Numerical Research Of Nonlinear Vibrations Of Isotropic Viscoelastic Plates With Variable Rigidity By The Method Of Computer Simulation
Abstract
In the given work the problem about vibrations of a isotropic viscoelastic plate with variable rigidity in geometrically nonlinear statement is considered. With the help of Bubnov-about nonlinear vibrations of viscoelastic isotropic plate in geometrically nonlinear statement on Kirchhoff-Love’s kinematic hypothesis, physical dependence between. Galerkin method the problem is reduced to the decision of system of nonlinear ordinary integro-differential equations of Volterra’s type. The numerical method based on the use of quadrature formulas is applied for the decision of the received system at weakly singular kernel of Koltunov- Rzhanitsin’s. Influences of viscoelastic properties of a material, geometrical characteristics, and also dependences.
References
Koltunov M.A. Creep and relaxation, Visshaya shkola,
Moscow, 1976.
Il’yushin A.A., Pobedrya B.E. Fundamentals of the
mathematical theory of thermoviscoelasticity, Nauka,
Moscow, 1970.
Volmir A.S. The nonlinear dynamics of plates and
shells, Nauka, Moscow, 1972.
Badalov F.B., Eshmatov Kh., Yusupov M. About some
methods of the decision of systems integro-differential
equations meeting in problems viscoelasticity. Soviet
Applied Mathematics and Mechanics [Translated from
Prikladnaya Matematika i Mekhanika], 1987; 51: 867–
Verlan A.F., Abdikarimov R.A., Eshmatov Kh.
Numerical simulation of nonlinear problems of
dynamics of viscoelastic systems with variable rigidity.
Electronic Modeling, 2010; 2(32): 3-13.
Copyright information
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (Creative Commons Attribution License 3.0 - CC BY 3.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
info@cbuni.cz, www.cbuni.cz, ojs.journals.cz
