Study on In-plane Vibration Instability of Circular Arches Under Vertical Base Excitation
Based on the energy principle,this paper establishes an energy equation for the in-plane dynamic stability of a circular arch subjec-ted to vertical base excitation.By applying Hamilton's principle,a coupled system of governing equations describing the radial and tangential vibrations of the arch surface is derived.Furthermore,using the multiple scales method,an analytical expression for the dynamic instability re-gion of the circular arch under simultaneous first-order antisymmetric parametric resonance and second-order symmetric resonance conditions is obtained.Additionally,the paper delves into the specific impacts of the arch's central angle and damping decay rate on the dynamic instability region.To validate the accuracy of the theoretical analysis,finite element simulation analysis is conducted,which not only confirms the validity of the theoretical solutions but also reveals the underlying mechanism of in-plane dynamic instability in circular arches.
Vertical base excitationCircular archDynanic instability regionVibration instability
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