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On the parametric excitation of a dynamic system having multiple degrees of freedom. Further results on parametric excitation of a dynamic system. (English) Zbl 0127.30503
J. Appl. Mech. 30, 367-372 (1963); 32, 373-377 (1965).
Paper I: see scanned image.
Paper II. Summary: A dynamic system having multiple degrees of freedom and being under parametric excitation has been studied in paper I. However, the analysis given there necessitates certain restrictions on the distribution of the natural frequencies of the system. In this paper those restrictions are removed. The analysis presented here shows how to obtain a constant matrix whose eigenvalues determine the stability or instability of a system of ordinary differential equations with periodic coefficients at a given excitation frequency. The constant matrix is expressed entirely in terms of the given system parameters and the excitation frequency.
Reviewer: H. Göcke

MSC:
70K28 Parametric resonances for nonlinear problems in mechanics
34D99 Stability theory for ordinary differential equations
70K20 Stability for nonlinear problems in mechanics
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