The dynamic stiffness matrix of a uniform isotropic beam element based on trigonometric shear deformation theory is developed in this paper. The theoretical expressions for the dynamic stiffness matrix elements are found directly, in an exact sense, by solving the governing differential equations of motion that describe the deformations of the beam element according to the trigonometric shear deformation theory, which include the sinusoidal variation of the axial displacement over the cross section of the beam. The application of the dynamic stiffness matrix to calculate the natural frequencies and normal mode shapes of two rectangular beams is discussed. The numerical results obtained are compared to the available solutions wherever possible and validate the accuracy and efficiency of the present approach.
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February 2008
Research Papers
Dynamic Stiffness Analysis of a Beam Based on Trigonometric Shear Deformation Theory
Jun Li,
Jun Li
Vibration, Shock & Noise Institute,
e-mail: LJY60023@yahoo.com
Shanghai Jiao Tong University
, 800 Dongchuan Road, Shanghai 200240, People’s Republic of China
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Hongxing Hua,
Hongxing Hua
Vibration, Shock & Noise Institute,
Shanghai Jiao Tong University
, 800 Dongchuan Road, Shanghai 200240, People’s Republic of China
Search for other works by this author on:
Rongying Shen
Rongying Shen
Vibration, Shock & Noise Institute,
Shanghai Jiao Tong University
, 800 Dongchuan Road, Shanghai 200240, People’s Republic of China
Search for other works by this author on:
Jun Li
Vibration, Shock & Noise Institute,
Shanghai Jiao Tong University
, 800 Dongchuan Road, Shanghai 200240, People’s Republic of Chinae-mail: LJY60023@yahoo.com
Hongxing Hua
Vibration, Shock & Noise Institute,
Shanghai Jiao Tong University
, 800 Dongchuan Road, Shanghai 200240, People’s Republic of China
Rongying Shen
Vibration, Shock & Noise Institute,
Shanghai Jiao Tong University
, 800 Dongchuan Road, Shanghai 200240, People’s Republic of ChinaJ. Vib. Acoust. Feb 2008, 130(1): 011004 (7 pages)
Published Online: November 12, 2007
Article history
Received:
March 13, 2006
Revised:
July 20, 2007
Published:
November 12, 2007
Citation
Li, J., Hua, H., and Shen, R. (November 12, 2007). "Dynamic Stiffness Analysis of a Beam Based on Trigonometric Shear Deformation Theory." ASME. J. Vib. Acoust. February 2008; 130(1): 011004. https://doi.org/10.1115/1.2775513
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