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.
Thermal buckling behavior of a functionally graded material (FGM) Timoshenko beam is studied based on the transformed-section method. The material and thermal properties of the FGM beam are assumed to vary across the beam thickness according to a power-law function, a sigmoid function and an exponential function. The results of buckling temperature for the FGM beams with respective temperature-dependent and temperature-independent properties under uniform and non-linear temperature rises are presented. Some results are compared with those in the published literature to verify the accuracy of the present work. The effects of the material distributions, temperature fields, temperature-dependent properties and slenderness ratios on the thermal buckling behaviors of FGM beams are discussed. It is believed that the present model provides engineers with a simple and effective method to study the effects of various parameters of the FGM beam on its thermal buckling behavior.