Internal resonances in geometrically nonlinear forced vibrations of laminated circular cylindrical shells are investigated by using the Amabili– Reddy higher-order shear deformation theory. A harmonic force excitation is applied in radial direction and simply supported boundary conditions are assumed. The equations of motion are obtained by using an energy approach based on Lagrange equations that retain dissipation. Numerical results are obtained by using the pseudo-arc length continuation method and bifurcation analysis. A one-to-one-to-two internal resonance is identified, giving rise to pitchfork and Neimark–Sacher bifurcations of the non-linear response. A threshold level in the excitation has been observed in order to activate the internal resonance.
Internal resonances in non-linear vibrations of a laminated circular cylindrical shell / M. Amabili. - In: NONLINEAR DYNAMICS. - ISSN 0924-090X. - 69(2012), pp. 755-770. [10.1007/s11071-011-0302-1]