Study On In-plane Parametric Dynamic Instability Of GFRP Circular Arch Under Vertical Periodic Excitation Of Foundation

Glass Fiber-Reinforced Polymer is widely used in bridge engineering due to its high specific strength and design ability.At present,more than 20 GFRP arch bridges have been built and put into service.The arch is mainly under pressure,and there is potential risk of dynamic destabilization under dynamic loads such as earthquake,impact or wave.Therefore,it is necessary to study the dynamic stability of GFRP arch.In-plane parameter dynamic instability of GFRP circular arch under vertical periodic excitation is studied for the first time in this paper.The main research contents are as follows:(1)Derivation of dynamic instability region of GFRP circular arch in plane under vertical periodic excitation.According to the energy method and Hamilton principle,the in-plane dynamic equilibrium differential equation of GFRP circular arch is established.The second-order ordinary differential Mathieu-Hill parametric vibration equation of circular arch is obtained by Galerkin method,the critical excitation frequency of in-plane dynamic instability is solved,and the in-plane dynamic instability region of GFRP circular arch is determined.(2)Fabrication of GFRP arch and testing of its properties.According to the relevant specifications,three groups of test specimens with laying angles of 0 degrees,±45 degrees and 90 degrees were processed.The material constants such as elastic modulus and Poisson ratio were measured by tensile test and shear test.In addition,18 GFRP test circular archs with different ratio of rise to span,different inclined angle layers and different combination of layers were designed and fabricated.(3)In-plane dynamic stability test of GFRP circular arc arch under vertical periodic excitation of foundation.Dynamic characteristics of GFRP circular arches with different laying angles,different laying modes and different ratios of rise to span were tested.First,the natural frequency and damping ratio of GFRP arch with different design parameters are obtained.Then,the upper and lower boundary values in the unstable area of GFRP circular arch under vertical periodic excitation are measured by means of reciprocating sweep frequency.The experimental results show that the inplane parametric resonance instability of GFRP circular arch occurs when the frequency of vertical periodic excitation of foundation is close to twice the natural frequency of GFRP circular arch.(4)Numerical analysis of dynamic stability in GFRP circular arch under vertical periodic excitation of foundation.ANSYS 15.0 is used to establish the finite element numerical analysis model of GFRP circular arch and carry out numerical simulation.The corresponding natural frequency and in-plane dynamic instability region are obtained.The validity of the experimental data is verified by comparing with the experimental data.(5)Analysis of in-plane dynamic stability parameters of GFRP circular arch under vertical periodic excitation of foundation.The effects of rise-span ratio,ply angle and ply mode on the natural frequency,damping ratio and dynamic instability region of GFRP arch are investigated.It is found that with the increase of the bedding angle,the natural frequency of GFRP circular arch decreases gradually,the damping ratio increases gradually,and the dynamic instability region moves towards the low frequency direction gradually.