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Abstract
Effect ofthermal gradient on the naturalfrequency, buckling load and dynamic stability ofa simply supported tapered beam under a pulsating axial load is investigaled by Jinite element method. A linear variation of the Young's modulus of the beam material, due to a sleady one-dimensional thermal gradient is assumed. It is observed that the naturalfrequency and the buckling load ofthe beam decrease with increase in thermal gradient and thermal gradient has a destabilizing effect on the beam
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References
- Beliaev, N.M., *Stability of Prismatic Rods Subjected to Variable Longitudinal Forces", Engg. Construct. Struct. Mech, l, pp. 149-167, 1924.
- Mettler, E., "Allgemeine Theory der Stabilitater zwungener schwingungen elastischer korper", Ing. Arch., 1 7, pp. 418-449, 1949.
- Lubkin, S. and Stoker, J.J., "Stability of Columns and Strings Under Periodically Varying Forces", Q. Appl. Math., l, pp. 216-236, 1943.
- Beilin, E.A. and Dzhanelidze, G., "Survey of Work on the Dynamic Stability of Elastic Systems", PMM, 16, pp. 635-648, 1952.
- Pipes, L.A., "Dynamic Stability of a Uniform Straight Column Excited by a Pulsating Load, J. Franklin lnsl., 277, pp. 534-551, 1964.
- Bolotin, V.V., The Dynamic Stability of Elastic Systems", Holden - Day, Ine., SanFrancisco,1964.
- Brown, J.E., Hutt, J.M. and Salama, A.E., "Finite Element Solution to Dynamic Stability of Bars", AIAA Journal, 6, 1423-1425, 1968.
- Ahuja, R. and Duffield, R.C., "Parametric Instability of Variable Cross-Section Beams Resting on an Elastic Foundation, J. Sound Vibration, 39, pp.159-174, 1975.
- Burney, S.Z.H. and Jaeger, L.G., "A Method of Determining the Regions of Instability of a Column by Numerical Method Approach", J. Sound Vibration, 15, pp. 75-91, 1971.
- Iwatsubo, T., Saigo, M. and Sugiyama, Y., "Parameteric Instability of Clamped-Clamped and Clamped Simply Supported Columns under Periodic Axial Load", J. Sound and Vibration, 3O, pp.65-7 7, 1973.
- Iwatsubo, T. Sugiyama, Y. and Ogrno, S., "Simple and Combination Resonances of Columns Under Periodic Axial Loads", J. Sound Vibration, 33,211221,1974.
- Datta, P.K. and Chakrabort5r, S., "Parametric Instability of Tapered Beams of Finite Element Method, J. Mech. Engg. Sciences, 24, pp.205-208, 1982.
- Abbas, B.A.H., "Dynamic Stability of a Rotating Timoshenko Beam with a Flexible Root", J. Sound Vibration, lO8, pp.25-32, I 986.
- Abbas, B.A.H., "Vibrations of Timoshenko Beams with Elastically Restrained Ends", J. Sound Vibration, 97,pp.541-548, 1984.
- Yokoyama, T., "Parametric Instability of Timoshenko Beams Resting on an Elastic Foundation", Computer Structure, 28, pp.207 -216, 1988.
- Wenchen, L. and Ming Ku, D., "Stability Analysis of a Timoshenko Beam Subjected to Distributed Follower Forces Using Finite Elements", Computer Structure, 41, 813-819, 1991.
- Datta, P.K. and Lal, M.K., "Parametric Instability of a Non-Prismatic bar with lolcalized Damage Subjected to an Intermediate Periodic Axial Load by Finite Element Method, Computer Structure, 43, pp.ll99-1202,1992.
- Tomar, J.S. and Jain, R., "Thermal Effects on Frequencies of Coupled Vibrations of Pretwisted Rotating Beam", AIAA Journal, 23, pp.1293-1296, 1985.
- Tomar, J.S. and Jain, R., "Effect of Thermal Gradient on Frequencies of Wedge Shaped Rotating beams", AIAA Journal, 22, pp. 848-850, 1984.
- Timoshenko, S.P. and Gere, J.M., "Theory of Elastic Stability", pp.l28-130, McGraw Hill Book Company, Second Edition.
References
Beliaev, N.M., *Stability of Prismatic Rods Subjected to Variable Longitudinal Forces", Engg. Construct. Struct. Mech, l, pp. 149-167, 1924.
Mettler, E., "Allgemeine Theory der Stabilitater zwungener schwingungen elastischer korper", Ing. Arch., 1 7, pp. 418-449, 1949.
Lubkin, S. and Stoker, J.J., "Stability of Columns and Strings Under Periodically Varying Forces", Q. Appl. Math., l, pp. 216-236, 1943.
Beilin, E.A. and Dzhanelidze, G., "Survey of Work on the Dynamic Stability of Elastic Systems", PMM, 16, pp. 635-648, 1952.
Pipes, L.A., "Dynamic Stability of a Uniform Straight Column Excited by a Pulsating Load, J. Franklin lnsl., 277, pp. 534-551, 1964.
Bolotin, V.V., The Dynamic Stability of Elastic Systems", Holden - Day, Ine., SanFrancisco,1964.
Brown, J.E., Hutt, J.M. and Salama, A.E., "Finite Element Solution to Dynamic Stability of Bars", AIAA Journal, 6, 1423-1425, 1968.
Ahuja, R. and Duffield, R.C., "Parametric Instability of Variable Cross-Section Beams Resting on an Elastic Foundation, J. Sound Vibration, 39, pp.159-174, 1975.
Burney, S.Z.H. and Jaeger, L.G., "A Method of Determining the Regions of Instability of a Column by Numerical Method Approach", J. Sound Vibration, 15, pp. 75-91, 1971.
Iwatsubo, T., Saigo, M. and Sugiyama, Y., "Parameteric Instability of Clamped-Clamped and Clamped Simply Supported Columns under Periodic Axial Load", J. Sound and Vibration, 3O, pp.65-7 7, 1973.
Iwatsubo, T. Sugiyama, Y. and Ogrno, S., "Simple and Combination Resonances of Columns Under Periodic Axial Loads", J. Sound Vibration, 33,211221,1974.
Datta, P.K. and Chakrabort5r, S., "Parametric Instability of Tapered Beams of Finite Element Method, J. Mech. Engg. Sciences, 24, pp.205-208, 1982.
Abbas, B.A.H., "Dynamic Stability of a Rotating Timoshenko Beam with a Flexible Root", J. Sound Vibration, lO8, pp.25-32, I 986.
Abbas, B.A.H., "Vibrations of Timoshenko Beams with Elastically Restrained Ends", J. Sound Vibration, 97,pp.541-548, 1984.
Yokoyama, T., "Parametric Instability of Timoshenko Beams Resting on an Elastic Foundation", Computer Structure, 28, pp.207 -216, 1988.
Wenchen, L. and Ming Ku, D., "Stability Analysis of a Timoshenko Beam Subjected to Distributed Follower Forces Using Finite Elements", Computer Structure, 41, 813-819, 1991.
Datta, P.K. and Lal, M.K., "Parametric Instability of a Non-Prismatic bar with lolcalized Damage Subjected to an Intermediate Periodic Axial Load by Finite Element Method, Computer Structure, 43, pp.ll99-1202,1992.
Tomar, J.S. and Jain, R., "Thermal Effects on Frequencies of Coupled Vibrations of Pretwisted Rotating Beam", AIAA Journal, 23, pp.1293-1296, 1985.
Tomar, J.S. and Jain, R., "Effect of Thermal Gradient on Frequencies of Wedge Shaped Rotating beams", AIAA Journal, 22, pp. 848-850, 1984.
Timoshenko, S.P. and Gere, J.M., "Theory of Elastic Stability", pp.l28-130, McGraw Hill Book Company, Second Edition.