A buckling analysis of temperature-dependent embedded plates reinforced by single-walled carbon nanotubes (SWCNTs) subjected to a magnetic field is investigated. The SWCNTs are distributed as uniform (UD) and three types of functionally graded nanotubes (FG), in which the material properties of the nano-composite plate are estimated based on the mixture rule. The surrounding temperature-dependent elastic medium is simulated as Pasternak foundation. Based on the orthotropic Mindlin plate theory, the governing equations are derived using Hamilton's principle. The buckling load of the structure is calculated based on an exact solution by the Navier method. The influences of elastic medium, magnetic field, temperature and distribution type, and volume fractions of SWCNT are shown on the buckling of the plate. Results indicate that CNT distribution close to the top and bottom are more efficient than that distributed near the mid-plane for increasing the stiffness of the plates.
This article employs the classical Euler–Bernoulli beam theory in connection with Green–Naghdi’s generalized thermoelasticity theory without energy dissipation to investigate the vibrating microbeam. The microbeam is considered with linearly varying thickness and subjected to various boundary conditions. The heat and motion equations are obtained using the modified couple stress analysis in terms of deflection with only one material length-scale parameter to capture the size-dependent behavior. Various combinations of free, simply-supported, and clamped boundary conditions are presented. The effect of length-to-thickness ratio, as well as the influence of both couple stress parameter and thermoelastic coupling, are all discussed. Furthermore, the effect of reference temperature on the eigenfrequency is also investigated. The vibration frequencies indicate that the tapered microbeam modeled by modified couple stress analysis causes more responses than that modeled by classical continuum beam theory, even the thermoelastic coupled is taken into account.
In this paper, thermally-excited, lateral free vibration analysis of a small-sized Euler-Bernoulli beam is studied based on the nonlocal theory. Nonlocal effect is exerted into analysis utilizing differential constitutive model of Eringen. This model is suitable for design of sensors and actuators in dimensions of micron and submicron. Sudden temperature rise conducted through the thickness direction of the beam causes thermal stresses and makes thermo-mechanical properties to vary. This temperature field is supposed to be constant in the lateral direction. Temperatures of the top and bottom surfaces of the system are considered to be equal to each other. Governing equation of motion is derived using Hamilton’s principle. Numerical analysis of the system is performed by Galerkin’s approach. For verification of the present results, comparison between the obtained results and those of benchmark is reported. Numerical results demonstrate that dynamic behavior of small-sized system is been effected by temperature shift, nonlocal parameter, and slenderness ratio. As a result, taking the mentioned parameters into account leads to better and more reliable design in miniaturized-based industries.