{'fraction_non_alphanumeric': 0.02138690861957226, 'fraction_numerical': 0.0, 'mean_word_length': 5.225806451612903, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
On thermo-mechanical vibration analysis of multi-scale hybrid composite beams

This article is primarily organized to analyze the thermo-elastic vibrational characteristics of multi-scale hybrid composite beams according to a refined beam model. In this novel type of composites, multi-scale reinforcing elements, carbon fiber (CF) and carbon nanotube (CNT) in particular, are presumed to be dispersed in an initial resin. The homogenization process is carried out employing a mixture of the Halpin–Tsai model and the rule of mixture. The effect of temperature and its gradient on the mechanical properties of CNTs and epoxy resin is rendered to present a more reliable thermal analysis. On the other hand, a refined trigonometric shear deformable beam theory is extended to derive the kinematic relations of the beam needless of any external shear correction coefficient. On the basis of Hamilton's principle, the partial differential equations of motion are developed. Thereafter, the natural frequencies are achieved by the means of Galerkin's method for both simply supported and fully clamped edge conditions. Then, the validity of the presented model is shown by comparing these results with those of previously published researches. Finally, effects of different parameters on the natural frequency of composite beams are rendered in the framework of some numerical case studies. It can be found that multi-scale hybrid composite beams can satisfy higher frequencies once compared with each of the CF- or CNT-reinforced composite beams.