While a train passing through a bridge made up of thin-walled steel members, the local vibrations of the members cause structural noises and fatigue failure at the joined parts. Such kind of dynamic behaviour is treated as instability problem of local vibration under periodic axial thrust and bending moment in our present research. Higher order finite strip method and harmonic balance method has been applied. We have known that periodic axial thrust creates main unstable regions of the simple parametric resonance, periodic bending moment creates main unstable regions of the combination resonance and these two kinds of force acting together creates both of the unstable regions.
