Free vibration of structures with cubic non-linearity-remarks on amplitude equation and Rayleigh quotient

ON THE PERIOD OF LARGE AMPLITUDE FREE VI

ON THE PERIOD OF LARGE AMPLITUDE FREE VIBRATION OF CONSERVATIVE AUTONOMOUS OSCILLATORS WITH STATIC AND INERTIA TYPE CUBIC NON-LINEARITIES

✍ M.N. Hamdan; N.H. Shabaneh 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 376 KB

The concern of this paper is the large amplitude free vibration of strongly non-linear oscillators u¨+ mu + o1u 2 u¨+ o2uu˙2 + o2u 3 = 0, where m =1, 0, or -1, o1 and o2 are positive parameters which may be arbitrarily large, and u(t) may be of order unity. Approximate analytical solutions for the p