Семинар за механику, 5. март 2014.

• 03. Март, 2014
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Наредни састанак Семинара биће одржан у среду, 5. марта 2014, са почетком у 18 часова у сали 301ф, Математичког института САНУ.

Предавач: Катица Стевановић Хедрих, Mathematical Institute САНУ

Наслов предавања: ELEMENTS OF MATHEMATICAL PHENOMENOLOGY IN DYNAMICS OF MULTI-BODY SYSTEM WITH FRACTIONAL ORDER DISCRETE CONTINUUM LAYERS

Садржај: Dynamics of multi deformable, ideal linear elastic bodies (beams. plates, membranes, belts with corresponding same boundary conditions) coupled by standard light fractional order discrete continuum layers is considered by using Petrovic’s theory of elements of mathematical phenomenology. The sixth chapter of Petrovic’s theory contain phenomenological analogies, including the mathematical analogies and qualitative analogy. Starting with coupled fractional order differential equations along transversal displacements of the linear elastic beams, same boundary conditions, and coupled by fractional order discrete continuum layers, system of coupled ordinary fractional order differential equations along eigen time functions in which eigen amplitude functions is obtained. Independent eigen main fractional order modes and set of characteristic numbers of the corresponding eigen time functions corresponding to eigen amplitude function are obtained. Using Petrovic’s theory of mathematical analogy and qualitative analogy properties of eigen main fractional order modes and characteristic numbers of time functions of vibrations of multi-plates as well as multi-membranes coupled by fractional order discrete continuum layer are obtained. A energy analysis is presented and fractional order dissipation of system energy defined. By phenomenological mapping between the eigen main fractional modes of eigen time functions in one eigen amplitude form and eigen main fractional order modes of a fractional order chain dynamics and of a fractional order electrical chain are identified qualitative and mathematical analogies.