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Nowadays, piezoelectric micro-beam structures are used in various industries, and knowing and analysis of these smart microstructures is important. However, in the modeling of these electromechanical microbeams, the torsion during bending is generally omitted for simplicity. Considering that in some cases, twisting and bending cannot be omitted and must be modeled simultaneously. Therefore, this article presents a coupled bending-torsion model for the first time for static deflection and free vibration analysis of piezoelectric microbeams with nonclassical continuum theories. The governing equations of the motion and boundary conditions of the Timoshenko beam at the micro-scale have been obtained using size-dependent electromechanical theory and Hamilton's principle. In addition, the Laplace transform is used to solve the static equations, while the generalized differential quadratic (GDQ) method is used to discretize and solve the free vibration equations. In the following, the influence of various parameters, such as the effect of size and geometric conditions, on the static displacements and the natural frequency of the microbeam is discussed. [ABSTRACT FROM AUTHOR]

The cantilevered micro-beam is an important component in the field of Atomic Force Microscope (AFM) and its behavior is governed by chaotic dynamics. To better understand these dynamics, a theoretical model based on the Euler–Bernoulli beam model has been developed and experiments have been conducted. The model incorporates both the modified couple stress theory (MCST) and external forces to account for the size-dependent effect and electrostatic load. The reduced model in one degree of freedom is obtained by the Galerkin method. The validity of the reduced model is tested by comparing the results from simulations and published results and experiments. The Melnikov method is then used to detect the chaotic threshold the cantilevered micro-beam. The numerical results test the effects of MCST on the complex responses of the micro-cantilever. Implications of the research can extend to the design and optimization of MEMS devices. [ABSTRACT FROM AUTHOR]

The purpose of this article is the comprehensive analysis of free vibration of beam-type liquid micro-pump with a free boundary approach. Besides the liquid loading on the micro-beam, the kinematic compatibility between liquid and micro-beam is modeled according to the free boundaries. Galerkin and separation of variables methods are employed to solve these equations. Based on the nonlinear nature of the equations, the Newmark method is applied to obtain the normal frequencies, mode shapes, and the fluid oscillation of the coupled system. The aim of this model is to achieve the exact results for the small oscillations of micro-beam in the liquid container. Comparing the free and fixed boundary method reveals that for small oscillation of Euler–Bernoulli micro-beam, there is a slight deviation on the natural frequency, which can be negligible. [ABSTRACT FROM AUTHOR]

The highly automated macromolecular crystallography beamline AMX/17-ID-1 is an undulator-based high-intensity (>5 × 1012 photons s−1), micro-focus (7 µm × 5 µm), low-divergence (1 mrad × 0.35 mrad) energy-tunable (5–18 keV) beamline at the NSLS-II, Brookhaven National Laboratory, Upton, NY, USA. It is one of the three life science beamlines constructed by the NIH under the ABBIX project and it shares sector 17-ID with the FMX beamline, the frontier micro-focus macromolecular crystallography beamline. AMX saw first light in March 2016 and started general user operation in February 2017. At AMX, emphasis has been placed on high throughput, high capacity, and automation to enable data collection from the most challenging projects using an intense micro-focus beam. Here, the current state and capabilities of the beamline are reported, and the different macromolecular crystallography experiments that are routinely performed at AMX/17-ID-1 as well as some plans for the near future are presented.

The highly automated macromolecular crystallography beamline AMX/17-ID-1 is an undulator-based high-intensity (>5 - 1012 photons s-1), micro-focus (7 mm - 5 mm), low-divergence (1 mrad - 0.35 mrad) energy-tunable (5-18 keV) beamline at the NSLS-II, Brookhaven National Laboratory, Upton, NY, USA. It is one of the three life science beamlines constructed by the NIH under the ABBIX project and it shares sector 17-ID with the FMX beamline, the frontier micro-focus macromolecular crystallography beamline. AMX saw first light in March 2016 and started general user operation in February 2017. At AMX, emphasis has been placed on high throughput, high capacity, and automation to enable data collection from the most challenging projects using an intense micro-focus beam. Here, the current state and capabilities of the beamline are reported, and the different macromolecular crystallography experiments that are routinely performed at AMX/17-ID-1 as well as some plans for the near future are presented. [ABSTRACT FROM AUTHOR]

This study analyzes the vibration movements of multi-support micro beams placed in an electrically smooth area using the modified couple stress theory. It has been assumed that the potential voltage that creates the electrical field strength varies harmonically. Large number of experiments in recent years have indicated that classical continuum theory is unable to predict the mechanical behavior of microstructure with small size. However, nonclassical continuum theory should be used to accurately design and analyze the microstructures. Modified couple stress theory models the micro and nanomechanical systems with higher accuracy because they employ additional material parameters to the equation considering size dependent behavior. The most general nonlinear motion equations for multi-support microbeams have been obtained by considering the material size parameter, the number of support and support positions, damping effect, axial stresses, electrical field strength, and nonlinear effects resulting from elongations. The nonlinear equations of motion are obtained according to the Hamilton method using the modified couple stress theory (MCST). The resulting equations of motion are nondimensionalized. In this way, the mathematical model has been made independent of the type and geometric structure of the material. Approximate solutions of the obtained dimensionless motion equation are obtained by the multi-scale method, which is one of the perturbation methods. As a result, an increase occurs in the first mode frequencies ( ω 1 ) and nonlinear correction effect parameters (λ (ω 1)) with the progress of the center support position gradually towards η = 0. 5 and the increase of the microbeam elasticity coefficient ( α 2 ). [ABSTRACT FROM AUTHOR]

To accurately capture size effect and geometrically nonlinear effect on thermal post-buckling of micro-beams, a new theoretical analysis model is presented. The model is based on modified gradient elasticity and von Kármán geometrically nonlinear theory. Considering the thermal effect, the governing equations of thermal post-buckling are derived by the principle of minimum total potential energy. The complete information including post-buckling bifurcation, configuration, amplitude of hinged–hinged and clamped–clamped micro-beams under different temperature rises is obtained by analytical solution. Comprehensive discussions are represented for size effect and geometrically nonlinear effect on thermal post-buckling of micro-beams. It confirms that taking into account the effect of geometric nonlinearity results in smaller post-buckling amplitude and the buckling resistance increase with the decrease in beam size. Both size effect of the critical buckling temperature rises and the post-buckling amplitude can be captured. Compared with other models, the ability of this model to predict the thermal buckling behaviors is improved. [ABSTRACT FROM AUTHOR]

• Nonlinear vibrations of viscoelastic functionally graded micro-beam is considered. • To consider the effects of micro scale, the modified couple stress theory is utilized. • Viscoelastic part is modeled using the fractional Kelvin-Voigt. • In the case of resonance, choosing the correct fractional order is vital. • Galerkin method and finite difference method were used to solve the fractional partial differential equations. In this paper, nonlinear vibrations of fractional viscoelastic functionally graded micro-beam are studied based on the fractional calculus. The Modified Couple Stress Theory (MCST) is utilized for considering the effect of the micro-scale. The micro-beam is modeled based on the Euler-Bernoulli theory and the Von Karman's nonlinear strain relations. The viscoelastic part of the micro-beam is considered using the fractional Kelvin-Voigt viscoelastic model. Functionally graded properties vary along the thickness based on a power-law function. The small-scale effects of the micro-beam are modeled using the MCST. Hamiltons principle is used to derive the governing equation of motion. For the solution, the Finite Difference Method (FDM) and the Finite Element Method (FEM) are employed. The FDM is used for discretizing the time domain, and the FEM is used for discretizing the space domain. Effects of the fractional-order, microstructure parameters, and Functionally Graded Material (FGM) properties on the time response of the viscoelastic micro-beam are analyzed numerically. Numerical results show that the fractional-order modeling of the viscoelastic micro-beam can change the behavior of the structure, and increasing the fractional-order, can increase the damping of the system. Numerical simulations also suggest that the effect of the fractional derivative order on the responses of free and forced vibrations is different because there is an important correlation between the fractional-order derivative and the excitation frequency. The results of this paper can be used for modeling the damping of the viscoelastic structures. [ABSTRACT FROM AUTHOR]

This work developed a piezoelectric micro-beam based energy harvester laminated with light activated shape memory polymer (LASMP). With noncontact mechanism and dynamic Young's modulus of LASMP, natural frequency of the energy harvester can be tuned during light exposure. Based on modified couple stress theory, the governing equation of the size-dependent micro-beam is derived via Hamilton's principle. Analytic solution of natural frequency and power output of the micro-beam is presented. Influence of size effect and dynamic Young's modulus of LASMP on natural frequency and power output is investigated. Present research suggested that application of LASMP in micro-engineering is potential and effective. [ABSTRACT FROM AUTHOR]

The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress (MCS) theory. Although many models have been incorporated into the literature, there is still room for introducing an improved model in this context. In this work, we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity. The MCS theory is used to investigate the material length scale effects. Using the Laplace transform, the temperature, deflection, displacement, flexure moment, and stress field variables of the micro-beam are derived. The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced. The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables. [ABSTRACT FROM AUTHOR]

This simulation study proposes a chemical mechanism to define a surrogate to the tumor control during micro- and mini-beam radiation therapy (MBRT). The main focus is proton-MBRT (pMBRT) and the methods developed are applied also to photon-MBRT (MRT). In both cases, the classical interpretation of physical dose cannot be used to explain the observed biological effect and a change of paradigm may be required. MBRT was reported to provide tumor control with reduced side effects when compared to standard dose delivery. The underlying mechanisms leading to a differential response of the normal tissue and the tumor are still unknown. In this work, we propose a chemical mechanism to describe the efficacy of MBRT. The model was developed starting from the observation that pMBRT led to long term survival without significant side effects of rats implanted with a high-grade glioma. We distribution of a generic radiation-induced molecule or radical could be a surrogate to describe the biological effect. The specific mechanisms leading to cell damage were outside the scope of this work. The molecules and radicals were selected according to a set of properties: (i) they should be stable to allow diffusion achieving coverage of the dose-valleys, (ii) they should reach a steady state in production versus removal, (iii) they should be a product of water radiolysis, and (iv) they should have oxidizing capacity. A convolution model was developed to assess the property (i) keeping the analysis as general as possible. The tumor coverage was defined widening the interpretation of the ICRU-62 recommendations. The properties (ii) and (iii) were investigated with the TRAX-CHEM software. The property (iv) was used to exclude not relevant chemical species. The results show that hydrogen peroxide fulfills all the requirements. Moreover, the modeling of its temporal and spatial distributions demonstrate that a uniform coverage of the target by this reactive oxygen specie (ROS) can be achieved during the beam-on time. The model was compared and proven to be compatible with three independent photon micro-beam and proton mini-beam animal experiments. We conclude that hydrogen peroxide is a good candidate to describe the mini-beam and micro-beam efficacy. Further experiments are proposed to experimentally benchmark the model and to correlate the hydrogen peroxide concentration to the tumor control probability.

Small size (micro/nano)‐scale beams constitute important building blocks of microelectromechanical systems (MEMS)/nanoelectromechanical systems (NEMS). Emerging roll‐based, high rate, manufacturing processes can make these small size‐beams vibrate, while they are axially moving. In this paper, an analytical‐numerical study on the nonlinear transverse vibration of the representative case of axially moving micro‐beam under an electrostatic force is conducted. The analytical model is realized by employing Hamilton's principle together with Galerkin discretization. The method of multiple time‐scales and Runge‐Kutta based numerical scheme are utilized to investigate the nonlinear dynamic behavior of the micro‐beam. Results are obtained for the influence of axial beam velocity and modified couple stress theory length scale parameter (i) on the values of pull‐in instability voltage of the small‐size beam, and (ii) on the small‐size beam nonlinear softening/hardening characteristics. The effect of axial load on the frequency response is investigated. [ABSTRACT FROM AUTHOR]

Thermoelastic damping (TED) is one of the main internal energy dissipation mechanisms in micro-/nano-resonators. Accurate evaluation of TED is important in the design of micro-electromechanical systems and nano-electromechanical systems. In this paper, a theoretical analysis on the TED in functionally graded material (FGM) micro-beam resonators is presented. Equations of motion and the heat conduction equation governing the thermodynamic coupling free vibration of non-homogenous micro-beams are established based on the Euler–Bernoulli beam theory associated with the modified couple stress theory. Material properties of the FGM micro-beam are assumed to change in the depth direction as power-law functions. The layer-wise homogenization method is used for solving the heat conduction equation. By using the mathematical similarity of eigenvalue problem between the FGM beam and the reference homogeneous one, the complex natural frequency including TED is expressed in terms of the natural frequency of the isothermal homogenous beam. In the presented numerical results, influences of various characteristic parameters, such as beam thickness, material gradient index, structure size, vibration mode and boundary conditions, on TED are examined in detail. It shows that TED decreases with the increases in the values of length scale parameters because the latter lead to the increase in structural stiffness. [ABSTRACT FROM AUTHOR]

Resonant sensors are widely used, especially in microsystems, for their high sensitivity, dynamic range, and resolution. In a typical resonant sensor, the measurand is converted to an axial force on a resonating beam, affecting its effective stiffness and consequently causing a shift in its resonance frequency. For a given operating frequency, it is desired to maximize the sensitivity of the resonance frequency to this axial force. In this paper, we propose new structural designs that significantly improve the sensitivity of resonant sensors to axial force. Our approach relies on structural modifications to resonant beams, including their boundary conditions, and hence, is amiable for implementation in different microfabrication processes. We present a mathematical model which is confirmed through simulations. Test devices were fabricated and used to validate the design principles. Our experimental findings indicate a sensitivity improvement of over four-fold for the test devices compared to the standard clamped-clamped beam structure. Without any modification to a fabrication process, the design principles presented in this work can be utilized to improve the performance of most micro- and nano-device designs that rely on conventional resonant beam force sensors. [Display omitted] • New micromechanical design approach proposed for resonant sensors. • These designs yield significant improvement in sensitivity to axial force. • Design principle modifies boundary conditions for resonant force sensors and is proven through modelling and simulations. • Sample devices fabricated and tested, supporting the proposed approach's utility. • Applicable to most device designs as direct replacements for the conventional resonance clamped-clamped beam force sensor. [ABSTRACT FROM AUTHOR]

To study the parametric resonance of series circuit and micro-beam coupling system subjected to the narrow-band random excitation, the stochastic differential equation of the micro-beam system subjected to narrow-band excitation is established. The frequency response equation of the system is obtained based on the method of multiple scales. Ito stochastic differential equation of system is derived. The first order and second order steady state response of the system are obtained and the corresponding to the amplitude-frequency curves are calculated. The influence of the system parameters on the response of the micro-beam is analyzed. The results show that the sufficient and necessary conditions for the stability of the parametric resonance are the same as the first order and second order moment stability of the system. The numerical simulation shows that with the increase of the width,thickness and length of the plate,the second order response of the plate amplitude is decreased. When the damping coefficient,the axial force and the distance between the two plates are increased,the second order response of the plate amplitude is increased.

The paper focuses on quantifying of vacuum and heat influence as unavoidable effects that appear during preparation and in-situ monitoring of micromechanical performance of cement pastes. Experimental tests at micrometer scale employ microscopic techniques of Scanning Electron Microscopy (SEM) and Focused Ion Beam (FIB). High vacuum is applied to samples during SEM-FIB procedures causing dessication and densification of primary cement paste constituents, the C S H gels. Collapse of pores and microstructural packing leads to their local stiffening and change in their fracture properties compared to usual partially saturated conditions of atmospheric pressures. The effect of vacuum is quantified for individual paste constituents in terms of their elastic moduli, tensile strengths and fracture energies measured on 15–20 μ m long cantilever micro-beams inside SEM chamber. It was found that application of vacuum in SEM increases elastic moduli of inner and outer products by ∼30%, tensile strength rises 2.3–2.5 times. The effect of local heating due to ionic interactions during FIB milling is studied by means of micromechanical measurements on micro-beams and finite element (FE) numerical model. It is shown that high energy milling (30 kV, 30 nA) causes substantial microstructural and subsequent mechanical changes leading to further stiffening and tensile strength increase in the micrometer scale. The effect originates from phase changes caused by elevated temperatures under the ion beam that can be locally very high (thousands of K according to the simplified FE model). The paper also reports micromechanical response received by low energy milling for which microstructural changes due to increased temperature are restricted to very small volumes and can be assumed to be negligible with respect to the micro-beam dimensions. [ABSTRACT FROM AUTHOR]

• A climb-enabled scale-dependent CP framework with GND and SSD effects was proposed. • A dislocation pile-up model for the long-range back stress of dislocation pile-ups at interfaces was developed. • Dislocation pile-ups breaking up due to climb was incorporated into the CP framework naturally. • The climb-affected thickness effect on micro-beam bending at elevated temperature is well captured. In this paper, a climb-enabled scale-dependent crystal plasticity (CP) framework with geometrically necessary dislocation (GND) and statistically stored dislocation (SSD) effects was proposed. A simple dislocation pile-up model, which can capture the long-range back stress due to the micro-structural constraint effect (i.e. grain-size effect, nano-layer thickness effect, nano-twin effect, etc.) and micro-deformational constraint effect (i.e. micro-bending, micro-torsion, micro-indentation, etc.), was developed. As an application of this framework, the size effect on the bending strength of cantilever micro-beams at elevated temperature was investigated. The long-range back stress from dislocation pile-ups near the neutral plane of bent micro-beams was specially considered, with the stress relaxation due to climb of piled up dislocations involved. The simulation results illustrated that thickness effect on the bending strength of micro-beams observed in experiments could be well captured by this CP framework. Dislocation climb, which can collapse the dislocation pile-ups near the neutral plane, plays a significant role in the thickness effect at high temperature. The stress relaxation due to dislocation pile-ups collapsing is stronger in thinner micro-beams, which contributes to the climb-affected thickness effect at high temperature. These are helpful for us to understand the temperature dependence of the second-order size effects induced by GNDs and dislocation pile-ups at various interfaces. Image, graphical abstract [ABSTRACT FROM AUTHOR]

In this paper, a new strategy for providing tensile force to suppress the transverse vibration of a micro-beam is introduced. This axial tensile force is supplied by a specific fluid flow called "magnetohydrodynamics" (MHD), which flows in a micro-pump, and then the fluid enters the micro-beam. The micro-beam is vibrated by an oscillating external force acting at its base. Therefore, a fluid structure interaction problem arises. The pressure of the fluid is increased due to the Lorentz force appears in the micro pump, and is directed by the channel towards the micro-beam and suppress the vibration of the micro-beam. It was observed that when the magnetic field rises from 0.25 Tesla to 0.5 Tesla, the amplitude of the micro-beam fluctuations will decrease from 6 × 10−13m to 3 × 10−13m. Assuming a laminar and incompressible flow, the finite volume method (FVM) is used to solve the governing equations. In the design of the micropump, the parameters studied are the value of the magnetic field, the amount of voltage applied to the micro-pump, the external force oscillation amplitude and the Reynolds number, and the effect of each parameter on the fluid and micro-beam behavior. The results show that with increasing fluid pressure in the micro-pump, the micro-beam vibration is suppressed. In addition, the pressure of the fluid along the micro-beam remains constant at 0.1 percent. [ABSTRACT FROM AUTHOR]

Abstract Free vibration behavior of bidirectional-functionally graded, double-tapered rotating micro-beam is investigated. An improved mathematical model based on Timoshenko beam theory and modified couple stress theory is developed that includes the effects of geometric non-linearity, spin-softening, Coriolis acceleration and high operating temperature. The problem is formulated in two steps. In the first step, the problem involving time-invariant inertia force due to rotation of the beam with constant angular speed is formulated using minimum potential energy principle and the governing non-linear equations are solved employing an iterative algorithm. In the next step, the free vibration problem is formulated employing Hamilton's principle and using the tangent stiffness of the deformed configuration induced due to time-invariant inertial loading. The governing equations for free vibration are transformed to state-space to formulate an eigenvalue problem. The governing equations are solved by approximating the displacement fields following Ritz method. The model is successfully validated with the available results. Extensive sets of results are presented for the first two chord-wise and flap-wise modes of vibration in non-dimensional speed versus frequency plane. The effects of different parameters such as size-dependent thickness, axial and thickness gradation indices, taperness parameters, hub parameter, length-thickness ratio, operating temperature and FGM composition are reported. [ABSTRACT FROM AUTHOR]

Similar to elasticity and viscoelasticity, anelasticity is one of the rheological models of materials. Like the viscoelastic materials, anelastic deformation is time dependent, while unlike viscoelasticity, it is full recoverable. Anelastic behavior is very sensitive to microstructure and is significant when things become small. In this paper, the nonlinear vibrations of an electrostatically actuated micro-beam made of anelastic material are studied based on the modified couple stress theory and considering compressible fluid media. The constitutive equation of micro-beams has been developed regarding the stress-strain behavior of classic anelastic materials. Considering the dependency of the effective viscosity on variable gap distance, an analytical model of an electrostatically actuated anelastic micro-beam has been developed through the variable Knudsen number. Then, multiple scales method has been applied to obtain an approximate analytical solution for nonlinear resonant curves. Additionally, the effects of different mechanical behaviors of materials including elasticity, viscoelasticity and anelasticity on the nonlinear dynamic response have been studied. Furthermore, influences of some effective parameters such as length scale, anelastic relaxation time, relaxation intensity, mid-plane stretching force, residual axial force, air-gap pressure and compressible fluid media on the nonlinear vibration analysis have been investigated and discussed in detail. The results demonstrate that resonance curves are strongly dependent on the mechanical behavior of materials. It is found that the relaxation intensity, relaxation time and air-gap pressure change the resonant amplitude significantly. Moreover, the results reveal that considering compressible fluid media, both the frequency response and the softening behavior of the system decrease. [ABSTRACT FROM AUTHOR]

Abstract This paper presents thermal-mechanical-electrical buckling analysis of micro-beams that are made of functionally graded materials(FGMs) with temperature-dependent thermo-elastic properties. The material properties of the micro-beam are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations are based on the principle of the minimum total potential energy, von Kármán geometric nonlinearity theory, and modified couple stress theory is employed to consider the size effect. A differential quadrature (DQ) method combined with an iteration process is used to predict the critical buckling external axial force and buckling temperature increment. The effects of the volume fraction profile parameter, dimensionless length scale parameter, initial gap ratio, ground electrode shape parameter, the applied voltage, slenderness ratio and the axial residual stress on the thermal-mechanical-electrical buckling behavior are evaluated in detail through parametric studies. [ABSTRACT FROM AUTHOR]

This paper focuses on the buckling behaviors of a micro-scaled bi-directional functionally graded (FG) beam with a rectangular cross-section, which is now widely used in fabricating components of micro-nano-electro-mechanical systems (MEMS/NEMS) with a wide range of aspect ratios. Based on the modified couple stress theory and the principle of minimum potential energy, the governing equations and boundary conditions for a micro-structure-dependent beam theory are derived. The present beam theory incorporates different kinds of higher-order shear assumptions as well as the two familiar beam theories, namely, the Euler-Bernoulli and Timoshenko beam theories. A numerical solution procedure, based on a generalized differential quadrature method (GDQM), is used to calculate the results of the bi-directional FG beams. The effects of the two exponential FG indexes, the higher-order shear deformations, the length scale parameter, the geometric dimensions, and the different boundary conditions on the critical buckling loads are studied in detail, by assuming that Young’s modulus obeys an exponential distribution function in both length and thickness directions. To reach the desired critical buckling load, the appropriate exponential FG indexes and geometric shape of micro-beams can be designed according to the proposed theory. [ABSTRACT FROM AUTHOR]

This paper presents a validation procedure of multi-scale modelling scheme by making, testing and modelling deformation and fracture of cement paste beam at sub- meso scale (between micro and meso scale). Miniaturized three-point bending testing concepts were adopted. Cement paste beams with a cross-section of 500 μm × 500 μm were fabricated using a micro dicing saw and subjected to bending using nanoindenter. Simultaneously, fracture behaviour of the same size specimens was predicted by a microstructure informed multi-scale lattice fracture model in which input microstructures are obtained by X-ray computed tomography at two scales (micro and sub- meso ). Uncoupled upscaling approach was used to relate the material's mechanical behaviour at sub-meso scale with the microstructures at lower scale. A good agreement between experimental and numerical results was observed which shows that starting from micro scale and with relatively simple mechanical considerations it is possible to correctly reproduce behaviour at upper scale. [ABSTRACT FROM AUTHOR]

The dynamic pull-in instability of a thermoelectromechanically loaded micro-beam is investigated based on the 'symmetric stress' gradient elasticity theory and Euler-Bernoulli beam theory. The beam is subjected to the combined action of an electric voltage, axial static force and a uniform temperature change. By employing Galerkin's method, the nonlinear partial differential governing equation is decoupled into a set of nonlinear ordinary differential equations, which are then solved using Runge-Kutta method. Numerical results show that compared with the size-dependent micro-beam model, the classical elasticity theory in which the size effect is ignored underestimates the pull-in voltage. The effects of size, temperature change, axial force, geometric nonlinearity, fringe effect, initial gap, beam length and width on the pull-in instability of the micro-beam are discussed in detail. [ABSTRACT FROM AUTHOR]

Micro-beams show size dependent structural response which is not predictable from classical beam theories. In this paper, a couple stress theory based analysis of large elasto-plastic deflection of micro-beams is carried out using an incremental moment-curvature constitutive modeling approach. An isotropic hardening model is used for illustration. The developed model is applied to solve the large deflection bending problem of a cantilever under the combined effect of distributed and concentrated load. The solution procedure adopted is based on linearization of the governing differential equation at every load step and subsequently solving the equation by numerical integration. Suitable normalization of the relevant variables have rendered generality. New results pertaining to large elasto-plastic deflections showing evident size-effects are investigated. [ABSTRACT FROM AUTHOR]

We have determined the distribution of aluminum in the epidermal cells of mature tea leaves using micro-beam particle-induced X-ray emission. The observed pattern of aluminum distribution in the epidermal cells suggests that aluminum exists in cell walls. Silicon exhibits a distribution that is nearly identical to that of aluminum, suggesting co-localization with aluminum.

The proton micro-beam of the CNA accelerator in Seville has been used to test two detectors based on single crystal diamond grown by chemical vapor deposition. The first diamond has a more traditional design, with dimensions 4.5 × 4.5 × 0.5 mm 3 , and features a large contact of the same size as the crystal. The second, with dimensions 2.0 × 2.0 × 0.3 mm 3 , features a small contact of 0.5 × 0.5 mm 2 . By using the micro-beam, the map of the charge collection efficiency for both the detectors have been measured. We show that the charge collection efficiency of the diamond with large contacts is generally uniform, while the diamond with smaller contacts needs further developments in this respect. A proof of principle test with a fast electronic chain has been performed to demonstrate that spatially resolved pulse shape analysis can be performed with this system. The micro-beam allowed also studying radiation-induced permanent damage and polarization, which are two irradiation effects of importance for the development of diamonds used in spectroscopy applications. [ABSTRACT FROM AUTHOR]

The present study investigates nonlinear forced vibration of dielectric elastomer-based micro-beam. The nonlinear terms in beam equation are geometric and material one. Geometric nonlinearity is considered by von-Karman strain displacement relationship and the material nonlinearity is modeled with Yeoh hyper-elastic model. Galerkin and Multiple scale methods solve the governing equation. This solution that includes primary resonance, leads to frequency response, so that we depict influence of detuning parameter on amplitude in variation of different parameters. [ABSTRACT FROM AUTHOR]

This paper presents a nonlinear electro-dynamic analysis for a size dependent micro-beam made of materials with nonlinear elasticity by employing the modified couple stress theory based on Euler–Bernoulli beam model. By employing Hamilton's principle, the nonlinear partial differential governing equation is derived then solved by using Galerkin method in the space domain and backward differential method in the time domain to obtain the nonlinear electro-dynamic response and phase portrait of the micro-beam. A parametric study is conducted, with a particular focus on the influences of nonlinear elasticity and size-dependency of the micro-beam on its nonlinear dynamic behavior. Numerical results show that a micro-beam exhibiting nonlinear elastic stress–strain relationship has reduced effective stiffness while the size effect has the opposite effect. [ABSTRACT FROM AUTHOR]

This research is on the nonlinear dynamics of a two-sided electrostatically actuated capacitive micro-beam. The micro-resonator is composed of silicon and PZT as a piezoelectric material. PZT is functionally distributed along the height of the micro-beam according to the power law distribution. The micro-resonator is simultaneously subjected to DC piezoelectric and two-sided electrostatic actuations. The DC piezoelectric actuation leads to the generation of an axial force along the length of the micro-beam and this is used as a tuning tool to shift the primary resonance of the micro-resonator. The governing equation of the motion is derived by the minimization of the Hamiltonian and generalized to the viscously damped systems. The periodic solutions in the vicinity of the primary resonance are detected by means of the shooting method and their stability is investigated by determining the so-called Floquet exponents of the perturbed motions. The basins of attraction corresponding to three individual periodic orbits are determined. The results depict that the higher the amplitude of the periodic orbit, the smaller is the area of the attractor. [ABSTRACT FROM AUTHOR]

The present paper deals with the study of nonlinear vibration of a functionally graded cantilever micro-beam imposed on a bias DC voltage and superimposed on a sinusoidal heat source. The governing equation of motion is derived extremizing the Lagrange's equation and Hamilton's principal under the assumption of Euler-Bernoulli beam theory. The thermo-elastic equation is obtained utilizing the first law of thermodynamics under the assumption of the classical Fourier heat conduction model. Due to the displacement dependency of the electrostatic force and time variability of the heat source, the governing differential equations of the system are nonlinear implicitly parametrically electro-thermo-elastic coupled equations. To evaluate the dynamic response of the micro-beam, the coupled equations are discretized applying a Galerkin-based reduced order model and then integrated numerically by the Runge-Kutta method. By solving the equations, the stable and unstable regions at different bias DC voltages are identified. By picking some special points from these regions and depicting the time history and phase portrait diagrams, their behaviors are investigated in detail. In addition to the classical dynamic pull-in, in which a homoclinic orbit separates stable periodic orbits from the unbounded solutions, a new kind of dynamic pull-in is presented, which separates unstable solutions, due to parametric resonance response, from unbounded rapidly growing solutions owing to the existence of saddle and singular fixed points in the system. [ABSTRACT FROM AUTHOR]

Transmission demonstration experiment of 0.1-0.2THz beam was performed with transmission system consisted of polymer fibers of φ3mm×300mmL coated with gold metal. THz beam was generated by high power compact gyrotron designed output power of 0.25kW and measured output power at terminal of metallic cladding polymer fibers in the transmission system and the following results were derived; (1) It was demonstrated that maximum output power of the order of 0.84W through the polymer fibers was observed by SBD detector at input power of the order of 7.5W. (2) Loss factor α(dB/m) of PMMA and PEEK polymer fiber was obtained in the range of 150-850(dB/m) and exhibits frequency dependence in the range of 0.1-0.2THz. (3) Present transmission system with metallic tapered wave guide and φ2-3mm×60mm polymer fiber is applicable with 10% power transmittance for hyperthermia therapy.

In this paper, the dynamic behavior of atomic force microscope (AFM) based on non-classical strain gradient theory was analyzed. For this aim atomic force microscope micro-beam with attached tip has been modeled as a lumped mass. Micro-beam has stimulated via a piezoelectric element attached to the end of clamped and non-linear partial differential equation of the system has extracted based on Euler-Bernoulli theory and to be converted into ordinary differential equation by using Galerkin and separation method. The classic continuum theory because of lack of consideration size effect that has been observed in many experimental studies, has little accuracy in predicting the mechanical behavior of Nano devices. In this study, the stability region of micro-beam are determined analytically and validated by comparison with numerical results. Difference between presented analysis in dynamic behavior of micro-beam by classic and non-classic theories has been shown with variety of diagrams. It is clear that consideration the size effect changes the dynamical behavior of the problem completely and it is possible while classical theory predicts stable behavior for microscope the size effect is caused bi-stability. The results in this paper are very useful for the design and analysis of atomic force microscope. [ABSTRACT FROM AUTHOR]

A tunable shock micro-switch based on piezoelectric excitation is proposed in this study. This model includes a clamped-clamped micro-beam sandwiched with two piezoelectric layers throughout the entire length. Actuation of the piezoelectric layers via a DC voltage leads to an initial axial force in the micro-beam and directly affects on its overall bending stiffness; accordingly enables two-side tuning of both the trigger time and threshold shock. The governing motion equation, in the presence of an electrostatic actuation and a shock wave, is derived using Hamilton's principle. We employ the finite element method based on the Galerkin technique to obtain the temporal and phase responses subjected to three different shock waves including half sine, triangular and rectangular forms. Subsequently, we investigate the effect of the piezoelectric excitations on the threshold shock amplitude and trigger time. [ABSTRACT FROM AUTHOR]

The paper is focused on the experimental investigation of cement paste's tensile strength and related mechanical properties at the micrometer level. Small scale specimens with micrometer dimensions in the form of cantilever beams having a triangular cross section and ≈20 μm in length are fabricated by means of a focused ion beam and tested in bending with the aid of a nanoindenter. Elastic properties are evaluated from both bending and nanoindentation tests for all the phases with very close agreement. The phase separation is performed with SEM-based image analysis and the deconvolution of grid nanoindentation results. The load-deflection curves of bent beams are monitored up to the failure for distinct microlevel phases, namely for inner and outer products and Portlandite. The tensile strength of the phases is directly derived from the load-deflection curves in the range of 264 MPa (for the outer product) to 700 MPa (for the inner product and Portlandite). Moreover, the load-deflection curves are used for the supremum estimates of fracture energies for individual hydrated cement phases. Low values of the energies in the range of 4.4 − 20 J/m 2 were found. The values obtained experimentally in this paper correspond well with those published in recent multiscale or molecular dynamics models. [ABSTRACT FROM AUTHOR]

Vibration of a beam has extensive applications in engineering and industry. The objective of this article is to provide a novel analytical model by free boundary approach to derive a more exact model for the small oscillations of a cantilever microbeam in contact with an incompressible bounded fluid in a cavity. First, a system of integral equations is proposed to solve and interpret the problem. Then, the existence of the solution is proved by the use of the Banach fixed point theorem. At the end, an example is presented for verifying the proposed method and comparing the results with the fixed boundary approach. [ABSTRACT FROM AUTHOR]

This paper investigated the size effect on the free vibration of functionally graded micro-beams under the combined electrostatic force, temperature change and Casimir force based on Euler–Bernoulli beam theory and von Kármán geometric nonlinearity. Taking into consideration the temperature-dependency of the effective material properties, material properties of the functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to the Voigt model and exponential distribution model. The principle of minimum total potential energy is used to derive the nonlinear governing differential equation which is then solved using the differential quadrature method (DQM). A parametric study is conducted to show the significant combined effects of the size effect, material gradient, temperature change, geometric parameters and Casimir force. [ABSTRACT FROM AUTHOR]

The present study investigates the thermo-elastic damping (TED) of transversal vibration in a functionally graded piezoelectric (FGP) micro-beam resonator. The model is a functionally graded silicon-piezoelectric fully clamped micro beam exposed to a DC piezoelectric tuning voltage. The object is to propose a novel FGP MEM system, with a controllable thermo-elastic damping. It is shown that the functionality of the material distribution not only reduces the TED ratio, but also enables tuning the resonance frequency of the resonator due to the piezoelectric actuation. The effects of portion of piezoelectric material, geometrical dimensions, the ambient temperature and tuning DC voltage, on the quality factor of the flexural vibrations of the structure is analyzed through solving the thermo elastically coupled dynamic equations of the motion. [ABSTRACT FROM AUTHOR]

Particle-induced X-ray emission (PIXE) is a phenomenon of atomic inner shell ionization and characteristic X-ray emission due to ion-atomic collisions. The intensity of continuous X-rays in the PIXE energy spectrum is much lower than that of characteristic X-rays. Therefore, PIXE can be used as a semi-monochromatic X-ray source. Furthermore, PIXE produced by a heavily charged particle beam with a diameter of several micrometers (micro-PIXE) can be used as a monochromatic X-ray point source for Xray computed tomography (CT) to investigate internal structures of objects <1 mm. We developed micron X-ray CT based on micro-PIXE with a spatial resolution of about 4 μm. Because the photoelectric effect cross-section is proportional to the fifth power of the atomic number, the distributions of small amounts of heavy elements can be investigated using this CT technique, and the element can be identified using its absorption edge. We applied this CT to observe the internal structure of hair, a head of an ant, and Drosophila. We were able to identify the medulla configuration and cortex of the hair, and the mandibular glands, pharynx, and brain in the ant head. We confirmed a high Mn concentration in the mandibular glands. We used a contrast agent to visualize the internal organs of Drosophila. Furthermore, we applied this CT to research clay particles contaminated by the Fukushima Dai-ichi nuclear accident and confirmed that cesium atoms were distributed on the surfaces of clay particles. [ABSTRACT FROM AUTHOR]

The dynamic characteristics of a quartz crystal resonator (QCR) in thickness-shear modes (TSM) with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inviscid and incompressible for simplicity. Dynamic equations of the coupled system are established. The added mass effect of liquid on micro-beams is discussed in detail. Characteristics of frequency shift are clarified for different liquid depths. Modal analysis shows that a drag effect of liquid has resulted in the change of phase of interaction (surface shear force), thus changing the system resonant frequency. The obtained results are useful in resonator design and applications. [ABSTRACT FROM AUTHOR]

Large genome size in plants is largely caused by presence of repetitive DNA, which makes it of great interest to study the chromosome specific markers and function of complex large plant genome. In order to investigate evolutionary patterns of repetitive DNA, random PCR was carried out for a comprehensive repeat characterization and amplification in micro-dissected and micro-cloned L. tigrinum. The isolated chromosome was amplified by using DOP-PCR (degenerate oligonucleotide primed PCR) and LA-PCR (linker adaptor-mediated PCR) by which 100 to 2500 bp smear fragments of DNA, and 300 to 2000 bp predominant fragments were obtained. To construct DNA library of chromosome 1, obtained PCR products were cloned in the plasmid vector. The size of cloned inserts varied in DOP-PCR from 100-1700 bp and 100-900 bp in LA-PCR, with predominant fragment at 500 to 1000 bp. Based on the BLAST-X search, 28% were matched with protein coding genes in the public database, while 72% of the sequences didn't exhibit any significant similarity with sequences already present in the plant database making up to 72% of unique sequences in the huge lily genome. Two clones obtained from micro-dissected chromosome were successfully detected on the chromosome 1 of diploid and triploid L. tigrinum. Among 513 genomic DNA sequences searches, 405 SSRs with perfect repeats were clearly verified and categorized based on number of repeats and their motifs. Six types of repeats were identified, among them penta-nucleotide repeats occurred at the high frequency. [ABSTRACT FROM AUTHOR]

This work investigates the nonlinear vibration of a fractional viscoelastic micro-beam exposed to random excitation. For the micro-scale effect, the micro-beam model is established based on the Modified Couple Stress Theory (MCST). The fractional nonlinear partial differential equation is obtained using Von-Karman's nonlinear strains and the Kelvin–Voigt fractional viscoelastic model. The micro-beam is exposed to a random force which its amplitude is considered as the Gaussian white noise. The Finite Difference Method (FDM) and the Galerkin method are applied to discretize the stochastic governing equation of motion. To solve the stochastic partial differential equation, a numerical discretization for the white noise excitation is applied. Moreover, the Statistical Linearization (SL) method and the Spectral Representation (SR) method are also employed and a comparison is done between these methods. The simulations show good agreement between the numerical method and other methods. In addition, it is shown that the proposed method can be used for different boundary conditions of the micro-beam. The impacts of the fractional derivative order, white noise intensity, viscoelastic model, and length-scale parameter on the statistical properties of the micro-beam are shown. The numerical simulations indicate that the high values of fractional-order can significantly affect the variance and the Root Mean Square (RMS) of the transverse amplitude, However, this influence for small values of the fractional-order is negligible; the impact of the fractional-order derivative on the statistical characteristics of the micro-beam is very different from 0 < α < 0. 6 , and 0. 6 < α < 1. • This work investigates the nonlinear vibration of a fractional viscoelastic microbeam exposed to random excitation. • To solve the stochastic partial differential equation, a numerical discretization for the white noise is proposed. • The results are compared with the Statistical Linearization Method and the Spectral Representation Method. • The impact of the fractional derivative on the statistical response of the micro-beam is very different for 0 < α < 0. 6 , and 0 < α < 1. [ABSTRACT FROM AUTHOR]

The thermal effect on the pull-in instability of functionally graded micro-beams under the combined electrostatic force, temperature change and Casimir force is studied based on Euler–Bernoulli beam theory and von Kármán geometric nonlinearity. Take into consideration the temperature-dependency of the effective material properties, the Voigt model and exponential distribution model is used to simulate the material properties of the functionally graded materials (FGMs). Principle of virtual work is used to derive the nonlinear governing differential equation which is then solved using the differential quadrature method (DQM). A parametric study is conducted to show the significant effects of material composition, temperature change, geometric nonlinearity and Casimir force. [ABSTRACT FROM AUTHOR]

This paper studies the dynamic instability of cantilever micro-beam submerged in an incompressible viscous fluid cavity and actuated by electrostatic force. Equivalent squeeze film damping is incorporated in the vibrational equation of the micro-beam to obtain the natural frequencies of the coupled system. Then, imposing various step voltages, dynamic responses, and pull-in conditions of the micro-beam are studied. A parametric study is conducted to evaluate the effect of fluidic confinement on the instability voltage. Dielectric constant of the fluid proves dominantly influential compared with viscosity and density. In addition, values of pull-in voltage are seen to be highly dependent on the vertical position as well as the length of the micro-beam. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a nonlinear dynamic analysis of a micro-actuator made of nonlinear elasticity materials. The theoretical formulations are based on Bernoulli–Euler beam theory and include the effects of mid-plane stretching due to large deformation and material nonlinearity. By employing Linstedt–Poincaré perturbation method, the nonlinear governing equation is transformed into a set of linear differential equations which are then solved using Galerkin’s method. Numerical results show that the linear constitutive relationship used in previous studies is valid for small deformation only whereas for large deformation, the nonlinear elasticity constitutive relationship must be used for accurate analysis. The effects of initial gap and beam length on the nonlinear electro-dynamic behavior of the micro-actuator are also discussed. [Copyright &y& Elsevier]