This paper presents a mathematical model and a computational approach for the thermal post-buckling and free vibration in the vicinity of the buckled equilibrium position of microbeams based on the modified couple stress Euler-Bernoulli beam theory and geometrically accurate relation. The governing equations for the whole analysis are established with a intrinsic material length scale parameter to capture the size effect. These equations, in conjunction with the corresponding boundary conditions, are decomposed into two two-point boundary value problems, which are solved using the shooting method. For static deformation, the geometric nonlinearity is involved and the size dependent postbuckling configuration is obtained as a function of temperature rise. For dynamic one, the small amplitude free vibration about the prebuckled position is developed following an assumed harmonic time mode, and the length scale and temperature rise dependent fundamental natural frequency is presented. Numerical computations are executed to illustrate the size dependency in the thermal postbuckling behaviors and fundamental frequency of the vibration around the buckled configuration of microbeams.

In this paper, a resonator is modeled as a microbeam under the effect of thermoelastic damping and actuated electrically. Two models, small and large deformation models, are represented by considering linear and nonlinear Euler-Bernoulli beam theory. These models are compared against voltage, and the difference between these models is shown and discussed. In the large deformation model, the microbeam deflected due to applied DC voltage, and vibration of microbeam occurs around this static deflection. The vibration equation is linearized around static deflection and by applying harmonic vibration, equation for mode shape and frequency is obtained. The complex frequency is calculated by numerical method and then used for obtaining the Q-factor of thermoelastic damping. The stretching effect and thermoelastic damping is validated with the literature. The result shows that for the high values of voltage, the large deformation model is more accurate. The behavior of thermoelastic damping is also investigated against the geometrical and material properties.

We have constructed an X-ray photoelectron microscopic system. An X-ray source is a laser-produced plasma in a scheme of an X-ray laser experiment. X rays involving amplified spontaneous emissions (ASE) at 15.47 nm were delivered with a 10-Hz repetition rate from a compact X-ray laser system. X rays were collected and focused by a Schwarzschild optics coated with Mo/Si multilayers for a 15.47-nm X ray. Photoelectron signals due to the Ga 3d and As 3d electrons were observed, when a GaAs wafer was used as a sample. The spatial resolution of about 1 μm was confirmed.