The main purposes of the present work are devoted to the investigation of the free axial vibration, as well as the time-dependent and forced axial vibration of a SWCNT subjected to a moving load. The governing equation is derived through using Hamilton's principle. Eringen’s nonlocal elasticity theory has been utilized to analyze the nonlocal behaviors of SWCNT. A Galerkin method based on a clo...

We present an existence theory based on minimization of the nonlocal energies appearing in peridynamics, which is a nonlocal continuum model in solid mechanics that avoids the use of deformation gradients. We employ the direct method of the calculus of variations in order to find minimizers of the energy of a deformation. Lower semicontinuity is proved under a weaker condition than convexity, w...

Nonlocal problems for hyperbolic equations of the first order describe the dynamic of population [1]–[3]. During the last thirty years the existence and uniqueness of the solution of nonlocal problems for the system of hyperbolic equations have been considered in a number of papers [4]–[8]. The authors assumed that the nonlinear functions satisfy the Lipschitz condition with respect to the unkn...

In this paper, the flow-induced vibration and flutter instability of cantilever carbon nanotubes conveying fluid and modeled as a thin-walled Timoshenko beam are investigated. Analytically nonlocal theory, transverse shear and rotary inertia effects are incorporated in this study. The governing equations and the boundary conditions are derived through Hamilton's principle. Numerical analysis is...

We prove that for compatible weakly nonlocal Hamiltonian and symplectic operators, hierarchies of infinitely many commuting local symmetries and conservation laws can be generated under some easily verified conditions no matter whether the generating Nijenhuis operators are weakly nonlocal or not. We construct a recursion operator of the two dimensional periodic Volterra chain from its Lax repr...