The free longitudinal vibration of tapered nanowires is investigated in the context of nonlocal continuum theory. The problem is studied for the nanowires with linearly varied radii under fixed–fixed and fixed–free boundary conditions. In order to assess the problem in a more general form, a perturbation technique is proposed based on the Fredholm alternative theorem. The natural frequencies, corresponding mode shapes, and phase velocities of the tapered nanowires are derived analytically up to the second-order perturbation for different boundary conditions. The predicted results by the perturbation technique are successfully verified with those of the exact solution. The obtained results reveal that the proposed methodology is a capable one in capturing the free longitudinal dynamic response of tapered nanowires with different boundary conditions. However, the differences of the results of the perturbation technique and those of the exact solution increase with the rate of radii change. In a special case, the obtained results are also compared with those of other researchers and a reasonably good agreement is achieved. It is also observed that for higher values of the small scale effect parameter, the variation of the rate of radii change has a more effect on the variation of the natural frequencies and phase velocities, irrespective of the boundary conditions of the tapered nanowire. Additionally, a scrutiny of the presented dispersion curves indicates that for a constant wavenumber, the value of the phase velocity decreases with the small scale effect parameter, particularly for higher wavenumbers.
Kiani, K. (2019). Free longitudinal vibration of tapered nanowires in the context of nonlocal continuum theory via a perturbation technique. Afribary. Retrieved from https://afribary.com/works/free-longitudinal-vibration-of-tapered-nanowires-in-the-context-of-nonlocal-continuum-theory-via-a-perturbation-technique
Kiani, Keivan "Free longitudinal vibration of tapered nanowires in the context of nonlocal continuum theory via a perturbation technique" Afribary. Afribary, 01 Jul. 2019, https://afribary.com/works/free-longitudinal-vibration-of-tapered-nanowires-in-the-context-of-nonlocal-continuum-theory-via-a-perturbation-technique. Accessed 09 Nov. 2024.
Kiani, Keivan . "Free longitudinal vibration of tapered nanowires in the context of nonlocal continuum theory via a perturbation technique". Afribary, Afribary, 01 Jul. 2019. Web. 09 Nov. 2024. < https://afribary.com/works/free-longitudinal-vibration-of-tapered-nanowires-in-the-context-of-nonlocal-continuum-theory-via-a-perturbation-technique >.
Kiani, Keivan . "Free longitudinal vibration of tapered nanowires in the context of nonlocal continuum theory via a perturbation technique" Afribary (2019). Accessed November 09, 2024. https://afribary.com/works/free-longitudinal-vibration-of-tapered-nanowires-in-the-context-of-nonlocal-continuum-theory-via-a-perturbation-technique