Asymptotic estimations and convergence estimations of functional series describing unstationary vibrations of shells
DOI:
https://doi.org/10.15587/2313-8416.2015.39198Keywords:
shell theory, nonstationary solutions, asymptotic estimations, functional seriesAbstract
Properties of solution of non-stationary tasks are set for the systems of differential equations of shell theory. Solutions are built as decompositions to on own the forms of vibrations of shells. With the use of the got functional rows asymptotic estimations are set for the small and large (in relation to the basic period of vibrations of the system) intervals of time. The general estimations of convergence of functional series are received
References
Lerman, L. B. (2000). On solution of problems of dynamics of plates and shells with local structure heterogeneities. Int. Appl. Mechanics, 35 (10), 1014–1020.
Zarutsky, V. A., Lerman, L. B. (1999). The realization of modal superposition method in shell dynamic problems with constructive heterogeneities. Zeszyty naukove politchniki Rrzeszowskie, Nr. 174, Mechanica, z. 52, Problemy dynamiki konstrukcji: Rzeszow, 127–132.
Lerman, L. B. (2001). About some properties of solutions of non-classic Eigen value problem for vibrations’ shell equations. Bulletin of University of Kyiv, Series: Physics & Mathematics, Part 3, 52–56.
Lerman, L. B. (2000). On determination of stationary states for systems of thin-walled elements at propagation of harmonic disturbances. Acoustic bulletin, 3 (1), 61–72.
Lerman, L. B. (2000). On solution of problems of dynamics of thin-walled elements of construction with inhomogeneous dynamics boundary conditions. Int. Appl. Mechanics, 36 (8), 97–103.
Gus’, A. N. (Ed.) (1980). Methods of shell design. In five volumes. Kyiv: Nauk. Dumka.
Bazhenov, V. A., Dacshenko, L. V., Kolomiez, L. V. (2005). Numerical method in mechanics. Odessa: Standard, 563.
Slepyan, L. I. (1972). Nonsteady elastic waves. Lviv: Shipbuilding, 376.
Gylin, P. A. (2006). Applied Mechanics rudiments of shell theory. Saint-Petersburg: Leningrad Polytechnic, 166.
Altenbach, H., Veremeyev, V. A. (2001). On the shell theory on nanoscale with surface stresses. International Journal of Engineering Science, 49 (12), 1294–1301. doi: 10.1016/j.ijengsci.2011.03.011
Ergin, A., Ugurlu, B. (2009). Linear vibration analysis of cantilever plates partially submerged in fluid. Journal of Fluids and Structures, 17 (7), 927–939. doi: 10.1016/s0889-9746(03)00050-1
Moffal, S., He, L. (2005). On decoupled and fully-coupled methods for lade curved cylindrical plates with variable thickness. Journal of Fluids and Structures, 20, 217–234. doi: 10.1016/j.jfluidstructs.2004.10.012
Zabegaev, A. I. (2002). Dynamical model of composite shell construction for calculation loads in conditions of intensive shearing actions. First Utkin reading. Math. All-Russian scientific and technical conference Saint-Petersburg, 2, 138–140.
Ivanco, T. G., Keller, D. F. (2012). Investigations of ground-wind loads for launch vehicles. Journal of Spacecraft and Rockets, 49 (4), 574–585. doi: 10.2514/1.59457
Alijant, F., Amabili, M. (2014). Non-linear vibrations of shells: A literature review from 2003 to 2013. International Journal of Non-Linear Mechanics, 58 (2064), 233–257. doi: 10.1016/j.ijnonlinmec.2013.09.012
Qatu, M. S., Sullivan, R. W., Wang, W. (2010). Recent research advances of the dynamic analysis of composite shells: 2000-2009. Composite Structure, 93 (1), 14–31. doi: 10.1016/j.compstruct.2010.05.014
Abel, J. F., Cooke, J. R. (Eds.) (2008). Proceeding of the 6th International Conference on Computation of Shell and Spatial Structures IASS-IACM 2008: Spanning Nano to Mega. Cornell University, Ithaca, NY, USA.
Naimark, M. A. (1969). Linear differential operators. Moscow: Nauka, 528.
Berezansky, Yu. M. (1965). Expansion by eigenfunctions of self-adjoint operators. Kyiv: Nauk. Dumka, 779.
Levitan, B. M., Sargsyan, I. S. (1970). Introduction in spectral theory (self-adjoint ordinary differential operators). Moscow: Nauka, 671.
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