Dynamic of Civil Engineering and Transport Structures and by Kamila Kotrasova, Jozef Melcer

By Kamila Kotrasova, Jozef Melcer

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1 2πx  2πy   1 − cos . w0 ( x, y ) = 1 − cos 4 l x  l y  (3) The meaning of remaining symbols is as follows: D slab stiffness [Nm2/m], K modulus of foundation [Nm-3], µ mass intensity [kgm-2], ωb angular frequency of damping [rad/s], p(x,y,t) is the intensity of the dynamic load. In the case of moving vehicles the discrete load due to the tire forces Fj(t) must be transformed on continuous load by the procedure proposed by Dirac [3] Applied Mechanics and Materials Vol. 617 p(x, y, t ) = ∑ ε j Fj (t )δ (x − x j )δ ( y − y j ) , 25 (4) j p ( x, y , t ) = ∑ j   1 m 2πx  n 2πy ∑∑ p (t ) 4 1 − cos l 1 − cos l  , ∞ ∞ mn , j m =1 n =1  x  y (5)  where 1 m2πx  n 2πy    ( ) ( ) ε F ( t ) δ x − x δ y − y 1 − cos 1 − cos dxdy = j j j j ∫0 ∫0 4  l x  l y  m2πx j  n 2πy j  4 1 .

The interesting dependence is obtained in the case of logarithmic scaling of axes X and Y as it is shown on the Fig. 2. The picture of functional dependence f(1) versus C1 is the straight line. Applied Mechanics and Materials Vol. 617 51 Winkler model 2000 j = 20 1800 1600 j = 15 1400 f(j) [Hz] 1200 1000 j = 10 800 600 j=5 400 j=1 200 0 0 1 2 3 4 5 6 C1 [N/m3] 7 8 9 10 9 x 10 Fig. 1 Natural frequencies f(j) versus C1, Winkler foundation Winkler model 4 10 j = 20 j = 15 3 10 j = 10 log f(j) [Hz] j=5 2 10 j=1 1 10 0 10 5 10 6 10 7 8 10 10 log C1 [N/m3] 9 10 10 10 Fig.

There is also possibility to write a short program for leading of this procedure. Acknowledgements This contribution is the result of the research supported by GA MŠVVaŠ SR VEGA, grant N° 1/0259/12. References [1] O. Sucharda, J. Brožovský, Failure and Plasticity Conditions of Concrete in the Finite Element Analysis. Applied Mechanics and Materials. 367 (2013) 165-168. [2] Adina Theory and Modeling Guide. M. Alani, D. Beckett, Mechanical Properties of a Large Scale Synthetic Fibre Reinforced Concrete Ground Slab, Construction and Building Materials.

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