-scale resonators. Therefore, it is crucial to minimize this dissipation in design of these resonators. The problem has been formulated by the nonlocal theory of elasticity to take into account the small scale effect. Moreover, the Timoshenko beam model has been used to capture the transverse shear deformation and rotary inertia effects. The coupled thermoelastic equations have been derived using the generalized thermoelasticity theory based on dual-phase-lagging heat conduction model for transverse vibration of an electrostatically deflected short beam. A step-by-step linearization method has been used to escape from the nonlinearity. Afterwards, the Galerkin’s weighted residual method has been applied to discretize the coupled dynamic equations of a beam resonator with both ends clamped and isothermal. Then, the complex-frequency approach has been utilized to obtain eigenvalue solution and TED ratio. The numerical results addressing importance of the nonlocal effect on the TED ratio of the short beam resonators have been presented.
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This paper deals with state estimation of micro tunable capacitor subjected to nonlinear electrostatic force. To this end, a nonlinear observer has been designed for state estimation of the structure. Necessary and sufficient conditions... more
This paper deals with state estimation of micro tunable capacitor subjected to nonlinear electrostatic force. To this end, a nonlinear observer has been designed for state estimation of the structure. Necessary and sufficient conditions for construction of the observer are presented. Stability of the observer is checked using Lyapunov theorem. Observer design is based on converting differential equation of dynamic error from heterogeneous to homogenous. Thereby, non-linear electrostatic term is presented as coefficient of error which is done using decomposition of Taylor expansion of non-linear term. By stabilizing of homogenous differential equation, gains of observer can be obtained. Ability of the observer in state estimation of micro tunable capacitor is checked and related results are presented.
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In this paper a novel method for construction of an exponential observer for nonlinear system is proposed. The method is based on direct solution of dynamic error without any linearizing of nonlinear terms. Necessary and sufficient... more
In this paper a novel method for construction of an exponential observer for nonlinear system is proposed. The method is based on direct solution of dynamic error without any linearizing of nonlinear terms. Necessary and sufficient conditions for construction of direct observer are presented. Stability of the observer is checked using Lyapunov theorem. Also, the ability of this observer is checked by implementing the observer for fault detection of micro tunable capacitor subjected to nonlinear electrostatic force.
In this paper, the free and harmonically excited torsional vibrations of a radially FGM micro-shaft have been investigated. The equation of motion has been acquired applying energy method and Hamilton’s principle. Resulting differential... more
In this paper, the free and harmonically excited torsional vibrations of a radially FGM micro-shaft have been investigated. The equation of motion has been acquired applying energy method and Hamilton’s principle. Resulting differential equation of free vibrations has been solved using the modal superposition method and the forced vibrations equation has been solved by Galerkin’s weighted residual method. The material properties of the shaft have been assumed to be varied through the radial direction following a power law distribution in terms of volume fractions of the constituents. The effects of boundary conditions on natural frequencies and the effects of variations of volume fraction index on natural frequencies and the frequency response of the FGM micro-shaft have been studied.
In the present article, a perceptive capacitive sensor for measuring angular speed of a rotating shaft is proposed. The proposed sensor is capable of measuring rotating shaft angular speed, and its changes. The proposed model’s sensing... more
In the present article, a perceptive capacitive sensor for measuring angular speed of a rotating shaft is proposed. The proposed sensor is capable of measuring rotating shaft angular speed, and its changes. The proposed model’s sensing part is a suspended clamped–clamped micro-beam, which is parallel with two fixed substrates from the upper and lower sides through the micro-beam’s width surface. An electric circuit is used to give out capacitance change as a result of angular speed change, in output voltage. The micro-beam undergoes non-linear electro-static pressure that is induced due to the applied bias DC voltage. The suggested sensor has high sensitivity for a large range of working machines rotating parts angular speed measurement. The governing nonlinear partial differential equation of the transversal motion of the beam is derived and solved by step by step linearization (SSLM) and Galerkin weighted residual methods and the stable region of the sensor is determined. The effe...
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In this paper a novel sensor is proposed to measure rotational shafts speed. The sensor is composed of a micro-cantilever, with a piezoelectric actuator layer on the upper surface and a sensor layer on the lower surface. The sensor is... more
In this paper a novel sensor is proposed to measure rotational shafts speed. The sensor is composed of a micro-cantilever, with a piezoelectric actuator layer on the upper surface and a sensor layer on the lower surface. The sensor is attached to the shaft while the deflection of the micro-cantilever, due to centrifugal force of the rotating shaft, is actively controlled. Therefore the sensor deflection is suppressed and the controller output or the piezoelectric actuating voltage is employed to measure the angular speed of the shaft (Force balance technique). The micro-cantilever is symmetrically located between two electrodes giving it a wider operating range and also increasing its sensitivity. Imposing different electrostatic bias voltages alters the equivalent stiffness of the structure and consequently affects the micro-beam deflections and the controller outputs. Simulation results reveal that for lower velocities the resolution increases by increasing the bias voltages. It i...
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This study investigates the dynamic response of an electrostatically deflected capacitive cantilever functionally graded (FG) micro-beam subjected to a harmonically varying thermal load, which is incited vibration due to different... more
This study investigates the dynamic response of an electrostatically deflected capacitive cantilever functionally graded (FG) micro-beam subjected to a harmonically varying thermal load, which is incited vibration due to different material properties of the beam constituents and thermo-elastic coupling effect. Moreover, the influences of the beam ceramic constituent percentage on the stability, vibrational behavior and natural frequency are presented.
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ABSTRACT This paper presents the stability analysis of a fluid-conveying micro-pipe axially loaded with a pair of piezoelectric layers located at its top and bottom surfaces. Based on Euler-Bernoulli beam theory, the governing equations... more
ABSTRACT This paper presents the stability analysis of a fluid-conveying micro-pipe axially loaded with a pair of piezoelectric layers located at its top and bottom surfaces. Based on Euler-Bernoulli beam theory, the governing equations of the system are derived by applying Hamilton’s variational principle. Galerkin projection technique is used to extract the frequency equations. Taking into account clamped-free boundary conditions with and without intermediate support, stability of the system is investigated to demonstrate the influence of flow velocity as well as the voltage of the piezoelectric layers on the flow-induced flutter instability. It is shown that imposing voltage difference to piezoelectric layers can significantly suppress the effect of fluid flow on vibrational frequencies and thus extend the stable margins. Moreover, effects of the intermediate support on the stability of the system are examined and it is shown that for some particular range of system configuration, the instability type may change from flutter to divergence.
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ABSTRACT In this paper, the influence of centrifugal forces on the stability of an electro-statically actuated clamped-clamped micro-beam has been investigated. The non-dimensional governing static and dynamic equations have been... more
ABSTRACT In this paper, the influence of centrifugal forces on the stability of an electro-statically actuated clamped-clamped micro-beam has been investigated. The non-dimensional governing static and dynamic equations have been linearized using based step by step linearization method (SSLM), then, a Galerkin- based reduced order model has been used to solve the linearized equations. For constant value of a bias DC voltage and different values of angular velocity the equilibrium points of the corresponding autonomous system including stable center points, unstable saddle points and singular points have been obtained using the equivalent mass-spring model. Subsequently the bifurcation diagram has been depicted using the obtained fixed point. The static pull-in voltage value for different values of angular velocity and the static pull-in angular velocity for different values of bias voltage have been calculated. The obtained results are validated using results of previous studies and a good agreement has been observed. The effect of the centrifugal force on the fixed points has been studied using the phase portraits of the system for different initial conditions. Moreover, the effects of centrifugal forces on the dynamic pull-in behavior have been investigated using time histories and phase portraits for different angular velocities.
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ABSTRACT This paper deals with analysis of the mechanical behavior of an electro-statically-actuated micro-beam-resonator from the bifurcation view of point. The non-local constitutive relation has been used to obtain the governing... more
ABSTRACT This paper deals with analysis of the mechanical behavior of an electro-statically-actuated micro-beam-resonator from the bifurcation view of point. The non-local constitutive relation has been used to obtain the governing deformation equations. The obtained static equation has been solved using two approaches. The dynamic equation of motion has been solved applying a Galerkin-reduced order model. Bifurcation behavior of the beam subjected to an electrostatic force has been analyzed using the both approaches. The fixed points of the beam for given voltages have been obtained and stability of them determined by studying the phase portraits for each fixed point.
ABSTRACT High acoustic noise and vibration are two of the main drawbacks, which have limited the widespread application of switched reluctance machine (SRM). Therefore, many studies have been performed to reduce the acoustic noise and... more
ABSTRACT High acoustic noise and vibration are two of the main drawbacks, which have limited the widespread application of switched reluctance machine (SRM). Therefore, many studies have been performed to reduce the acoustic noise and vibration of these machines. This study introduces a novel, practical and analytical structure for the switched reluctance generator (SRG). The proposed generator consists of four magnetically independent stator and rotor layer sets. Each layer works exactly in a complementary way with the neighboring layers to convert mechanical energy into electrical energy perfectly. In the proposed generator special switching technique is implemented in order to reduce the amount of torque-ripple and vibration which can also reduce the amount of acoustic noise. Extensive computer simulations are performed to investigate the theory and feasibility of the proposed SRG structure of this study.
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ABSTRACT This paper presents a new model for the free transverse vibrations of an Euler-Bernoulli beam using the couple stress theory of elasticity with micro-structure. Introducing the kinematic variables, the strain and kinetic energy... more
ABSTRACT This paper presents a new model for the free transverse vibrations of an Euler-Bernoulli beam using the couple stress theory of elasticity with micro-structure. Introducing the kinematic variables, the strain and kinetic energy expressions (involving micro-inertia effect) has been obtained and the Hamilton principle has been used to derive the governing equations and the related boundary conditions of the free vibrations of fixed-fixed and simply-supported beams. A numerical solution has been used to study the natural frequencies, mode shapes and free vibrations of the beams. A comparative result has shown that the bending rigidity predicted by the couple stress, is closer to the experiment result than that predicted by the modified couple stress theory. The results have shown that the bending rigidity of the beams depends on the ratio of the length scale to the beam thickness whereas; the micro-inertia term depends on the ratio of the length scale to the beam length.
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ABSTRACT This paper deals with the study of bifurcational behavior of a capacitive microbeam actuated by asymmetrically located electrodes in the upper and lower sides of the microbeam. A distributed and a modified two degree of freedom... more
ABSTRACT This paper deals with the study of bifurcational behavior of a capacitive microbeam actuated by asymmetrically located electrodes in the upper and lower sides of the microbeam. A distributed and a modified two degree of freedom (DOF) mass-spring model have been implemented for the analysis of the microbeam behavior. Fixed or equilibrium points of the microbeam have been obtained and have been shown that with variation of the applied voltage as a control parameter the number of equilibrium points is changed. The stability of the fixed points has been investigated by Jacobian matrix of system in the two DOF mass-spring model. Pull-in or critical values of the applied voltage leading to qualitative changes in the microbeam behavior have been obtained and has been shown that the proposed model has a tendency to a static instability by undergoing a pitchfork bifurcation whereas classic capacitive microbeams cease to have stability by undergoing to a saddle node bifurcation.
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ABSTRACT Present investigation is focused on studying the effect of mass diffusion on the quality factor of the micro-beam resonators. Equation of motion is obtained using Hamilton’s principle and also the equations of thermo-diffusive... more
ABSTRACT Present investigation is focused on studying the effect of mass diffusion on the quality factor of the micro-beam resonators. Equation of motion is obtained using Hamilton’s principle and also the equations of thermo-diffusive elastic damping are established using two dimensional non-Fourier heat conduction and non-Fickian mass diffusion models. Free vibration of a clamped–clamped micro-beam with isothermal boundary conditions at both ends, and also a cantilever micro-beam with adiabatic boundary condition assumption at the free end, is studied using Galerkin reduced order model formulation for the first mode of vibration. Mass diffusion effects on the damping ratio are studied for the various micro-beam thicknesses and temperatures and the obtained results are compared with the results of a model in which the mass diffusion effect is ignored. In addition to the classic critical thickness of thermoelastic damping, a new critical thickness concerning mass diffusion is introduced.
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ABSTRACT Effects of Ohmic resistance on MEMS/NEMS vibrating structures that have always been dismissed in some situations may cause important changes in resonance properties and impedance parameters of the MEMS/NEMS based circuits. In... more
ABSTRACT Effects of Ohmic resistance on MEMS/NEMS vibrating structures that have always been dismissed in some situations may cause important changes in resonance properties and impedance parameters of the MEMS/NEMS based circuits. In this paper it is aimed to present a theoretical model to precisely investigate the problem on a simple cantilever-substrate resonator. In this favor the Ohm’s current law and charge conservation law have been merged to find a differential Equation for voltage propagation on the beam and because mostly nano structures are expected as the scope of the problem, modified couple stress theory is used to formulate the dynamic motion of the beam. The two governing equations were coupled and both nonlinear that have been solved simultaneously using a Galerkin based state space formulation. The obtained results that are in exact agreement with previous works show that dynamic pull-in voltage, switching time, and impedance of structure as a MEMS capacitor especially in frequencies higher than natural resonance frequency strongly relay on electrical resistance of the beam and substrate material.
ABSTRACT This paper presents a novel model for investigating squeeze film effect on a simple flexural beam resonator based on modal Galerkin reduced order method, step by step linearization and state space formulation. In contrast to... more
ABSTRACT This paper presents a novel model for investigating squeeze film effect on a simple flexural beam resonator based on modal Galerkin reduced order method, step by step linearization and state space formulation. In contrast to conventional equivalent circuit model, this method enables the user to calculate scattering parameters of the filter as a two port network directly from geometry, consequently has the capability for considering any physical phenomena (in this case squeeze film effect) without losing generality. In this study a clamped-clamped beam has been considered as the resonating structure of the filter and the problem has been solved for dynamic motion of the beam simultaneously with gas pressure, voltages, and electrical current of input and output port of the filter. The results were verified with previous experimental and theoretical studies and an acceptable agreement achieved.
ABSTRACT This paper reports a capacitive angular velocity trip sensor designed for protection of sensitive and accurate spinning equipment by utilizing alarm and trip. The recommended sensor can be able to measure rotating machinery... more
ABSTRACT This paper reports a capacitive angular velocity trip sensor designed for protection of sensitive and accurate spinning equipment by utilizing alarm and trip. The recommended sensor can be able to measure rotating machinery angular speed and subsequently it sends alarm messages using LEDs and buzzers in the domain of an angular velocity that it can be programmable with micro-processer packages. Of course in the critical angular speed the sensor can trip the system. Moreover, the resolution of the trip sensor is determined and it is shown that with increasing of the width of the micro-beam high trip resolution is observed.
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ABSTRACT In this paper, the thermally induced vibration of a functionally graded (FG) cantilever micro-beam subjected to a moving laser beam is investigated via simulating the equivalent third-order dynamic system. The material properties... more
ABSTRACT In this paper, the thermally induced vibration of a functionally graded (FG) cantilever micro-beam subjected to a moving laser beam is investigated via simulating the equivalent third-order dynamic system. The material properties of the FG micro-beam are defined by an exponential function through the thickness. The coupled thermo-elastic equations are obtained utilizing the first law of thermodynamics under the assumption of the classical Fourier heat conduction model and Euler–Bernoulli beam theory. To evaluate the dynamic response of the micro-beam, the coupled equations are first discretized by employing a Galerkin based reduced-order model and then decoupled by applying the Cramer's rule. Solving the decoupled equations analytically, effects of key parameters are illustrated by means of time histories and phase portraits. Furthermore, by investigating the case of resonant excitation, the critical velocity corresponding to mobile heat source is obtained.
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Abstract A novel model to study the pull-in behavior of nonlinear electromechanically coupled systems has been developed. The proposed model is based on the multilayered cantilever and fixedfixed micro beam type MEMS switches. Due to the... more
Abstract A novel model to study the pull-in behavior of nonlinear electromechanically coupled systems has been developed. The proposed model is based on the multilayered cantilever and fixedfixed micro beam type MEMS switches. Due to the complexity of the nonlinear ...
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ABSTRACT This paper deals with the study of structural noise in a capacitive MEMS microphone, which consists of a fully clamped circular micro-plate. The micro-plate is subjected to a bias DC voltage and sound pressure waves. Due to the... more
ABSTRACT This paper deals with the study of structural noise in a capacitive MEMS microphone, which consists of a fully clamped circular micro-plate. The micro-plate is subjected to a bias DC voltage and sound pressure waves. Due to the nonlinearity and displacement dependency of the electrostatic force, the amplitude of the applicable bias DC voltage has some limitations and also this nonlinearity causes the generation of super or sub harmonic responses and consequently the initiation of the structural noise in capacitive microphones. In order to determine the amplitude of the generated structural noise in these microphones, the first order multiple scales method is used and asymptotic analytical solution of the dynamic response is presented. The effects of the bias DC voltage value on the fundamental frequency, sensitivity and consequently on the amplitude of the structural noise of the microphone are studied. In addition the effects of the sound pressure frequency and amplitude on the value of structural noise are investigated.
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ABSTRACT This paper studies the size dependent behavior of materials in MEMS structures. This behavior becomes noticeable for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale... more
ABSTRACT This paper studies the size dependent behavior of materials in MEMS structures. This behavior becomes noticeable for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter and is insignificant for the high ratio of the characteristic size to the length-scale parameter, which is the case of the silicon base micro-beams. However, in some types of micro-beams like gold or nickel bases, the size dependent effect cannot be overlooked. In such cases, ignoring this behavior in modeling will lead to incorrect results. Some previous researchers have applied classic beam theory on their models and imposed a considerable hypothetical value of residual stress to match their theoretical results with the experimental ones. The equilibrium positions or fixed points of the gold and nickel micro-beams are obtained and shown that for a given DC voltage, there is a considerable difference between the obtained fixed points using classic beam theory, modified couple stress theory, and modified strain gradient theory. In addition, it is shown that the calculated static and dynamic pull-in voltages using higher order theories are much closer to the experimental results and are higher several times than those obtained by classic beam theory.