Out-of-plane Free Vibration Analysis of Curved Timoshenko Beams by the Pseudospectral Method

다국어 초록 (Multilingual Abstract)

The pseudo spectral method is applied to the analysis of out-of-plane free vibration of circularly curved Timoshenko beams. The analysis is based on the Chebyshev polynomials and the basis functions are chosen to satisfy the boundary conditions. Natural frequencies are calculated for curved beams of circular cross sections under hinged-hinged, c1amped-clamped and hinged-clamped end conditions. The present method gives good accuracy with only a limited number of collocation points.

목차 (Table of Contents)

• ABSTRACT
• 1. Introduction
• 2. Pseudospectral Formulations
• 3. Numerical Examples
• 4. Conclusions
• Acknowledgement
• References
• Appendix: Constants of Function DKｋ(ξ)

참고문헌 (Reference)

1 "Vibration of Plane Curved Beams Journal of Sound and Vibration" 39 : 135-146, 1975.

2 "Vibration Analysis of Shear Deformable Circular Arches by the Differential Quadrature Method" 183 (183): 353-360, 1995.

3 "Natural Frequencies of Out-of-plane Vibration of Arcs Journal of Applied Mechanics Transactions of ASME" 49 : 910-913, 1982.

4 "Natural Frequencies of In-plane Vibration of Arcs Journal of Applied Mechanics Transactions of ASME" 50 : 449-452, 1983.

5 "Locking Free Curved Beam Element Based on Curvature International Journal for Numerical Methods in Engineering" 37 : 989-1007, 1994.

6 "Extensional Vibrations of Continuous Circular Curved Beams with Rotary Inertia and Shear Deformation I Journal of Sound and Vibration" 114 : 297-308, 1987.

7 "Exact Out-of-plane Natural Frequencies of Curved Timoshenko Beam" 125 (125): 1999.

8 "Exact Natural Frequencies for Out-of-plane Motion of Plane Structures Composed of Curved Beam Members" 55 (55): 989-995, 1995.

9 "Eigenvalue Analysis of Rectangular Mindlin Plates by Chebyshev Pseudospectral Method" 17 (17): 370-379, 2003.

10 "Eigenvalue Analysis of Axisymmetric Circular Mindlin Plates by Pseudospectral Method" 3 (3): 44-49, 2002.

11 "Dynamic Stiffness Analysis for In-plane Vibrations of Arches with Variable Curvature" 207 (207): 15-31, 1997.

12 "Curvature Base Beam Element for the Analysis of Timoshenko and Shear-Deformable Beam" 187 (187): 569-584, 1995.

13 "Constant Curvature Beam Finite Elements for In-plane Vibration Journal of Sound and Vibration" 25 : 561-576, 1972.

14 "An Isoparametric Quadratic Thick Curved Beam Element" 23 (23): 1583-1600, 1986.

15 "An Element for Studying the Vibration of Unrestrained Curved Timoshenko Beams Journal of Sound and Vibration" 158 : 387-404, 1992.

16 "A Computer Program for the free Vibration Analysis of Elastic Arcs" 62 (62): 475-485, 1997.