# Natural frequencies of thin-walled curved beams

Ki Young Yoon, Nam Hoi Park, Young Joon Choi, Young Jong Kang

Research output: Contribution to journalArticle

17 Citations (Scopus)

### Abstract

New equations of motion governing dynamic behavior of thin-walled curved beams were investigated based on the study of Kang and Yoo [Thin-walled curved beams, I: formulation of nonlinear equations, J. Eng. Mech., ASCE 120 (10) (1994) 2072-2101; Thin-walled curved beams, II: analytical solutions for buckling of arches, J. Eng. Mech., ASCE 120 (10) (1994) 2102-2125]. Explicit numerical expressions were derived to predict the complex dynamic behavior of the thin-walled curve beams. Stiffness and mass matrix of the curved beam element for finite element analyses were formulated to allow explicit evaluation of the dynamic behavior. The formulations were conducted using not only typical six degree of freedom but also additional warping degree of freedom at each node. This paper proved the validity and the convergence of the presented formulation using the curved beam element. The paper included comparisons of the natural frequencies of the thin-walled curved beams from the finite element formulations with those from other researchers' study. The presented formulation and the new equations are sufficiently accurate for use in study and evaluation of curved architectural structures and bridges.

Original language English 1176-1186 11 Finite Elements in Analysis and Design 42 13 https://doi.org/10.1016/j.finel.2006.05.002 Published - 2006 Sep 1

### Fingerprint

Thin-walled Beam
Curved Beam
Natural Frequency
Natural frequencies
Formulation
Dynamic Behavior
Arches
Nonlinear equations
Equations of motion
Buckling
Degree of freedom
Stiffness
Finite Element
Warping
Arch
Evaluation
Complex Dynamics
Equations of Motion
Analytical Solution
Nonlinear Equations

### Keywords

• Equation of motion
• Free vibration
• Mass matrix
• Natural frequency
• Seven degree of freedom of curved beam element
• Variational method

### ASJC Scopus subject areas

• Computer Science Applications
• Computational Mechanics

### Cite this

Natural frequencies of thin-walled curved beams. / Yoon, Ki Young; Park, Nam Hoi; Choi, Young Joon; Kang, Young Jong.

In: Finite Elements in Analysis and Design, Vol. 42, No. 13, 01.09.2006, p. 1176-1186.

Research output: Contribution to journalArticle

Yoon, Ki Young ; Park, Nam Hoi ; Choi, Young Joon ; Kang, Young Jong. / Natural frequencies of thin-walled curved beams. In: Finite Elements in Analysis and Design. 2006 ; Vol. 42, No. 13. pp. 1176-1186.
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