Abstract
UDC 539.3 We carried out a general analysis of the mixed systems of six equations of a Timoshenko-type theory of vibrations of plates in rectangular and polar coordinates. It is shown that these systems can be represented in the operator canonical (Hamiltonian) form with respect to the spatial coordinate under the appropriate choice of “canonical” variables and the operator Hamilton function. Some functionals for canonical systems are constructed. For a mixed Hamiltonian system, a reduced Hellinger–Reissner functional of the spatial coordinate in the rectangular coordinates is obtained. The variation of the functional yields six canonical equations.
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