In the current work, the nonlinear vibration of an embedded double-walled carbon nanotube (DWCNT) aroused by nonlinear van der Waals (vdW) interaction forces from both surrounding medium and adjacent tubes is studied. Using both Euler–Bernoulli and Timoshenko beam models, the relation between deflection amplitudes and resonant frequencies of the DWCNT is derived through harmonic balance method....

In this paper we propose an optimal control design technique for a class of nonlinear and control non-affine equations. The dynamic equations of a flexible shaft supported by a pair of active magnetic bearings (AMBs) are used as the nonlinear control nonaffine equations. The basic model of the system will be a Timoshenko beam supported at the ends by magnetic frictionless bearings. The effectiv...

Collocation methods are popular in providing numerical approximations to complicated governing equations owing to their simplicity in implementation. However, point collocation methods have limitations regarding accuracy and have been modified upon with the application of B-spline approximations. The present study reports the stress and deformation behavior of shear deformable functionally grad...

In this paper, we present rapid boundary stabilization of a Timoshenko beam with anti-damping and anti-stiffness at the uncontrolled boundary, by using infinite-dimensional backstepping. We introduce Riemann transformation to map states into set coordinates that verify 1-D hyperbolic PIDE-ODE system. Then backstepping is applied obtain control law guaranteeing closed-loop stability origin in <i...