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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.

Micro-beam scanning system for PIXE analysis newly installed in National Institute of Radiological Sciences (NIRS) was introduced in this paper. Fine ring structure of a fish scale was observed using elemental mapping with proton micro-beam scanning. Pollen was analyzed as one example of single cell to demonstrate the elemental distribution. The minimum size of the proton beam is estimated as 0.4×0.65 μ m.

Bismuth (Bi) content of electrum from Mongolian artisanal/small-scale mining sites was determined by micro-PIXE at CSIRO. This is to provide artisanal/small-scale miners information on the valuable trace element in electrum which they recover from quartz veins. The analysis was done using a 3 MeV micro-beam (30 micrometer in diameter) with an aluminum filter of 125 micrometer thickness. The result showed that electrum grains from the study area contains Bi with a range from 0 to 2,530 ppm.

The concentration and distribution of fluorine in mature leaves of Camellia sinensis were determined using micro-PIGE. The elemental concentration was measured as 2210 ± 450 ppm. Fluorine showed clear localization in the epidermis. Fluorine was distributed uniformly in the upper epidermis, suggesting that fluorine was localized in the cytoplasm. On the other hand, extremely concentrated areas of fluorine were observed in the lower epidermis.

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.

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.

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 (${\omega }_1$) and nonlinear correction effect parameters ($\lambda ({\omega }_1)$) with the progress of the center support position gradually towards $\eta =0.5$ and the increase of the microbeam elasticity coefficient (${\alpha }_2$).

In this paper, the thermally induced vibration of a functionally graded (FG) cantilever micro-beam subjected to a moving laser beam is investigated via simulating the equivalent third-order dynamic system. The material properties of the FG micro-beam are defined by an exponential function through the thickness. The coupled thermo-elastic equations are obtained utilizing the first law of thermodynamics under the assumption of the classical Fourier heat conduction model and Euler–Bernoulli beam theory. To evaluate the dynamic response of the micro-beam, the coupled equations are first discretized by employing a Galerkin based reduced-order model and then decoupled by applying the Cramer's rule. Solving the decoupled equations analytically, effects of key parameters are illustrated by means of time histories and phase portraits. Furthermore, by investigating the case of resonant excitation, the critical velocity corresponding to mobile heat source is obtained.

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.

This paper studies the characteristics of a micro-beam interacting with an incompressible fluid in a fluid chamber with an opening in its bottom face for fluid flow. The Euler–Bernoulli equation for transverse deformation of an elastic beam is coupled with the fundamental hydrodynamic equation, which is solved by Galerkin and separation of variables method. The 2D fluid flow assumption in Cartesian coordinate has been used. Natural frequencies and mode shapes of wet beam are calculated and compared with the dry beam. The effects of geometrical parameter changes are also computed as a benchmark for the design of the micro-pump. It is observed that fluid coupling causes a decrease for beam’s natural frequencies, especially in higher modes. Furthermore, since the results of the dry and wet beam show a small discrepancy in lower modes, the mode related to the dry beam was employed as the trial function in the forced vibration analysis of the coupled system.