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ARTICLE

Exact Solutions and Mode Transition for Out-of-Plane Vibrations of Nonuniform Beams with Variable Curvature

Sen-Yung Lee1, Shueei-Muh Lin2,3, Kai-Ping Chang1

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, Re-public of China
Mechanical Engineering Department, Kun Shan University, Tainan, Taiwan 710-03, Republic ofChina
Corresponding author E-mail: smlin45@gmail.com

Computers, Materials & Continua 2016, 51(1), 1-19. https://doi.org/10.3970/cmc.2016.051.001

Abstract

The two coupled governing differential equations for the out-of-plane vibrations of non-uniform beams with variable curvature are derived via the Hamilton's principle. These equations are expressed in terms of flexural and torsional displacements simultaneously. In this study, the analytical method is proposed. Firstly, two physical parameters are introduced to simplify the analysis. One derives the explicit relations between the flexural and the torsional displacements which can also be used to reduce the difficulty in experimental measurements. Based on the relation, the two governing characteristic differential equations with variable coefficients can be uncoupled into a sixth-order ordinary differential equation in terms of the flexural displacement only. When the material and geometric properties of the beam are in arbitrary polynomial forms, the exact solutions with regard to the outof- plane vibrations of non-uniform beams with variable curvature can be obtained by the recurrence formula. In addition, the mode transition mechanism is revealed and the influence of several parameters on the vibration of the non-uniform beam with variable curvature is explored.

Keywords

APA Style
Lee, S., Lin, S., Chang, K. (2016). Exact solutions and mode transition for out-of-plane vibrations of nonuniform beams with variable curvature. Computers, Materials & Continua, 51(1), 1-19. https://doi.org/10.3970/cmc.2016.051.001
Vancouver Style
Lee S, Lin S, Chang K. Exact solutions and mode transition for out-of-plane vibrations of nonuniform beams with variable curvature. Comput Mater Contin. 2016;51(1):1-19 https://doi.org/10.3970/cmc.2016.051.001
IEEE Style
S. Lee, S. Lin, and K. Chang "Exact Solutions and Mode Transition for Out-of-Plane Vibrations of Nonuniform Beams with Variable Curvature," Comput. Mater. Contin., vol. 51, no. 1, pp. 1-19. 2016. https://doi.org/10.3970/cmc.2016.051.001

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