258
6 Free Vibration of Multiple Degrees of Freedom System
6.25 Determine the natural frequencies of lumped mass system by Myklestad’s
method.
References
1. E.C. Pestel and E.A. Leckie, Matrix Methods in Elasto-mechanics, McGraw Hill, 1963
2. A.K. Chopra, Dynamics of Structures, Prentice-Hall of India Pvt. Ltd., New Delhi, 1995
3. A. Jennings, Eigenvalue methods for vibration analysis, Shock and Vibration Digest, V.12, No.
2, 1980, pp. 3–16.
4. H. Rutihauser, Deflection der Bandmatrizen, ZAMP, V.10, 1959, pp. 314–319.
5. G.W. Stewart, The economical storage of plane rotations, Numerical Mathematics, V. 25, 1976,
pp. 137–138.
6. R.H. Anderson, Fundamentals of Vibrations, McMillan Co., New York, 1967.
7. N.Y. Myklestad, Vibration Analysis, McGraw Hill, New York, 1965.
8. G.L. Rogers, Dynamics of Framed Structures, John Wiley, 1959.
9. K.J. Bathe and E.L. Wilson, Large eigenvalue problem in dynamic analysis, Journal of
Engineering Mechanics Division, ASCE, V.98, 1972, pp. 1471–1485.
10. K.J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, 1996.
11. K.J. Bathe and E.L. Wilson, Solution methods for eigenvalue problems in structural mechanics,
International Journal for Numerical Methods in Engineering, V.6, 1973, pp. 213–226.
12. R.B. Corr and A. Jennings, A simultaneous iteration algorithm for symmetric eigenvalue problems, International Journal for Numerical Methods in Engineering, V.10, 1976,
pp. 657–663.
13. R.J. Guyan, Reduction of stiffness and mass matrices, AIAA Journal, V.3, No.2, Feb, 1965,
p-380.
14. B.M. Irons, Structural eigenvalue problems: elimination of unwanted variables, AIAA Journal,
V.3, No.5, 1965, pp. 961–962.
15. W.C. Hurty, Vibrations of structural systems by component mode synthesis, Journal of
Engineering Mechanics Division, ASCE, V.86, August 1960, pp. 57–69.
16. S.N. Hou, Review of modal synthesis techniques and a new approach, Shock and Vibration
Bulletin, Vol.40, No.4, 1965, pp. 25–39.
17. R.D. Henshell and J.H.Ong, Automatic masters of eigenvalue economisation, International
Journal for Earthquake Engineering and Structural Dynamics, V.3, 1975, pp. 375–383.
18. V.N.Sha and R.Raymund, Analytical selection of masters for reduced eigenvalue problem,
International Journal for Numerical Methods in Engineering, V.18, 1982, pp. 89–98.
6 Free Vibration of Multiple Degrees of Freedom System
6.25 Determine the natural frequencies of lumped mass system by Myklestad’s
method.
References
1. E.C. Pestel and E.A. Leckie, Matrix Methods in Elasto-mechanics, McGraw Hill, 1963
2. A.K. Chopra, Dynamics of Structures, Prentice-Hall of India Pvt. Ltd., New Delhi, 1995
3. A. Jennings, Eigenvalue methods for vibration analysis, Shock and Vibration Digest, V.12, No.
2, 1980, pp. 3–16.
4. H. Rutihauser, Deflection der Bandmatrizen, ZAMP, V.10, 1959, pp. 314–319.
5. G.W. Stewart, The economical storage of plane rotations, Numerical Mathematics, V. 25, 1976,
pp. 137–138.
6. R.H. Anderson, Fundamentals of Vibrations, McMillan Co., New York, 1967.
7. N.Y. Myklestad, Vibration Analysis, McGraw Hill, New York, 1965.
8. G.L. Rogers, Dynamics of Framed Structures, John Wiley, 1959.
9. K.J. Bathe and E.L. Wilson, Large eigenvalue problem in dynamic analysis, Journal of
Engineering Mechanics Division, ASCE, V.98, 1972, pp. 1471–1485.
10. K.J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, 1996.
11. K.J. Bathe and E.L. Wilson, Solution methods for eigenvalue problems in structural mechanics,
International Journal for Numerical Methods in Engineering, V.6, 1973, pp. 213–226.
12. R.B. Corr and A. Jennings, A simultaneous iteration algorithm for symmetric eigenvalue problems, International Journal for Numerical Methods in Engineering, V.10, 1976,
pp. 657–663.
13. R.J. Guyan, Reduction of stiffness and mass matrices, AIAA Journal, V.3, No.2, Feb, 1965,
p-380.
14. B.M. Irons, Structural eigenvalue problems: elimination of unwanted variables, AIAA Journal,
V.3, No.5, 1965, pp. 961–962.
15. W.C. Hurty, Vibrations of structural systems by component mode synthesis, Journal of
Engineering Mechanics Division, ASCE, V.86, August 1960, pp. 57–69.
16. S.N. Hou, Review of modal synthesis techniques and a new approach, Shock and Vibration
Bulletin, Vol.40, No.4, 1965, pp. 25–39.
17. R.D. Henshell and J.H.Ong, Automatic masters of eigenvalue economisation, International
Journal for Earthquake Engineering and Structural Dynamics, V.3, 1975, pp. 375–383.
18. V.N.Sha and R.Raymund, Analytical selection of masters for reduced eigenvalue problem,
International Journal for Numerical Methods in Engineering, V.18, 1982, pp. 89–98.