Engineering Mechanics

Proceedings Vol. 14 (2008)

ENGINEERING MECHANICS 2008

Copyright © 2008 Institute of Thermomechanics, Academy of Sciences of the Czech Republic, v.v.i., Prague

 

Malenovský E., Pochylý F.
pages 150 - +20p., full text

This contribution is focused on the analysis of dynamic behavior of elastic body moving in liquid. In many technical applications this motion is with large displacements. Some technical applications can be vibration of blades or rotors in centrifugal pumps or water turbines. But on other hand presented approach has more general application. In general case dynamic behavior are the modal behavior, steady state response and nonstationary response. Because of are assumed the large displacements, this analysis is nonlinear and modal behavior depends on a parameters. There is very difficult or impossible to do this analysis using commercial programme systems. It is caused by limited number of boundary conditions for contact between body and liquid in these systems. In this contribution is presented the mathematical model of a new type of boundary conditions which allowed the modal analysis and computing the steady state response. In principle this analysis is if the frequency domain. It is necessary provided some testing, because this approach is new. For this case, the curvilinear co-ordinates were chosen. The Bézier body was chosen for the description of geometrical configuration and also for approximation the solution. MATLAB programme code was chosen for software processing. Nomenclature mij , bij , kij - elements of local matrices of mass, damping and stiffness, ui - i - base function (see appendix), S E - area of element with pressure lay - out, p,σ - vectors of pressure and viscous forces in the i direction, reached on surface unit, p - pressure, Π ij - nonreversible stress tensor, ni , n j - one - unitary vector of external normal line element with regard to liquid, f - function dependent on p and σ as a consequence of FEM, η1 - dynamic viscosity, ci - velocity, xi , z - coordinates, ql - time function for l th shape of vibration, vil - ith deformation parameter for l th shape of vibration, S , Γ1 , Γ2 , Γ3 - denotation of surfaces enclosing liquid volume, α il , α, α1 , α 2 - velocity functions, β1il , β 2il , β, β1 , β 2 , β 3 - pressure

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