Wave propagation analysis for a second strain gradient rod theory

Wave transmission and reflection analysis through complex media based on the second strain gradient theory

“…Wave propagation in complex rod has been studied by Zhu et al [19] by employing SSG theory-based rod model. Assuming Young's modulus of rod 2 is E 2 , mass density ρ 2 and circular cross-section area A = πr 2 .…”

“…The research of Li et Wei [17,18] shows the reflection and transmission coefficients at the interface of two dipolar gradient media are dependent on the microstructure parameters along with the incident angular frequency. Mention can also be made of the study proposed by Zhu et al in 2019 [19], the proposed generalized theory-based rod model predicts that extra evanescent waves are generated along with the dispersive longitudinal wave, and these evanescent waves have a great impact on wave diffusion at a discontinuity between non-local media.…”

“…How the introduction of the SSG theory-based inserts in a classical theory (CT) based elastic waveguide affects wave conversion and for which benefits are the main focus of this paper. SSG theory-based Timoshenko beam model has been established by Asghari et al [23], and SSG theory-based rod model by Zhu et al [19] with Hamilton principle to exploit the structural free-vibration behaviors and wave propagation features. The resulting non-classical wave dispersion relations are employed in the present paper to investigate the wave reflection and transmission properties through a non-classical coupling region with the transfer matrix method (TMM).…”

Dynamic analysis of second strain gradient elasticity through a wave finite element approach

“…Micro-structures have been widely investigated for their dynamic behaviors [1,2,3]. For example, nano-sized Phononic Crystals (PCs) are studied because of their properties for manipulating acoustic and elastic waves.…”

“…This result was embedded into the formulation of SSG theory as a direct expression of the material surface characteristics. For the continuum model, the well known Hamiltonian principle [3] is the most general method for calculating the governing equations as well as determining the associated boundary conditions.…”