Engineering Transactions, 51, 1, pp. 3–24, 2003

The Investigation of the Influence of a Local Elastic Nonlinearity on Vibrations of Plane Truss Members

A. Pielorz
Institute of Fundamental Technological Research, Polish Academy of Sciences
Poland

The paper concerns theoretical investigations of plane trusses subject to longitudinal de-formations, using nonlinear discrete-continuous models. An external excitation is applied to a rigid body located in a truss joint. In this joint a visco-elastic discrete element with a spring having a nonlinear symmetric stiffness is also located. It is assumed that the spring characteristic is of a soft type. Four nonlinear functions describing this characteristic are proposed. In the considerations the wave method is applied similarly to the case of a hard characteristic in [1]. The numerical analysis focus on the investigation of the effect of the local nonlinearity with a soft characteristic for two examples of plane trusses.
Keywords: nonlinear dynamics; discrete-continuous models; plane trusses
Full Text: PDF

References

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

J.M. GERE, W. WEAYER, Analysis of framed structures, D.Van Nostrand Company, Inc. New York 1965.

W. NADOLSKI, A. PIELORZ, The use of elastic waves in dynamic investigations of plane truss members, The Archive of Mechanical Engineering, 43, 105–123, 1996.

A. NIEMIERKO, On the trusses [in Polish], WKiŁ, Warsaw 1987.

CHR. BOILER, T. SEEGER, Materials data for cyclic loading, Parts A–E, Elsevier, New York 1987.

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

W. GUTKOWSKI, J. BAUER, Z. IWANÓW, Explicit formulation of Kuhn–Tucker necessary conditions in structural optimization, Computers and Structures, 37, 753–758, 1990.

U. BERNHARD, W. HAUGER, The propagation of waves in impact-loaded spatial trusses, Archive of Applied Mechanics, 63, 556–566, 1993.

T.P. DESMOND, Theoretical and experimental investigation of stress waves injunction of three bars, J. Applied Mechanics, 48, 148–154, 1981.

J.P. LEE, Elastic waves produced by longitudinal impact on system with symmetrically branched rods, Int. J. Solids Structures, 8, 699–707, 1972.

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

A. PIELORZ, Non-linear vibrations of a discrete-continuous torsional system with non-linearities having characteristic of a soft type, J. Sound and Vibration, 225(2), 375–389, 1999.




Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland