Open AccessON THE USE OF EXTENDED PLATE THEORIES OF VEKUA – AMOSOV TYPE FOR WAVE DISPERSION PROBLEMS
Author(s) -
Sergey I. Zhavoronok
Publication year - 2018
Publication title -
international journal for computational civil and structural engineering
Language(s) - English
Resource type - Journals
eISSN - 2588-0195
pISSN - 2587-9618
DOI - 10.22337/2587-9618-2018-14-1-36-48
Subject(s) - dimensionless quantity , formalism (music) , lagrangian , mathematics , mathematical analysis , boundary value problem , plate theory , dispersion (optics) , type (biology) , classical mechanics , mechanics , physics , quantum mechanics , art , musical , ecology , visual arts , biology
he extended plate theory of I.N. Vekua – A.A. Amosov type is constructed on the background of the dimensional reduction approach and the Lagrangian variational formalism of analytical dynamics. The proposed theory allows one to obtain the hierarchy of refined plate models of different orders and to satisfy the boundary conditions on plates’ faces exactly by introducing the corresponding constraint equations into the Lagrangian model of two-dimensional continuum. The normal wave dispersion in an elastic layer is considered, the convergence of the two-dimensional solutions to the exact one is studied for the locking phase frequencies, the dimensionless stress distributions across the thickness of a layer are shown.