Engineering Transactions, 47, 2, pp. 155–171, 1999

Discrete-Continuous Models In Nonlinear Dynamic Investigations of Selected Physical Systems

A. Pielorz
Polish Academy of Sciences

The paper deals with dynamic investigations of nonlinear discrete-continuous models in which elastic elements are deformed torsionally, longitudinally or transversally, and the classical wave equation can be used for the description of their motion. The investigations focus on nonlinear vibrations of the discrete-continuous models with a local nonlinearity described by the polynomial of a third degree. The detailed analysis for a simple nonlinear discrete-continuous system is done. It is shown that amplitude jumps in the case of a hard characteristic and the escape phenomenon in the case of a soft characteristic can occur.
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A. PIELORZ, The use of one-dimensional waves in dynamic investigations of selected multimass mechanical systems and engineering structures [in Polish], Engng. Trans., 28, 469–486, 1980.

W. NADOLSKI and A. PIELORZ, Shear waves in buildings subject to seismic loading, Building and Environment, 16, 279–285, 1981.

W. NADOLSKI and A. PIELORZ, Dynamic investigation of the main journals of two-cylinder crankshaft with damping, Int. J. Mech. Sci., 25, 887–898, 1983.

W. NADOLSKI, Application of wave method in investigations of single gear transmission, Ingenieur-Archiv, 58, 329–338, 1988.

A. PIELORZ, Elastic waves in discrete-continuous mechanical systems [in Polish), Habilitation Thesis, Prace IPPT 21/1992.

T. SZOLC, Modelling of the crack mechanisms of internal combustion engines using torsional elastic waves [in Polish], Doctoral Thesis, Institute of Fundamental Technological Research, Warsaw 1985.

W. NADOLSKI, Dynamic investigations of loads on gear teeth in single gear transmission, Arch. Appl. Mech., 61, 523–531, 1991.

R. BOGACZ, T. SZOLC and H. IRRETIER, An Application of torsional wave analysis to turbogenerator rotor shaft response, J. of Vibration and Acoustics, 114, 149–153, 1992.

R. BOGACZ and T. SZOLC, On torsional elastic waves in the vehicle geared drive systems, Periodica Polytechnica Ser. Trans. Eng., 21, 37–53, 1993.

R. BOGACZ and T. SZOLC, Nonlinear torsional vibration analysis of the drive systems using one-dimensional elastic waves, Arch. Mech., 45, 65–75, 1993.

R. BOGACZ and T. SZOLC, On non-linear analysis of the geared drive systems by means of the wave method, J. Theor. Appl. Mech., 31, 1–10, 1993.

T. SZOLC and R. BOGACZ, An influence of gear teeth impacts on torsional vibrations of a discrete continuous model of the drive system, Proc. of the 4th IFToMM Rotordynamics Conference, Vibration Institute Ed., Chicago, 253–258, Sept. 1994.

A. PIELORZ, Dynamic analysis of a nonlinear discrete-continuous torsional system by means of wave method, ZAMM, 75, 691–698, 1995.

W. NADOLSKI, Influence of nonlinear stiffness of teeth on dynamic loads in gear transmissions, Meccanica, 31, 665–672, 1996.

A. PIELORZ, Nonlinear discrete-continuous models in dynamic investigations of plane truss members, Engng. Trans., 45, 133–152, 1997.

R. BOGACZ and T. SZOLC, Analysis of dynamic interaction between the continuous string and moving oscillator, Engng. Trans., 41, 361–380, 1993.

A. PIELORZ, Nonlinear discrete-continuous models in the analysis of low structures subject to kinematic excitations caused by transversal waves, J. Theor. Appl. Mech., 33, 979–999, 1998.

O. MAHRENHOLTZ and T. SZOLC, Experimental verification of the wave approach for the torsional vibration analysis, Proc. of the 4th Polish-German Workshop, Berlin 1995, "Dynamical Problems in Mechanical Systems", IPPT PAN, Warszawa, 209–220, 1996.

P. HAGEDORN, Non-linear oscillations, Clarendon Press, Oxford 1981.

W. SZEMPLIŃSKA-STUPNICKA, The behavior of nonlinear vibrating systems, Vol. I, II, Kluwer Academic Publishers, Dordrecht 1990.

H.B. STEWART, J.M.T. THOMPSON, Y. UEDA and A.N. LANSBURY, Optimal escape from potential wells – patterns of regular and chaotic bifurcation, Physica D, 85, 259–295, 1995.

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