On the equations of the analytical dynamics of the quasi-3D plate theory of I. N. Vekua type and some their solutions

Journal of Vibroengineering

Sergey I. Zhavoronok¹  Lev N. Rabinskiy²  Ekaterina L. Kuznetsova²  Elena L. Kuznetsova² 

[1]Institute of Applied Mechanics of Russian Academy of Sciences, Moscow, Russia

[2]Moscow Aviation Institute, National Research University, Moscow, Russia

关键词: shells;    plates;    thin-walled waveguides;    analytical dynamics;    Lagrangian formalism;    normal waves;    phase and group velocities;   

DOI  :  10.21595/jve.2018.19366

来源: DOAJ

【 摘 要 】

The plate theory of Nth order is constructed on the background of the Lagrangian variational formalism of analytical dynamics of continuum systems and the dimensional reduction approach of I. N. Vekua – A. A. Amosov. The plate model is defined within the configuration space, the set of field variables, and the Lagrangian density. The field variables are determined by the coefficients of the biorthogonal expansion of the spatial displacement vector field with respect to the dimensionless normal coordinate. The dynamic equations are derived as Lagrange equations of the second kind of the two-dimensional continuum system. The dynamics of the plane elastic layer is considered as an example, the normal wave propagation is described on the basis of refined plate theories of various orders, and the convergence of approximate solutions to the exact solution of the three-dimensional elastodynamics problem is analyzed for different wavenumbers.

【 授权许可】

Unknown