Axial and torsional free vibrations of restrained single-walled boron nitride nanotube (swbnnt) embedded in an elastic medium via nonlocal strain gradient theory

Abstract

The effect of the surrounding elastic matrix on the axial and torsional vibrations of embedded single-walled boron nitride nanotube (SWBNNT) is studied in this work. The SWBNNT is modeled as a nanorod and the nonlocal strain gradient theory is utilized to derive the size-dependent equation of motion. Also, the surrounding elastic matrix is simulated by employing a one-parameter foundation model. Stokes' transformation method as an accurate and efficient mathematical tool in conjunction with the Fourier trigonometric series solution is utilized to discretize the equation of motion. These two mathematical methods create two different eigenvalue problems, which can solve any boundary conditions for torsional and axial vibrations. Calculated Eigen frequencies are validated with earlier works in the literature. The effects of the surrounded elastic matrix parameter together with the other deformable boundary coefficients and also the small scale parameter on the axial and torsional vibration frequencies are researched and some conclusions are outlined.