Theoretical And Experimental Study On The Out-of-plane Stability Of Circular Arch Under Harmonic Foundation Excitation

In the field of civil engineering,arch has been playing an important role.Because of its beautiful shape and large bearing capacity,arch was mainly used in bridge field in the past.With the development of modern science and technology and the application of new materials,archs are more and more used in water conservancy engineering,mechanical engineering,aerospace engineering and other fields.However,It is well known that arch is prone to parametric resonance instability,which can lead to structural failure under periodic vibration of the foundation.However,its instability mechanism is still unclear.So,the theoretical and numerical study for the out-of-plane dynamic parametric resonance instability of the circular arch under periodic harmonic excitation is carried out in this paper.The main research contents are as follows:(1)The waveform analysis method is proposed to distinguish the forced vibration,forced resonance,transient virbration and parametric resonance of the arch.(2)A method for solving the unstable region of out-of-plane parametric resonance instability under the vertical harmonic periodic excitation of foundation is proposed.Based on Hamiltonian principle and considering the influence of damping,the energy balance equation for the out-of-plane instability of the circular arch is established,the equations for the out-of plane dynamic instability in the form of Mathieu-Hill are constructed,as well as the unstable region for the out-of-plane dynamic parametric resonance instability are obtained.(3)The excitation experiment of the circular arch under the basic periodic excitation is performed.Firstly,the damping ratio and natural frequency of vibration are obtained through the “tap method” for different rise-span ratio arch.Then,the critical frequency of out-of-plane instability for arch under vertical harmonic periodic excitation of foundation are determinedby the method of frequency sweep.Finally,the instability mode of out-of-plane parametric resonance and instability mechanism for circular arch are revealed.(4)The parameter analysis of the out-of-plane instability for the circular arch under the basic periodic excitation is carried out.The influence of foundation excitation force,structural damping ratio and rise-span ratio on the unstable region of out-of-plane dynamic instability for the circular arch are expounded,showing that:(1)The vibration amplitude of the circular arch increases with the increase of the excitation force.As the excitation frequency enters the unstable region,the vibration amplitude firstly increases exponentially and then linearly.After that,it decreases rapidly after moving out the unstable region;(2)With the decrease of the rise-span ratio,the natural frequency of the circular arch decreases,while the range width of the unstable domain increases.(3)With the increase of structural damping ratio,critical excitation force for parametric resonance instability increases consequently.