High mode natural frequencies of nanobeam: nonlocal two-variable refined theory, differential quadrature method and molecular dynamics simulation

In this paper the free vibration of nanobeam based on nonlocal two-variable refined theory is investigated. The theory takes into account the effects of small scale and the quadratic variation of the transverse shear stains through the thickness of the nanobeam and hence, it does not require the use of shear correction factors. The equations of motions and the related boundary conditions are derived based on the nonlocal differential constitutive relations of Eringen in conjunction with the refined theory via Hamilton’s principle. For the differential governing equations solution in various supported boundary conditions, differential quadrature method (DQM) used along the longitudinal and Influences of nonlocal parameter, length to thickness ratio on the three mode of nanobeam non-dimensional natural frequencies with various boundary conditions are studied as well. Finally, mechanical properties of pristine single walled carbon nanotube (SWCNT) and defective SWCNT containing Stone Wales, vacancy, and Adatom defects were determined using MD simulations and were used to obtain SWCNT natural frequencies. Results indicate that increasing the length to thickness ratio causes the natural frequency to increase and the frequency parameter decrease by increasing the nonlocal parameter. In addition, Stone Wales and vacancy defects have large effects on SWCNT natural frequencies.

کلیدواژه ها:

Free Vibration ، High mode Natural frequency ، Two variable theory ، Differential quadrature method ، Molecular dynamics simulation.