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Liu, C. H.

On coherent oscillations of a string. (English) Zbl 0283.34056

J. Franklin Inst. 294, 87-93 (1972).

MSC:

34F05 Ordinary differential equations and systems with randomness
70L05 Random vibrations in mechanics of particles and systems
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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References:

[1] Carrier, G. F., A note on the vibrating string, Quart. appl. Math., Vol. 7, 97-110 (1949) · Zbl 0033.03003
[2] McLachlan, N. W., Ordinary Non-linear Differential Equations (1950), Clarendon Press: Clarendon Press Oxford · Zbl 0037.18901
[3] Lubkin, S.; Stoker, J. J., Stability of columns and strings under periodically varying forces, Quart. appl. Math., Vol. 1, 215-242 (1943) · Zbl 0063.03669
[4] Carrier, G. F., Stochastically driven dynamical systems, J. Fluid Mech., Vol. 44, 249-264 (1970) · Zbl 0213.54903
[5] kryloff, N.; Bogoliuboff, N. N., Introduction to Nonlinear Mechanics (1943), Princeton University Press · JFM 63.1303.03
[6] Bourret, R. C., Propagation of randomly perturbed fields, Can. J. Phys., Vol. 40, 782-790 (1962) · Zbl 0111.39301
[7] Cole, J. D., Perturbation Methods in Applied Mathematics (1968), Blaisdell: Blaisdell Waltham, Mass · Zbl 0162.12602
[8] Frisch, U., Wave propagation in random media, (Bharucha-Reid, A. T., Probabilistic Methods in Applied Mathematics (1968), Academic Press: Academic Press New York) · Zbl 0727.76064
[9] Mendelson, K. S., Perturbation theory for damped nonlinear oscillations, J. Math. Phys., Vol. 11, 3413-3415 (1970) · Zbl 0211.12002
[10] Murty, I. S.N., A unified Krylov-Bogoliubov method for solving second order nonlinear systems, Int. J. non-linear Mech., Vol. 6, 45-53 (1971) · Zbl 0214.09601
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