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Due to the importance of the usage of nano-technology based fluids in several industrial processes, the presented research deals with mathematical modeling of a comb-drive MEMS-based sensor for determinations of the physical properties of nanofluids. The proposed sensor is made up of a driving comb, sensing comb, and a sensing plate. It is actuated longitudinally via the electrostatic force created by applying an AC voltage to the driving section of the sensor. The coupled equations of the vibration of the lumped dynamic mass and the nanoscale fluid field have been derived and solved simultaneously. Frequency analysis of the dynamic model indicates that a nanofluid has inertial and damping effects on the longitudinal vibration of the structure. Therefore, the viscosity and density of a nanofluid can be measured simultaneously via the detection of the resonance frequency and resonance amplitude changes of the structure. The practical restrictions of the applied AC voltage for the linear dynamic behavior of the structure have also been presented.

In this paper, a novel application of a giant chimney is presented with the practical purpose of helping to ventilate and decrease the local air pollution in metropolises. The solar collector around the chimney absorbs solar radiations, so the air is heated as a result of enhanced greenhouse effect in the collector. The structure stays on a foundation and works on the buoyancy principle. The air density difference between the outside and inside of the chimney causes the stack pressure to be produced in the chimney. The equations describing the movement of the air flow have been introduced and simplified considering assumptions. Effects of the geometrical parameters of the chimney, ambient temperature, geographical location, and weather condition on the performance of the chimney have been studied. Results show that a chimney with high altitude, working in low ambient temperature and unstable weather conditions, and in expanded cities near sea level will typically produce better performance.

In this paper, we present a full derivation of a new model based on the partial inductance method to calculate the mutual inductance between two planar spiral coils with an arbitrary number of sides. The planar spiral coils are approximated by regular concentric polygons and then each polygon is decomposed to its sides. The mutual inductance between each side of the primary and secondary polygons is analyzed considering geometrical properties of the sides with respect to each other. The method developed in the present study is general and straightforward in comparison with those available in the literature as it includes only required sequential steps to calculate the mutual inductance between the independent segments of the coils. We validated the results of the proposed method with those available in the literature, simulation and measurement results. Moreover, the developed method was implemented for the percent error analysis to assess the error of the approximation of the circular coils with n-sided polygons.

In this paper, the transient temperature and vibration response of skin tissue to different types of laser heating sources are studied. Two-dimensional heat conduction equation of skin tissue based on the Cattaneo–Vernotte model is extracted considering the thermoelastic effect. Two-sided coupled differential equations governing heat transfer and displacement of skin tissue have been non-dimensionalized and solved numerically. Due to the appearance of extremely complicated boundary conditions, the Galerkin-based reduced-order model has been utilized to solve the equations properly. The effect of relaxation time on the temperature and vibration response of tissue has been studied. The thermomechanical response of tissue has been investigated considering various types of laser heat sources. Results indicated that the relaxation time creates a delay in the transient dynamic response of the tissue. It was also observed that when energy is delivered to skin tissue via the repetitive laser heating pulses, the relaxation time reduces the vibration amplitude of skin tissue in the radial direction as well as depth direction. The effect of the thermoelastic coupling term on the temperature response of tissue was not considerable.

This paper studies the incorporation of Casimir and van der Waals forces applied to a nanostructure with parallel configuration. The focus of this study is in a transition region in which Casimir force gradually transforms into van der Waals force. It is proposed that in the transition region, a proportion of both Casimir and van der Waals forces, as the interacting nanoscale forces, can be considered based on the separation distance between upper structure and substrate during deflection. Moreover, as the separation distance descends during deflection, the nanoscale forces could transform from Casimir to a proportion of both Casimir and van der Waals forces and so as to van der Waals. This is also extended to the entire surface of the nanostructure in such a way that any point of the structure may be subjected to Casimir, van der Waals or a proportion of both of them about its separation distance from the substrate. Therefore, a mathematical model is presented which calculate the incorporation of Casimir and van der Waals forces considering transition region and their own domination area. The mechanical behavior of a circular nano-plate has been investigated as a case study to illustrate how different approaches to nanoscale forces lead to different results. For this purpose, the pull-in phenomena and frequency response in terms of magnitude have been studied based on Eringen nonlocal elasticity theory. The results are presented using different values of the nonlocal parameter and indicated in comparison with those of the classical theory. These results also amplify the idea of studying the mechanical behavior of nanostructures using the nonlocal elasticity theory.

This study explores heat-induced nonlinear vibration of a functionally graded (FG) capacitive nanobeam within the framework of nonlocal strain gradient theory (NLSGT). The elastic FG beam, which is firstly deflected by a DC voltage, is driven to vibrate about its deflected position by a periodic heat load. The nano-structure, which consists of a clamped-clamped nanobeam, is modeled assuming Euler–Bernoulli beam assumption which accounts for the nonlinear von-Karman strain and the electrostatic and intermolecular forcing. To simulate the static and dynamic responses, a model reduction procedure is carried out by employing the Galerkin method. The method of Averaging as a regular semi-analytic perturbation method is applied to obtain governing equations of the steady-state responses. With the purpose of establishing the validity of the solution, a Shooting technique in conjunction with the Floquet theory is used to capture the periodic motions and then examine their stability. The nonlinear resonance frequency of the FG nanobeam near its fundamental natural frequency (primary resonance) and near principal parametric resonance is investigated while the emphasis is placed on studying the effect of various parameters including DC voltage, amplitude of the periodic heat source, material index, damping ratio, and small scale parameters. The main objective of this study is to model a miniature structure which can be used as either a sensitive remote temperature sensor or a high-efficiency thermal energy harvester.

This paper presents a closed form formula for the mutual inductance of coaxial hexagonal and octagonal planar spiral coils. For analysis, spiral coils are assumed to be composed of concentric filaments and Biot–Savart law has been utilized to scrutinize the mutual inductance between two filaments. Two planar spiral coils of seven turns is simulated in Ansys Maxwell software and fabricated on FR4 substrate to demonstrate the validity of the proposed formulas. Calculation results also have been confirmed by Grover formula for the mutual inductance of two identical hexagonal and octagonal filaments. The measurement and simulation results are in very good agreement with calculation that indicates the feasibility of theoretical formulas.

MEMS shock sensors are widely used with applications ranging from aircraft to electrical measurement systems. They are designed to operate at the shocks above a predefined threshold level. The conventional single-mass switches may lose their reliability at shock levels smaller than the threshold, if experience smaller unwanted pulse duration. This paper has proposed a dual-mass switch with auxiliary mass-spring attached to the main system which increases the reliability of the sensor against the unwanted pulse durations. By providing a mathematical model, the shock response spectrum of the novel system has been obtained and shown that by changing the system parameters, the peak amplitude of the main mass can be tuned to a minimum value. Moreover, the interval between the designed threshold, and the minimum shock which leads to switch at smaller unwanted pulse durations, has been decreased up to 45% in the proposed dual-mass model compared to the conventional one.

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.

We have proposed a new RF MEMS variable capacitor to achieve high linearity, wide tunability and low actuation voltage. The idea is based on increasing the linear region in the gap between the plates of the capacitor. It is done by adding a fixed-fixed beam below the fixed-free beam. The fixed-free beam is one plate of the capacitor. The voltage is applied to the fixed-free beam. In the vicinity of the pull-in voltage, the fixed-free beam losses its equivalent stiffness. The fixed-fixed beam is located in the vicinity of pull in situation of the fixed-free beam. This condition increases the equivalent stiffness of the fixed-free beam and allows the beam to continue moving down linearly and consequently increases the maximum capacitance of the structure. Geometrical and material property effects of the second beam on the linearity, tunability and voltage are investigated. The governing nonlinear equation for static deflection of the beam based on the Euler-Bernoulli beam theory has been presented.

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 the 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.

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.

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) have 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.

Size dependent behavior of materials arises for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter. In these cases, ignoring this behavior in modeling may leads to incorrect results. In this paper, strong effects of size dependence on static and dynamic behavior of electro-statically actuated nano-beams have been studied. The fixed points of the Aluminum nano-beams have been determined and shown that for a given DC voltage, there is a considerable difference between the calculated fixed points using classic beam theory and modified couple stress theory. In addition, it has been also shown that ignoring couple stress theory results in an order of magnitude error in calculated static and dynamic pull-in voltages. Some previous studies have applied the classic beam theory in their models and introduced a considerable hypothetical value of residual stress to justify the discrepancies between experimental and theoretical results.

The present paper is aimed at studying the effects of mass diffusion on the quality factor of a functionally graded cantilever micro-beam in which the material properties of the micro-beam vary continuously along the beam thickness according to a power-law. The governing equation of a micro-beam deflection is obtained using Hamilton’s principle and also the governing equations of thermo-diffusive elastic damping are established by using two dimensional non-Fourier heat conduction and non-Fickian mass diffusion models with one relaxation time based on continuum theory frame. The free vibration of the micro-beam resonators is analyzed by using Galerkin reduced order model formulation for the first mode of vibration. The mass diffusion effects on the quality factor are studied for the various micro-beam thicknesses and temperatures. Numerical computations are performed for specific materials and the results obtained are represented graphically. The effect of different power law exponent on the quality factor of the micro-beam is studied and Comparisons are made within the theory in the presence and absence of the mass diffusion effect.

This article deals with the effect of the intrinsic length-scale on the stability and fundamental frequency of a fully clamped circular micro-plate, which can be used as a RF MEMS resonator. A modified couple stress theory is utilized to model the micro-plate, considering the variable length-scale parameter. A variational formulation based on Hamilton's principle is used to obtain the nonlinear governing equation of motion. The static and dynamic pull-in phenomena, limiting the stable regions of capacitive resonators, are determined and compared to those obtained by the classical theory. The numerical results reveal that the intrinsic size dependence of materials leads to an increase in the pull-in voltage and natural frequency depending on the thickness of the micro-plate. Comparing these results with the experimental ones reveals that utilizing the fixed material length-scale leads to unrealistic results in some manner.

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 effects of the applied bias voltage and geometrical properties of the micro-beam on the sensitivity and the range of the measurable angular speed of the sensor are discussed.

Stability of a functionally graded (FG) micro-beam, based on modified couple stress theory (MCST), subjected to nonlinear electrostatic pressure and thermal changes regarding convection and radiation, is the main purpose of this paper. It is assumed that the functionally graded beam, made of metal and ceramic, follows the volume fraction definition and law of mixtures, and its properties change as an exponential function through its thickness. By changing the ceramic constituent percent of the bottom surface, five different types of the micro-beams are investigated. The static pull-in voltages in presence of temperature changes are obtained by using step-by-step linearization method (SSLM) and, by adapting Runge–Kutta approach, the dynamic pull-in voltages are obtained numerically. Though the temperature distribution through the thickness of FG micro-beam (due to its too small measurement) is considered uniform, owing to the different thermal expansions of layers, temperature changes cause deflection in the micro-beam, and consequently affect pull-in values. Hence the profound effects of different material constituent over the pull-in voltages are illustrated and it is graphically displayed that how in some cases neglecting components of the couple stress leads to inaccurate results.

This paper studies the mechanical and bifurcation behavior of a capacitive micro-beam suspended between two conductive stationary plates, which can be used as a micro-switch or as a RF resonator. The equation of dynamic motion of the micro-switch is obtained using Euler–Bernoulli beam theorem. The equilibrium positions or the fixed points of the micro-switch are obtained by solving the equation of the static deflection using the step-by-step linearization method (SSLM) and discretizing by Galerkin weighted residual method. In order to study the global stability of the obtained fixed points a modified non-linear mass–spring model is used. Non-linear motion trajectories in phase portraits are given and regions of bounded and unbounded solutions separated by a homoclinic or heteroclinic orbits and positions of the stationary conductive plates are illustrated. Critical values of the applied voltage leading to qualitative changes in the micro-beam behavior through a saddle node or pitch fork bifurcations for different values of the gap and voltage ratios are obtained. The effects of different gaps and voltage ratios also are investigated.

This paper deals with investigation into the stability analysis for transverse motions of a cantilever micro-beam, which is axially loaded due to a voltage applied to the piezoelectric layers located on the lower and upper surfaces of the micro-beam. The piezoelectric layers are pinned to the open end of the micro-beam and not bonded to it through its length. Application of the DC and AC piezoelectric actuations creates steady and time varying axial forces. The equation of the motion is derived using variational principal, and discretized using modal expansion theorem. The differential equations of the discretized model are a set of Mathieu type ODEs, whose stability analysis is performed using Floquet theory for multiple degree of freedom systems. Considering first two eigen-functions in the modal expansion theorem leads in the prediction of flutter type of instability as a consequence of Hopf bifurcation, which is not seen in the reduced single degree of freedom system. The object of the present study is to passively control the flutter instability in the proposed model by applying AC voltage with suitable amplitude and frequency to the piezoelectric layers. The effect of various parameters on the stability of the structure, including damping coefficient, amplitude of the DC and AC voltages, and the frequency of the applied AC voltage is studied.

In this paper a novel remote temperature sensor based on a bi-layer micro cantilever beam has been proposed, which can sense the temperature of a given heat source from a finite distance dynamically. Proposed sensor works based on radiation heat transfer and thermally induced vibration. In order to dispose a relationship between temperature of the heat source, and a sensible characteristic like as tunneling current or capacitance, thermo-mechanical behavior of such a structure has been investigated. Heat transfer equation of such a beam includes a nonlinear term due to the radiation heat transfer that has been solved numerically using Rung-Kutta explicit integration method. Galerkin based mode summation method has been utilized to solve the partial differential equation of the beam dynamics and the Houbolt implicit integrating method is used to solve obtained ordinary differential equations. Dynamic response to a step, and semi-harmonic excitations and frequency responses, for the proposed sensor with different geometrical or physical properties have been presented and discussed considering the temperature relaxation time of the sensor. In order to gain a semi explicit solution a perturbation method has been disposed and the results have been compared to the numerical direct integration ones, the accuracy and agreement are excellent.

In this paper the mechanical behavior of a parametrically actuated functionally graded piezoelectric (FGP) clamped–clamped micro-beam is investigated. The micro-beam is supposed to be a composite material with silicon and piezoelectric base. The mechanical properties of the structure, including elasticity modulus, density, and piezoelectricity coefficient are supposed to vary along the height of the micro-beam with an exponential functionality. It is supposed that the FGP clamped–clamped micro-beam is actuated with a combination of direct and alternative electric potential difference. Application of DC and AC actuation voltage leads in a constant and a time-varying axial force. The governing differential equation of the motion is derived using Hamiltonian principle and discretized using expansion theorem with the corresponding shape functions of a clamped–clamped beam. The discretized system is governed by Mathieu equation which’s stability is investigated using Floquet theory for single degree of freedom systems and verified using multiple time scales of perturbation technique.

This paper deals with the study of parametric oscillation of an electrostatically actuated microbeam using variational iteration method. The paper considers a micro-beam suspended between two conductive micro-plates, subjected to a same actuation voltage. The nonlinear governing differential equation of motion about static equilibrium position using calculus of variation theory and Taylor series expansion has been linearized and implementing a Galerkin based reduced order model a Mathieu type equation has been obtained. By improving variational iteration method combining with method of strained parameters transition curves, separating stable from unstable regions have been obtained. The results of variational iteration method, perturbation and direct numerical integration methods for some cases selected from different regions (stable and unstable regions) have been compared.

Electrostatic torsional micro-mirrors have wide spread use in different industries for diverse purposes. This paper investigates the development of superharmonics and chaotic responses in electrostatic torsional micro-mirrors near the pull-in condition. Appearance of nonlinear phenomena is investigated in models accounting for and disregarding the coupling of torsional and flexural deflections. Analysis of the system response to step and harmonic excitation reveals the appearance of DC and AC symmetry breaking. Increasing the amplitude of harmonic excitation, the response in the form of distinct superharmonics changes to a broad band response, where there is loss of periodicity and the response becomes chaotic. Accounting for flexural deflections in coupled model reduces the voltage thresholds corresponding to symmetry breaking and chaotic responses. It is also shown that damping has a regularizing effect and introduction of damping changes the chaotic undamped response into quasi-periodic one.

In the present article an investigation is presented into the stability of an electro-statically deflected clamped–clamped micro-beam sandwiched by two piezoelectric layers undergoing a parametric excitation applying an AC voltage to these layers. Applying an electrostatic actuation not only deflects the micro-beam but also decreases the bending stiffness of the structure, which can lead the structure to an unstable position by undergoing a saddle node bifurcation. Utilizing an appropriate AC actuation voltage to the piezoelectric layers produces a time varying axial force, which can play the role of a stabilizer exciting the system parameter. The governing equation of the motion is a nonlinear electro-mechanically coupled type PDE, which is derived using variational principle and discretized, applying Eigen-function expansion method. The resultant is a Mathieu type equation in its damped form. Using Floquet theory for single degree of freedom system the stable and unstable regions of the problem are investigated. The effects of viscous damping and electrostatic actuation on the stable regions of the problem are also studied.

This paper deals with effects of residual and axial stresses on thermoelastic damping (TED) in micro-beam resonators. Equations of coupled thermoelastic case for a capacitive micro-beam resonator have been governed using two dimensional non-Fourier heat conduction model based on continuum theory frame. A Galerkin based finite element formulation has been used to analyze TED for the first mode of vibration of the micro-beam resonator with both ends clamped and isothermal. Effect of axial stresses owing to stretching of the micro-beam on the TED ratio has been investigated. As results illustrate, this effect gets importance only when the resonator is vibrating about a large static deflection due to a bias DC voltage close to the pull-in voltage of the resonator, otherwise it can be neglected in calculations. Effect of compressive and tensile residual stresses has been also studied. The results show that compressive (tensile) residual stresses increase (decrease) the TED ratio considerably. The residual stresses effect has been also studied for various values of the micro-beam thicknesses. The results illustrate that the effect of residual stress on the TED ratio decreases by increasing the thickness of the micro-beam. The results show that, applying DC voltages near the pull-in voltage increases energy dissipation due to the TED considerably, therefore, there is a limitation for applied DC voltage for resonators, since residual stresses change the pull-in voltage of the resonator, hence, existing residual stresses can change the interval of the applied voltage limitation.

This paper deals with the effects of mechanical shock loads on the stability and dynamic response of a MEMS circular capacitive microphone. As results demonstrate, mechanical shock loads affect the dynamic response and the stability region of the capacitive microphone. The results show that the mechanical shock loads can induce considerable noise in the response of the microphone. Therefore, noise filtering is an important issue to eliminate the output response distortions. To achieve this aim we propose a structure for the capacitive microphone with an electrical circuit in order to eliminate the shock noise. In addition the effect of a delay in shock application is also studied, and it is illustrated that a delay in shock application plays an important role in the stability of the capacitive microphone.

In the present work, mechanical behavior of a functionally graded cantilever micro-beam subjected to a nonlinear electrostatic pressure and temperature changes has been studied. It has been assumed that the top surface is made of pure metal and the bottom surface from a metal–ceramic mixture. The ceramic constituent percent of the bottom surface varies from 0% to 100%. In addition to the Volume Fractional Rule of material, exponential function has been used for representation of continuous gradation of the material properties through micro-beam thickness. Attention being paid to the ceramic constituent percent of the bottom surface, five different types of FGM micro-beams have been investigated. Nonlinear integro-differential thermo-electro mechanical equation based on Euler–Bernoulli beam theory has been derived and solved using Step-by-Step Linearization Method and Finite Difference Method. The effects of temperature changes and the electrostatic pressure on the deflection and stability of FGM micro-beams having various amounts of the ceramic constituent have been studied and normal stress distributions in the cross section along the beam thickness have been given and compared with a classic metal beam.

This paper deals with the stability analysis of transverse motions of a cantilever microbeam sandwiched by two piezoelectric layers located on the lower and upper surfaces of the microbeam. Application of same DC and AC voltages to the upper and lower piezoelectric layers creates an axial force with steady and time-varying components. The eigenfunction expansion of the transverse motion equation leads to the creation of a Mathieu type parametric equation which is mostly seen in the stability analysis of the structures in the literature; using Floquet theory for single degree of freedom systems the stable and unstable regions of the problem are investigated. The effect of viscous damping and DC voltage on the stability region of the problem is also studied. The results show the stabilizing effect of the viscous damping and positive DC voltage on the behavior of the microbeam. The achieved results are finally compared with those reported in the literature.

This article deals with effects of thermal stresses on stability and frequency response of a fully clamped circular microplate, which acts as the diaphragm of a capacitive MEMS microphone. Static and dynamic pull-in phenomena limit the stable regions of a capacitive MEMS microphone. The results show that the non-dimensional static pull-in voltage of the studied case is about 5.23 (38.6V). On the other hand, according to the results, the non-dimensional dynamic pull-in of the diaphragm is about 4.74 (34.98V), which is as low as 90.63% of the static pull-in threshold. Because of the thermal expansion coefficient, diaphragm temperature increment leads to compressive thermal stresses and conversely, decrement of the diaphragm temperature creates tensile thermal stresses. The effect of temperature on the pull-in parameters is given by a design-correcting factor. As results demonstrate, the deflection of the diaphragm subjected to a given electrostatic force can be controlled by means of the temperature changes. In the absence of electrostatic force, as the results show, although temperature changes do not create any deflection, but for a critical temperature increment the diaphragm stiffness vanishes and the buckling phenomenon takes place. Effects of the electrostatic force and the temperature variation on the frequency response of the microphone subjected to a sound pressure wave are investigated. As the results illustrate, increment of the electrostatic force or increment of the diaphragm temperature increases the output level and sensitivity of the microphone and decreases the fundamental frequency of the microphone, limiting the upper band of its bandwidth. It is obvious that decrement of the diaphragm temperature acts conversely. In addition, the results show that in the presence of the electrostatic force sensitivity of the output level of the diaphragm to the temperature change increases.

This paper deals with the analysis of a novel micro–electro-mechanical (MEM) fluid density and viscosity sensor. The proposed sensor consists of a micro-beam and a sensing micro-plate immersed in a fluid. In order to actuate longitudinally the micro-beam and micro-plate, the sensor includes a pair of piezoelectric layers bonded to the upper and lower surfaces of the micro-beam and subjected to an AC voltage. The coupled governing partial differential equations of longitudinal vibration of the micro-beam and fluid field have been derived. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions. The enhanced equations have been discretized over the beam and fluid domains using a Galerkin based reduced order model. The dynamic response of the sensing plate for different piezoelectric actuation voltages and different exciting frequencies has been investigated. The effects of viscosity and density of fluids and geometrical parameters of the sensor on the response of the sensing plate have been studied.

In this paper a model based on distributed parameters has been presented to study temperature effects on the mechanical behavior of an electrostatically actuated microplate. This work consists of two major parts. First part deals with the effect of temperature, stretching and residual stresses on the static instability of an electrostatically actuated microplate. To do this, the governing nonlinear integro differential equation has been derived using Kirchhoff thin plate theory and linearized using step-by-step linearization method (SSLM). The obtained linearized differential equation has been discretized applying finite difference method (FDM). The results obtained have been compared to other existing experimental results and good agreement is observed. In the second part, in order to study the natural or eigenfrequencies of the system, small vibrations of the electrostatically deflected microplate about the equilibrium position have been studied. Here, the governing linear eigenvalue partial differential equation has been solved using a Galerkin based reduced-order model, and the natural frequencies of the microplate have been determined. The results show that temperature changes and residual stress have considerable effects on the system characteristics such as pull-in voltage and natural frequencies.

Applying integrated variational principles on fluid and deck plate to the large deflection analysis of floating roofs, this paper investigates the significance of the flexural and membrane components in the formulations of the deck plate. Integrated variational principles facilitate the treatment of the compatibility of deformation between floating roof and supporting liquid. Analysis results show that different assumptions about deck plate formulation commonly used in the literature, results in considerably different deflection and stress patterns on the floating roof. The results show that modeling of the deck plate as a flexural element rather than the membrane, by eliminating the need for nonlinear analysis, gives reasonable results for deflections and stresses in the deck plate. Finally, to check the results of the variational formulation, employing Bessel functions and ignoring membrane stiffness an approximate solution is derived and its results compared with those of the variational formulation. This comparison shows that the approximate solution closely follows the variational formulation.

In this paper, the electrostatic pull-in behavior of two elastic parallel fixed–fixed and cantilever microbeams in microelectromechanical systems (MEMS) are investigated. The nonlinear electrostatic equations are considered due to some important effects including: residual stresses, fringing field and axial stresses. Various residual stresses in two elastic parallel fixed–fixed models are considered. Step by step linearization method is used to solve the equations. The numerical results reveal that the step by step linearization method is highly efficient, and it is the easiest one to calculate the pull-in voltage. In the proposed models, the pull-in voltages are considerably decreased when compared to the pull-in voltages of simple fixed–fixed and cantilever models.

This paper presents a comprehensive comparison study between the generalized differential quadrature (GDQ) and the well-known global Galerkin method for analysis of pull-in behavior of nonlinear micro-electro-mechanical coupled systems. The nonlinear governing integro-differential equation for double clamped MEMS devices which was derived using variational principle by the authors [Sadeghian H, Rezazadeh G, Osterberg PM. Application of the generalized differential quadrature method to the study of pull-in phenomena of MEMS switches. J Microelectromech Syst 2007;16(6):1334–40] is discretized by applying Galerkin and GDQ methods. The divergence instability or pull-in phenomenon is analyzed. Obtained results are compared with the results of the pervious works. The Galerkin method is implemented with effect of number of used shape functions. Different types of trail functions on calculated pull-in voltage are examined. Furthermore, compare to one term and two terms truncation Galerkin method, it is observed that the GDQ with small number of grid points (non-uniform) performs accurate results for nonlinear micro-electro-mechanical coupled behavior which requires a large number of grid points at high-order approximation.

In this paper, a microcapacitive wall shear stress sensor for the measurement of skin friction is developed. The design objective is to measure wall shear stress in the range of 1.25–2.45 kPa in laminar boundary layers. Mechanical behavior of the sensing elements, capacitive variations, and sensor’s static response has been investigated using numerical methods. The governing equation whose solution holds the answer to all our questions about the sensor’s characteristics is the nonlinear elasto-electrostatic equation. The results indicate that with this sensor design it is possible to measure wall shear stress values of 1.25 kPa and larger with a maximum uncertainty of 1.13%. Apparently, uncertainty depends on magnitude of wall shear stress. The higher the value of wall shear stress is, the smaller the uncertainty becomes. If we need the sensor to detect wall shear stress values less than 1.25 kPa with the same accuracy as cited, it is essential to replace the sensing microplate of the device with a thinner one.

The drying characteristics of pretreated seedless grapes were studied using a laboratory-scale tray dryer with the air temperature varied from 40 to 70 °C at air velocity of 1 m s −1 . The effective moisture diffusivities were determined using an analytical–numerical solution method considering shrinkage, while variable thermal diffusivity was calculated from experimentally estimated values of thermo-physical properties at a given moisture contents. These parameters were correlated with the corresponding moisture content and temperatures in an empirical model using a non-linear regression method. This shows that the seedless grapes of the same clone vines, as subjected to the hot water (HW) and alkaline emulsion of ethyl oleate (EO) pretreatments, exhibited average effective moisture diffusivities that ranged from 3.34 to 8.46×10 −10 m 2 s −1 at 50 °C. The increase in mass transfer coefficients at a given moisture content at different temperatures for the EO-pretreated samples was two times that for the HW-pretreated samples during the drying. However, the pretreatments had no the significant effect on the thermal diffusivities of the grapes during the drying.