A simple analytical method for in-plane and out-of-plane coupled vibration of curved panels (Vibration analysis as combination of straight and curved beam coupled structure)

Abstract

This paper presents an analytical method for in-plane and out-of-plane coupled vibration in thin curved panels. To treat such vibrations simply, a structure consisting of the combination of straight and curved beams is proposed and the connecting conditions of these beams are satisfied by means of artificial springs introduced at their joints. Firstly, the strain energy of the curved beam is derived based on a shell theory, and the validity is checked by comparing the modal characteristics with those obtained by beam theory. Then the straight and curved beam coupled system (SCBS) is introduced. The analytical procedure to derive the equation of motion of the SCBS is described in detail. Numerical result shows that the SCBS can successfully express the coupling effect between roof-floor relative vertical displacement and side panel’s lateral deformation. As some numerical examples, vibration responses for the different bending rigidities and loss factors in the SCBS are calculated. The influence of the loss factors in the curved beams is observed upon the vibration response of the floor section, particularly in the motion with large relative displacement between roof and floor.

Keywords

• elastic vibration
• curved beam
• coupled vibration
• energy method
• cylindrical shell