We study the initial-value problem for a general class of nonlinear nonlocal wave equations arising in one-dimensional nonlocal elasticity. The model involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We show that some well-known examples of nonlinear wave equations, such as Boussinesq-type equations, follow from the present model for...

In this paper, the bending behaviour of small-scale Bernoulli–Euler beams is investigated by Eringen’s two-phase local/nonlocal theory elasticity. Bending moments are expressed in terms elastic curvatures a convex combination local and nonlocal contributions, that with non-negative scalar coefficients summing to unity. The contribution convolution integral curvature field suitable averaging ker...

This study presents a generalized multiscale nonlocal elasticity theory that leverages distributed order fractional calculus to accurately capture coexisting and effects within macroscopic continuum. The behavior is captured via constitutive relations derived from thermodynamic formulation. governing equations of the inhomogeneous continuum are obtained Hamilton principle. As generalization con...

The paper is concerned with comparative analysis of differential and integral formulations for boundary value problems in nonlocal elasticity. For the sake simplicity, focus on an antiplane problem a half-space prescribed shear stress along surface. In addition, 1D exponential kernel depending vertical coordinate considered. First, surface loading form travelling harmonic wave studied. This pro...

Abstract. The dynamic stability problem is solved for onedimensional structures subjected to time-dependent deterministic or stochastic axial forces. The stability analysis of structures under time-dependent forces strongly depends on dissipation energy. The simplest model of viscous damping with constant coefficient was commonly assumed in previous papers despite the fact that there are other ...

Hardy’s non-locality theorem for multiple two-level systems is explored in the context of generalized nonlocal theory. We find nonlocal but non-signaling probabilities, providing Hardy’s nonlocal argument, which are higher than those in Quantum Mechanics. Maximum probability of success of Hardy’s argument is obtained for three two-level systems in quantum as well as in a more generalized theory...

In this paper, an analysis of free vibration in functionally graded nanoplate is presented. Third-order shear deformation plate theory is used to reach more accuracy in results. Small-scale effects are investigated using Eringen`s nonlocal theory. The governing equations of motion are obtained by Hamilton`s principle. It is assumed that the properties of nanoplates vary through their thicknesse...