A general bi-Helmholtz nonlocal strain-gradient elasticity for wave propagation in nanoporous graded double-nanobeam systems on elastic substrate

In this paper, a general bi-Helmholtz nonlocal strain-gradient elasticity model is developed for wave dispersion analysis of porous double-nanobeam systems on elastic substrate. The present model incorporates three scale coefficients to examine wave dispersion relations much accurately. Porosity-dependent material properties of inhomogeneous nanobeams are defined via a modified power-law function. Based on Hamilton's principle, the governing equations of double-nanobeam system on elastic substrate are obtained. Solving analytically these equation gives wave frequencies and phase velocities as a function of wave number. It is demonstrated that phase velocities of a nanoporous double-nanobeam system rely on the porosities, material gradation, nonlocal parameters, strain gradient parameter, interlayer springs, elastic substrate and wave number.