In-Plane Transient Responses of Arch with Variable Curvature Using Dynamic Stiffness Method
Publication: Journal of Engineering Mechanics
Volume 124, Issue 8
Abstract
A procedure combining the dynamic stiffness method with the Laplace transform is proposed to obtain accurate transient responses of an arch with variable curvature. The dynamic stiffness matrix and equivalent nodal force vector for an arch with variable curvature subjected to distributed loading are explicitly formulated based on a series solution. The effects of shear deformation, rotary inertia, and damping are considered. As examples, the accurate transient responses of a parabolic and a semielliptic arch subjected to either point loading or base excitation are given. The effects of the shapes of the arches and the phase-shift in the multiple input for base excitation are also discussed.
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References
1.
Benedetti, A., Deseri, L., and Tralli, A.(1996). “Simple and effective equilibrium models for vibration analysis of curved rods.”J. Engrg. Mech., ASCE, 122(4), 291–299.
2.
Beskos, D. E., and Narayanan, G. V.(1983). “Dynamic response of frameworks by numerical Laplace transform.”Comp. Method in Appl. Mech. and Engrg., 37(3), 289–307.
3.
Chidamparam, P., and Leissa, A. W.(1993). “Vibrations of planar curved beams, rings, and arches.”Appl. Mech. Rev., 46(9), 467–483.
4.
Durbin, F.(1974). “Numerical inversion of Laplace transforms: An efficient improvement to Dubner and Abate's method.”Comp. J., 17(4), 371–376.
5.
Huang, C. S., Teng, T. J., and Leissa, A. W.(1996). “An accurate solution for the in-plane transient response of a circular arch.”J. Sound and Vibration, 196(5), 595–609.
6.
Laura, P. A. A., and Maurizi, M. J.(1987). “Recent research on vibrations of arch-type structures.”Shock and Vibration Digest, 19(1), 6–9.
7.
Lee, B. K., and Wilson, J. F.(1989). “Free vibrations of arches with variable curvature.”J. Sound and Vibration, 136(1), 75–89.
8.
Manolis, G. D., and Beskos, D. E.(1982). “Dynamic response of framed underground structures.”Comp. and Struct., 15(5), 521–531.
9.
Markus, S., and Nanasi, T.(1981). “Vibration of curved beams.”Shock and Vibration Digest, 13(4), 3–14.
10.
Narayanan, G. V., and Beskos, D. E.(1982a). “Numerical operational methods for time-dependent linear problems.”Int. J. Numer. Methods in Engrg., 18(12), 1829–1854.
11.
Narayanan, G. V., and Beskos, D. E.(1982b). “Dynamic soil-structure interaction by numerical Laplace transform.”Engrg. Struct., 4(1), 53–62.
12.
Romanelli, E., and Laura, P. A. A.(1972). “Fundamental frequencies of non-circular, elastic, hinged arcs.”J. Sound and Vibration, 24(1), 17–22.
13.
Suzuki, K.(1985). “In-plane impulse response of a curved bar with varying cross-section.”Bull. Japanese Soc. of Mech. Engr., 28(240), 1181–1187.
14.
Suzuki, K., and Takahashi, S.(1979). “In-plane vibrations of curved bars considering shear deformation and rotatory inertia.”Bull. Japanese Soc. of Mech. Engr., 22(171), 1284–1292.
15.
Suzuki, K., Takahashi, S., and Ishiyama, H.(1978). “In-plane vibrations of curved bars.”Bull. Japanese Soc. of Mech. Engr., 21(154), 618–627.
16.
Takahashi, S., Suzuki, K., Fukazawa, K., and Nakamachi, K.(1977). “In-plane vibrations of elliptic arc bar and sinus curve bar.”Bull. Japanese Soc. of Mech. Engr., 20(148), 1236–1243.
17.
Thakkar, S. K., and Arya, A. S. (1973). “Dynamic response of arches under seismic forces.”Proc., 5th World Conf. on Earthquake Engrg., Vol. 1, Int. Assoc. for Earthquake Engrg., Rome, Italy, 952–956.
18.
Tseng, Y. P., Huang, C. S., and Lin, C. R.(1997). “Dynamic stiffness analysis for in-plane vibrations of arches with variable curvature.”J. Sound and Vibrations, 207(1), 15–31.
19.
Volterra, E., and Morell, D.(1961). “Lowest natural frequencies of elastic hinged arcs.”J. Acoustical Soc. of Am., 33(12), 1787–1790.
20.
Wang, T. M.(1972). “Lowest natural frequency of clamped parabolic arcs.”J. Struct. Div., ASCE, 98(1), 407–411.
21.
Wang, T. M.(1975). “Effect of variable curvature on fundamental frequency of clamped parabolic arcs.”J. Sound and Vibration, 41(2), 247–251.
22.
Whittaker, E. T., and Watson, G. N. (1965). A course of modern analysis, 4th Ed., Cambridge Univ. Press, London.
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Copyright © 1998 American Society of Civil Engineers.
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Published online: Aug 1, 1998
Published in print: Aug 1998
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