This study investigates nonlinear dynamics of a fixedfixed buckled beam with

1∶3

internal resonance in the first two symmetric modes subject to uniform base harmonic excitation. The Galerkin method is employed to discretize the governing equation

the traditional incremental harmonic balance (IHB) method with single time scale is used to track periodic responses of the buckled beam，and the Floquet theory is used to analyze stability and bifurcation of the solution. It is found that the antisymmetric modes can be excited with increasing the excitation amplitude due to

1∶3

internal resonance

continuously increasing the excitation amplitude

Hopf bifurcation occurs which leads to quasi-periodic motion whose spectrum contains uniformly spaced sidebands around integer multiples of excitation frequency with increasing the excitation amplitude. The IHB method with two timescales is used to investigate quasi-periodic motion

whose solutions are in good agreement with those from numerical integration using the fourth-order Runge-Kutta method.