Asymmetric solutions in large amplitude free periodic vibrations of plates

When the in-plane inertia is neglected, the equations of motion that represent free, large amplitude, periodic vibrations of perfect plates only contain cubic nonlinear terms. It is here shown that, unlike often assumed, these equations admit asymmetric solutions. For that purpose, the time domain equations of motion are mapped into the frequency domain by the harmonic balance method, keeping the constant term and the second harmonic in the truncated Fourier expansion of the transverse displacements. A test plate is analysed and a bifurcation due to a 1:2 internal resonance is found. This bifurcation results in a branch of solutions where the equilibrium position is not the flat one and where odd and even harmonics coexist.