Multi-mode propagation and diffusion analysis using the three-dimensional second strain gradient elasticity

The multi-mode propagation and diffusion properties are crucial informations when studying complex waveguides. In this paper, firstly, the three-dimensional modeling of micro-sized structures is introduced by using second strain gradient theory. constitutive relation deduced while six quintic Hermite polynomial shape functions employed for displacement field. weak formulations including element stiffness mass matrices force vector calculated through Hamilton’s principle global dynamic matrix a unit cell assembled. Then, free wave characteristics analyzed solving eigenvalue problems within direct finite method framework. dispersion relations positive going waves considering size effects illustrated. Furthermore, higher order parameters on curves discussed forced responses with two boundary conditions expounded. Eventually, reflection transmission coefficients illustrated simple coupling conditions, respectively. analysis coupled waveguides equipped novel work. results show that proposed approach significant potential investigating structures.