Transverse vibration analysis of nonlocal beams with various slenderness ratios, undergoing thermal stress

Abstract

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.

Keywords

• small-sized beam
• nonlocal theory
• temperature-dependent properties
• free lateral vibration