Engineering Transactions, 46, 2, pp. 217–227, 1998
10.24423/engtrans.653.1998

Free Vibration of The System of Two Strings Coupled by a Viscoelastic Interlayer

K. Cabańska-Płaczkiewicz
Pedagogical University In Bydgoszcz
Poland

This paper introduces an analytical method of solving the free vibration problem for a continuous system of two strings coupled by a viscoelastic interlayer. The phenomenon of free vibration has been described using a homogenous system of conjugate partial differential equations. After separation of variables in the system of differential equations, the boundary problem has been solved and two complex sequences have been obtained: the sequence of frequency, and the sequence of modes of free vibration. Then, the property of orthogonality of complex modes of free vibration has been demonstrated. Based on complex eigenfunctions, the polyharmonic free vibration has been expanded into the complex Fourier series, coefficients of which have been determined for arbitrarily assumed initial conditions.
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

K. CABAŃSKA-PŁACZKIEWICZ, Dynamics of the system of two Bernoulli-Euler's beams with a viscoelastic interlayer, XXXVII Symposium of Model, in Mech., 7, Silesian Univ. of Tech., 49–54, Gliwice 1998.

K. CABAŃSKA-PŁACZKIEWICZ, Free vibration of the system of string-beam with a visco-elastic interlayer, Theor. Found, in Civil Engng., 6, Faculty of Civil Engng. Warsaw Univ. of Tech., 59–68, Warsaw 1998.

K. CABAŃSKA-PŁACZKIEWICZ, Free vibration of the system of two visco-elastic beams coupled by a viscoelastic interlayer, Qualifying Journal, Kiev 1998 (in rev.).

R. GUTOWSKI, The ordinary differential equations, WNT, Warsaw 1971.

S. KASPRZYK, Dynamics of the continuous system, Publ. of AHG, Krakow 1989.

J. NIZIOŁ, J. SNAMINA, Free vibration of the discrete-continuous system with damping, J. Theor. and Appl. Mech., 28, 1–2, 149–160, Warsaw 1990.

W. NOWACKI, The building dynamics, Arkady, Warsaw 1972.

W. NOWACKI, The building mechanics, Arkady, Warsaw 1976.

Z. ONISZCZUK, Vibration analysis of the compound continuous systems with elastic constraints, Publ. of the Rzeszow Univ. of Tech., Rzeszow 1997.

Z. OSIŃSKI, The theory of vibration, PWN, Warsaw 1978.

Z. OSIŃSKI, Damping of the mechanical vibration, PWN, Warsaw 1979.

W. SZCZEŚNIAK, The selection of problems of beams and shells subjecting the inertial moving load, Building Engineering, 125, Publ. of the Warsaw Univ. of Tech., Warsaw 1994.

W. SZCZEŚNIAK, The selection of railway problems, Building Engineering, 129, Publ. of the Warsaw Univ. of Tech., Warsaw 1995.

F. TSE, I. MORSE, R. HINKLE, Mechanical vibrations theory and applications, Allyn and Bacon, Boston 1978.




DOI: 10.24423/engtrans.653.1998