Free wave propagation in two-dimensional periodic beam grillage

Changwei Zhou (1) , Jean-Pierre Lainé (1) , Mohamed Ichchou (1) , Abdelmalek Zine (2)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes
2 MMCS - Modélisation mathématique, calcul scientifique

Two-dimensional periodic structures are widely applied in the engineering domain, such as the orthogonally rib-stiffened panels used in the fuselage of an aircraft or the cellular structures like honeycombs used in sandwich construction. The dynamic behaviour of these structures has drawn a lot of attention among researchers for the last decades. In this paper, A beam grillage is studied as a particular example of a two-dimensional periodic structure. A single unit cell is modelled by the finite element method and periodic structure theory is employed to study the whole beam grillage. The method is known as the Wave Finite Element method (WFEM), which is usually used to study the one-dimensional waveguide or two-dimensional homogeneous waveguide. This work has extended the WFEM to the two-dimensional periodic beam grillage to calculate the wave dispersion characteristics. It also extended the model reduction based on Craig-Bampton method in WFEM to two-dimensional periodic structures. The simulation has been validated by the theoretical result in the literature. It is also compared with the dispersion relation by using the Fourier transformation of the displacement field under harmonic excitation. The WFEM shows a good agreement with little computational cost. The fixed frequency dispersion relation deduced from WFEM is used to predict the direction of wave propagation and to investigate the existence of direction where waves cannot propagate in the beam grillage.

Domaines: Analyse numérique [math.NA]; Vibrations [physics.class-ph]; Vibrations [physics.class-ph]

Changwei Zhou, Jean-Pierre Lainé, Mohamed Ichchou, Abdelmalek Zine. Free wave propagation in two-dimensional periodic beam grillage. 21st International Congress on Sound and Vibration, Jul 2014, Beijing, China. ⟨hal-01054912⟩