Higher order mixture nonlocal gradient theory of wave propagation

The higher order mixture nonlocal gradient theory of elasticity is conceived via consistent unification of the higher order stress- and strain-driven mixture nonlocal elasticity and the higher order strain gradient theory. The integro-differential constitutive law is established applying an abstract variational approach and appropriately replaced with the equivalent differential condition subject to nonclassical boundary conditions. The introduced higher order elasticity theory provides, as special cases, a variety of generalized elasticity theories adopted in nanomechanics to assess size effects in continua with nanostructural features. The well-posed higher order mixture nonlocal gradient theory is elucidated and invoked to examine the flexural wave propagation. The closed-form wave propagation relation between the phase velocity and the wave number is analytically derived. The determined wave propagation response and ensuing results are compared and calibrated with the pertinent molecular dynamic simulations. The demonstrated results of the phase velocity of the flexural wave propagation detect new benchmarks for numerical analyses. The proposed higher order size-dependent elasticity approach can be profitably employed in rigorous analysis of pioneering nanotechnological devices.