Symplectic analysis of dynamic properties of hexagonal honeycomb sandwich tubes with plateau borders

A new type of hexagonal honeycomb sandwich tube with plateau borders are introduced in this work and the Symplectic analysis with its high computational efficiency and high accuracy is applied to obtain the structural dynamic properties. The effects of material distribution (β) and relative density (ρ¯) on the dynamic properties of the structure are also studied. Based on the definition of the elastic constants and the homogenization method, the independent elastic constants are obtained. By introducing dual variables and applying the variational principle, the canonical equations of Hamiltonian system are constructed. The precise integration method and extended Wittrick-Williams algorithm are adopted to solve the canonical equations. The dispersion relations of sandwich tubes are obtained, and the effects of material distribution and relative density on the normalized frequencies of the sandwich tubes are investigated. The proposed homogenization method is verified by comparing with other researchers׳ works. Dispersion relations of the sandwich tubes are obtained. The material distribution parameter and the relative density have significant effects on the dynamic properties of the structures. This work expects to offer new opportunities for the optimal design of metallic honeycomb sandwich tubes and future applications in the engineering sector.