Straight-Beam Approach for Vibration Analysis of Horizontal Curved Beams

Abstract

This paper investigates the use of straight-beam elements to simulate the vibration of curved beams that is mathematically more challenging. First, analytical solutions of the out-of-plane and in-plane dynamic responses of the curved beam are derived for reference. Then, for the straight beam approach, the elastic stiffness matrix, consistent mass matrix, consistent nodal loads, and transformation matrix are derived and included in a procedure for computing the dynamic responses of the curved beam. The effectiveness of the straight beam approach in analyzing the free vibration and forced vibration (induced by moving vehicle) of the curved beam is validated, with the results compared with the theoretical solutions and those by Abaqus. It can be concluded that the straight beam approach is a simple and efficient means for analyzing the out-of-plane and in-plane vibrations of curved beams with high precision.