STUDIES ON IN-PLANE DYNAMIC INSTABILITY OF VERTICALLY AND PARAMETRICALLY BASE MULTI-FREQUENCY EXCITED CIRCULAR ARCHES

Seismic wave, shock wave and the ambient vibration excitation may be transmitted to an arch through the base, resulting in the dynamic instability and the loss of bearing capacity of the arch. In order to deeply study the dynamic stability of the arch under a vertical base excitation, the energy equations of the in-plane dynamic stability of the circular arch under a vertical base excitation are established based on the energy method. The coupled governing equations of the in-plane radial and tangential vibration of the investigated arch are obtained by using Hamilton principle. The analytical solutions of the dynamic axial forces and the dynamic bending moments prior to the in-plane dynamic instability are solved. For decoupling the in-plane dynamic governing equation, it is assumed that the arch is incompressible. Using the Galerkin method, the in-plane second-order ordinary differential dynamic stability equations of the circular arch under a vertical base multi-frequency excitation are established. The analytical equations of critical excitation frequencies of the circular arch under a vertical base multi-frequency excitation are derived via the multi-scale method, and the dynamic instability regions for the simultaneous first-order antisymmetric parametric resonance and second-order symmetric resonance instability of the circular arch verified by FEA are determined accordingly. Furthermore, the influences of span ratio, slenderness ratio and central angle on the dynamic instability region are analyzed.