Drgania Swobodne Układu z Nieliniowa Bezwładnością
The present considerations are generalized to the case of the bar having an initial curvature and a nonlinear elastic characteristic of the Duffing type. A first integral of the relevant differential equation is obtained by quadratures, thus enabling the representation of the motion in the phase plane.
For a study of the stability of vibration of a linearly elastic system with no initial deflection, the Lapunov function is obtained in an evident form. In the general case the stability is investigated on the basis of Lapunov's first method.
Numerical examples show the influence of a nonlinear inertion and an initial curvature on the (fundamental) natural frequency and the amplitude of lateral vibration of a bar having an additional mass at the end.
The equations obtained are characterized by considerable simplicity which enables convenient application to engineering problems.
W. J. CUNNINGHAM, Introduction to nonlinear analysis, New York-Toronto-London 1958
I.N. M'c DUFF, J.R. CURRERI, Vibration control, New York-Toronto-London 1958.
R. GRYBOŚ, Drgania poprzeczne pręta dwuprzegubowego z masą skupioną na końcu, Z.N. Pol.
S1. nr 72, Gliwice 1963.
N.J. HOFF, Buckling and stability, J. of the Royal Aeron. Soc., 58 (1954).
H. KAUDERER, Nichtlineare Mechanik, Berlin-Göttingen-Heidelberg 1958.
N. MINORSKY, Modern trends in nonlinear mechanics, Advances in Appl. Mech., 1 (1948).
J. LA SALLE, S. LEFSCHETZ, Stability by Liapunov's Direct Method with Applications, New York 1961.
S. TIMOSHENKO, Vibration Problems in Engineering, New York-Toronto-London 1955.