CABAŃSKA - PŁACZKIEWICZ KATARZYNA

WSP, Institute of Technical,

Bydgoszcz

ul. Chodkiewicza 30

POLAND

METODA ROZWIĄZANIA ZAGADNIENIA DRGAŃ UKŁADU DWÓCH

BELEK Z TŁUMIENIEM

THE METHOD OF A SOLUTION OF A PROBLEM OF VIBRATION OF

THE SYSTEM OF TWO BEAMS WITH DAMPING

In this paper a method of solution of a problem of free vibration of system of two Bernoulli's - Eulera beams with the visco - elastic interlayer is presented (Fig.1), [1].

Fig.1. Dynamics model of system of two beams with the visco - elastic interlayer

The mathematical model is the coupled system of two differential equations, which

describing a phenomenon of the transverse vibration of beams, namely

(1)

After application of separation of variables in the ordinary differential equations (1) are obtained of the system of two ordinary differential equations, which describing forms of vibration in the following complex form:

(2)

and ordinary differential equations of motion

(3)

where:

(4)

In the elaboration this method are applied complex functions of real variable and some complex arbity. The boundary problem is solved by the different boundary conditions for two beams, where are obtained different the characteristic equations. In the paper [2] is solved this problem by alike boundary conditions for two beams. The orthogonality of complex forms of free vibrations are utilized for terminal of free vibration by arbitrary initial conditions.

REFERENCES

[1] Cabańska - Płaczkiewicz K.: Dynamics of system of two Bernoulli's - Eulera beams with the visco - elastic interlayer. The copy -book of Applied Mechanics, no 6, Śląsk University of Technology, Gliwice 1998.

[2] Oniszczuk Z.: Vibrations analysis of the compound continuous systems with elastic constrain. Rzeszów University of Technology, Rzeszów 1997.

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