An analytical method for free vibration analysis of Timoshenko beam theory applied to cracked nanobeams using a nonlocal elasticity model

Free transverse vibration analysis of size dependent Timoshenko FG cracked nanobeams resting on elastic medium

“…They used molecular dynamics modeling and analyzed the effect of the cracks of nanowires. Investigating the flexural and longitudinal vibrations of cracked nanobeams was discussed in the base of the both nonlocal Timoshenko and nonlocal Euler-Bernoulli theories (Loya et al 2009;Torabi and Dastgerdi 2012;Hsu et al 2011). Hasheminejad et al (2011 were presented the transverse vibration of cracked Euler-Bernoulli nanobeams incorporating surface effects.…”

Non-linear dynamic response to simple harmonic excitation of a thin-walled beam with a breathing crack

“…And at the same time it is simple enough for extensive computational treatment, an essentially useful feature when damage diagnosis must be performed in real time. Most studies have focused on Bernoulli-Euler beams [5][6][7][8][9] and, to a lesser extent, on Timoshenko beams [10][11][12][13].…”

Semi-analytical solution for free transverse vibrations of Euler–Bernoulli nanobeams with manifold concentrated masses

“…A test was carried out by Loya [39] to calculate free transverse vibration of cracked nanobeam using a nonlocal elasticity theory. Recently, Torabi and Nafar Dastgerdi [40] proposed an analytical method for free vibration analysis of Timoshenko beam theory which can be applied to cracked nanobeams. They calculated the frequency parameters and the vibration modes of cracked nanobeams for variant crack positions, crack ratio and small scale effect parameters.…”