oa Stabilization of transverse vibrations of an inhomogeneous beam

References

1. Love AEH. A Treatise on the Mathematical Theory of Elasticity. New York, NY: Dover Publications 1927;
   [Google الباحث العلمي]
2. Timoshenko SP. History of Strength of Materials. New York, NY: Dover Publications 1953;
   [Google الباحث العلمي]
3. Benaroya H. Mechanical Vibration. Englewood Cliffs, NJ: Prentice Hall 1998;
   [Google الباحث العلمي]
4. Inman D. Engineering Vibration. Englewood Cliffs, NJ: Prentice Hall 1994;
   [Google الباحث العلمي]
5. Meirovitch L. Analytical Methods in Vibrations. New York, NY: Macmillan Publications 1967;
   [Google الباحث العلمي]
6. Meirovitch L. Elements of Vibration Analysis. New York, NY: McGraw-Hill Book Company 1986;
   [Google الباحث العلمي]
7. Meirovitch L. Principles and Techniques of Vibrations. Englewood Cliffs, NJ: Prentice Hall 1997;
   [Google الباحث العلمي]
8. Rao SS. Mechanical Vibrations. 3rd ed. Reading, MA: Addison-Wesley Publishing Company 1995;
   [Google الباحث العلمي]
9. Thomson W. Theory of Vibration with Applications. 4th ed. Englewood Cliffs, NJ: Prentice Hall 1993;
   [Google الباحث العلمي]
10. Lions JL. Exact controllability, stabilization and perturbations for distributed systems. SIAM Rev. 1988; 30:1:1–68
    [Google الباحث العلمي]
11. Ammari K, Tuesnak M. Stabilization of Bernoulli-Euler beams by means of a point feedback force. SIAM J Control Optim. 2000; 39:4:1160–1181
    [Google الباحث العلمي]
12. Liu K, Liu Z. Exponential decay of energy of the Euler-Bernoulli beam with locally distributed Kelvin-Voigt damping. SIAM J Control Optim. 1998; 36:3:1086–1098
    [Google الباحث العلمي]
13. Nagaya K. Method of control of flexible beams subjected to forced vibrations by use of inertia force cancellations. J Sound Vibr. 1995; 184:2:185–194
    [Google الباحث العلمي]
14. Rebarber R. Exponential stability of coupled beams with dissipative joints: a frequency domain approach. SIAM J Control Optim. 1995; 33:1:1–28
    [Google الباحث العلمي]
15. Chen G, Delfour MC, Krall AM, Payre G. Modeling, stabilization and control of serially connected beams. SIAM J Control Optim. 1987; 25:3:526–546
    [Google الباحث العلمي]
16. Chen G. Energy decay estimates and exact boundary-value controllability for the wave equation in a bounded domain. J Math Pures Appl. 1979; 9:58:249–273
    [Google الباحث العلمي]
17. Chen G. A note on the boundary stabilization of the wave equation. SIAM J Control Optim. 1981; 19:1:106–113
    [Google الباحث العلمي]
18. Lagnese JE. Note on boundary stabilization of wave equations. SIAM J Control Optim. 1988; 26:5:1250–1256
    [Google الباحث العلمي]
19. Lagnese J. Decay of solutions of wave equations in a bounded region with boundary dissipation. J Diff Eqns. 1983; 50:2:163–182
    [Google الباحث العلمي]
20. Komornik V. Rapid boundary stabilization of the wave equation. SIAM J Control Optim. 1991; 29:1:197–208
    [Google الباحث العلمي]
21. Komornik V, Zuazua E. A direct method for boundary stabilization of the wave equation. J Math Pures Appl. 1990; 69:1:33–54
    [Google الباحث العلمي]
22. Nandi PK, Gorain GC, Kar S. Uniform exponential stabilization for flexural vibrations of a solar panel. Appl Math. 2011; 02:06:661–665
    [Google الباحث العلمي]
23. Mitrinović DS, Pečarić JE, Fink AM. Inequalities Involving Functions and Their Integrals and Derivatives. Dordrecht, The Netherlands: Kluwer 1991;
    [Google الباحث العلمي]
24. Gorain GC. Exponential energy decay estimates for the solutions of n-dimensional Kirchhoff type wave equation. Appl Math Comput. 2006; 177:1:235–242
    [Google الباحث العلمي]
25. Gorain GC, Bose SK. Exact controllability and boundary stabilization of torsional vibrations of an internally damped flexible space structures. J Optim Theory Appl. 1998; 99:2:423–442
    [Google الباحث العلمي]