Abstract
By introducing two physical parameters, the analysis of free in-plane vibrations of curved non-uniform beams is simplified. The explicit relations between the flexural displacement and the longitudinal displacement are derived. With these explicit relations, the two coupled governing differential equations are reduced to a complete sixth-order ordinary differential equation with variable coefficients in the longitudinal displacement, and a limiting study from the curved beam theory to the straight beam theory is successfully revealed. Finally, the influence of taper ratio, center angle and arc length on the first two natural frequencies of the beams is illustrated.
| Original language | English |
|---|---|
| Pages (from-to) | 173-189 |
| Number of pages | 17 |
| Journal | Acta Mechanica |
| Volume | 155 |
| Issue number | 3-4 |
| DOIs | |
| Publication status | Published - 2002 Jul 6 |
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All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Mechanical Engineering
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Free in-plane vibrations of curved nonuniform beams. / Lee, Sen-Yung; Hsiao, J. Y.
In: Acta Mechanica, Vol. 155, No. 3-4, 06.07.2002, p. 173-189.Research output: Contribution to journal › Article
TY - JOUR
T1 - Free in-plane vibrations of curved nonuniform beams
AU - Lee, Sen-Yung
AU - Hsiao, J. Y.
PY - 2002/7/6
Y1 - 2002/7/6
N2 - By introducing two physical parameters, the analysis of free in-plane vibrations of curved non-uniform beams is simplified. The explicit relations between the flexural displacement and the longitudinal displacement are derived. With these explicit relations, the two coupled governing differential equations are reduced to a complete sixth-order ordinary differential equation with variable coefficients in the longitudinal displacement, and a limiting study from the curved beam theory to the straight beam theory is successfully revealed. Finally, the influence of taper ratio, center angle and arc length on the first two natural frequencies of the beams is illustrated.
AB - By introducing two physical parameters, the analysis of free in-plane vibrations of curved non-uniform beams is simplified. The explicit relations between the flexural displacement and the longitudinal displacement are derived. With these explicit relations, the two coupled governing differential equations are reduced to a complete sixth-order ordinary differential equation with variable coefficients in the longitudinal displacement, and a limiting study from the curved beam theory to the straight beam theory is successfully revealed. Finally, the influence of taper ratio, center angle and arc length on the first two natural frequencies of the beams is illustrated.
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U2 - 10.1007/BF01176241
DO - 10.1007/BF01176241
M3 - Article
VL - 155
SP - 173
EP - 189
JO - Acta Mechanica
JF - Acta Mechanica
SN - 0001-5970
IS - 3-4
ER -