Geodesic
Modified spline collocation method in the problems of thin rectangular viscoelastic plate vibrations
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 3, pp. 59-64 
P. F. Nedorezov; O. M. Romakina; R. A. Safonov. Modified spline collocation method in the problems of thin rectangular viscoelastic plate vibrations. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 3, pp. 59-64. http://geodesic.mathdoc.fr/item/ISU_2010_10_3_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Numerical method for evaluation of critical frequencies during steady-state bending vibrations of viscoelastic plate is presented. The solution is based on applying modified spline collocation method for lowering the problem's dimension and numerical solving of the obtained problem via discrete orthogonalization method. The application of this approach with different boundary conditions is examined in detail.

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[2] Nedorezov P. F., “Ustanovivshiesya poperechnye kolebaniya vyazkouprugoi plastinki s dvumya sharnirno opertymi storonami”, Mekhanika deformiruemykh sred: mezhvuz. nauch. sb., 8, Izd-vo Sarat. un-ta, Saratov, 1983, 114–125

[3] Nedorezov P. F., “Metod splain-kollokatsii v zadache o vibratsionnom izgibe vyazkouprugoi plastinki pri slozhnom zakreplenii kraev”, Mat. modelirovanie i kraevye zadachi, Tr. shestoi mezhvuz. nauch. konf., ch. 1, SamGTU, Samara, 1996, 64–66

[4] Nedorezov P. F., Primenenie V-splainov v zadache opredeleniya NDS pri ustanovivshikhsya kolebaniyakh pryamougolnoi plastinki iz vyazkouprugogo matepiala, Dep. v VINITI 1093-V97, Sapat. gos. un-t, Saratov, 1997, 12 pp.

[5] Nedorezov P. F., Shevtsova Yu. V., Romakina O. M., “Modifitsirovannyi metod splain-kollokatsii v zadachakh izgiba pryamougolnykh plastinok”, Trudy Vtoroi Vserossiiskoi nauchnoi konferentsii (1–3 iyunya 2005 g.), Chast 1, Matem. modelirovanie i kraev. zadachi, Matematicheskie modeli mekhaniki, prochnost i nadezhnost konstruktsii, SamGTU, Samara, 2005, 203–209

[6] Zavyalov Yu. S., Kvasov Yu. I., Miroshnichenko I. L., Metody splain-funktsii, Nauka, M., 1980, 352 pp. | MR