Effect of thermal axial load on vibration of cracked nanomaterial beam using nonlocal elasticity theory under different boundary conditions

Abstract

      The aim of this paper is to investigate the free vibration of single-cracked nanomaterials beams under thermal axial load. The beam model is Euler-Bernoulli. The well-known nonlocal elasticity theory is used for analyzing the nanomaterial beams in which the size effect nonlocal parameter is considered. Crack is modeled as a rotational spring that connects the beam segments with each other. The thermal load acts as an axial force on the nanomaterial beam. The effect of the thermal load, the crack location, the crack severity, and the nonlocal parameter are examined in this paper. Two cases of the non-cracked nanomaterial beam and the single-cracked nanomaterial beam are analyzed for three different types of the boundary conditions as simply supported (SS), clamped-clamped (CC), and clamped-simply supported (CS). The results show that when the crack severity is increased the natural frequencies are decreased but in some cases in which the nonlocal parameter value is high, the reverse phenomenon occurs. The temperature changes have a great effect on the frequencies as the temperature is decreased to a value lower than the room temperature, the natural frequencies for all modes decrease and when the temperature is increased to a value higher than the room temperature, the all mode frequencies increase.