Vibration analysis of beams with multi-layers of corrugations

• We propose a method for free vibration analysis of beams with multi-layers of corrugations.
• The corrugation is modeled as curved beam whereas the liner is as straight beam.
• The frequency equation is derived by assembling impedance of each structure segment.
• The accuracy of proposed method is validated using commercial software ANSYS.
• Influences of corrugation and layer number on the bending stiffness are investigated.

In this paper, an impedance method for the free vibration analysis of beams with multi-layers of corrugations is introduced. In particular, the vibration response of a beam with layers of corrugations is formulated using the impedance method. The corrugated beam is divided into two kinds of structural segments: one, the corrugation that is modeled as a curved beam and the other, the liner treated as a straight beam. The frequency equation is derived by assembling the impedance of each structure segment based on conditions of force equilibrium and velocity compatibility. The accuracy of the proposed modeling is accessed using numerical examples analyzed both with the proposed method and the finite element commercial software ANSYS. A good agreement between the results for the proposed method and those from ANSYS analysis is observed. Then the influences of the number of corrugated layers and the corrugation number in each layer on the beam bending stiffness are investigated.