جستجوی مقالات مرتبط با کلیدواژه "static deflection" در نشریات گروه "فنی و مهندسی"

The present paper is aimed to analyze static deformation, natural frequency and subharmonic resonance of a bilayer cantilever microbeam, the second layer of which has a variable width and is located on a point along the microbeam's length. Electrostatic actuation is induced by applying the voltage between the microbeam and its opposite electrode. The importance of such configuration is revealed particularly in mass and pollutants micro-sensors. First, the nonlinear equation of motion, which has been extracted in previous studies using Hamilton's principle and considering the bending neutral axis shortening assumption, was rewritten for a microbeam with variable-width second layer. Then differential equations governing the static deflection and free vibration equation around the stability point are solved using Galerkin method. Three mode shapes of a doubled stepped-microbeam are employed as the comparison function. The shapes such as triangular, parabolic, symmetric parabolic and hyperbolic are considered for the second layer. In order to find the optimal length and thickness for the selected form, the relevant diagrams were plotted for static deformation and natural frequency at constant volume and different lengths and thicknesses, and then were analyzed and investigated. The discretized equations are solved by the perturbation theory. The excitation frequency is tuned near twice the fundamental natural frequencies (subharmonic excitation). The results show that system behavior depends on the size, position and width of the coated layer. The results of this paper can be used for optimum design of microsystems such as microswitches and mass and pollutant microsensors.

In this research static deflection and free vibration of homogeneous nanobeams coated by a functionally graded (FG) layer is investigated according to the nonlocal elasticity theory. A higher order beam theory is used that does not need the shear correction factor. The equations of motion (equilibrium equations) are extracted by using Hamilton’s principle. The material properties are considered to vary in the thickness direction of FG coated layer. This nonlocal nanobeam model incorporates the length scale parameter (nonlocal parameter) that can capture the small scale effects. In the numerical results section, the effects of different parameters, especially the ratio of thickness of FG layer to the total thickness of the beam are considered and discussed. The results reveal that the frequency is maximum for a special value of material power index. Also, increasing the ratio of thickness of FG layer to the total thickness of the beam increases the static deflection and decreases the natural frequencies. These results help with the understanding such coated structures and designing them carefully. The results also show that the new nonlocal FG nanobeam model produces larger vibration and smaller deflection than homogeneous nonlocal nanobeam.