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

Babaei Alireza, Rahmani Arash, Ahmadi Isa

Archive of Mechanical Engineering

2019

Vol. LXVI, nr 1

5--24

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.

Srovnání dvou přístupů pro výpočet příčného kmitání rotoru s uvážením rázů kotoučů na stacionární část data

Obruča Z.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

2002

z. 19

113-118

This contribution deals with analysis of lateral vibration of a rotor taking into account impacts of the discs on the stationary part. The shaft was represented by a beam-like body that was discretized into finite elements. For solving the equation of motion an implicit Newmark method has been chosen and modified for the purpose of the calculation. In the paper there are compared two approaches to incorporation of components of the contact force into the equation of motion.