Analysis of stability for parametric resonance of circular deep arch considering influence of shear deformation
ZHAO Hong-jin1; LIU Chao1 2; DONG Ning-juan3; WU Min-zhe1
1. School of Civil Engineering, Xi’an University of Architecture& Technology, Xi’an,710055, China ; 2. School of Science, Xi’an University of Architecture & Technology, Xi’an,710055, China; 3. Aircraft Strength Research Institute of China, Xi’an,710065, China
Abstract：Based on the theory of elastic stability of structure, the total potential energy of circular deep arch for unknown variables with displacement was obtained according to energy method, dynamic stability differential equation of circular deep arch subject to under distributing radial periodic load was established through applying the energy method and Hamilton principle. Galerkin’s method was used to convert the partial differential equations into the ordinary differential Mathieu equations, so as to deduce the critical frequency equations of primary parameter resonance of deep arch, and then dynamic instability regions surrounded by periodic solutions were obtained. Dynamic stability problems of parametric vibration was discussed about circular deep arch，through analyzing the influences of shear deformation, radius of circle and central angle etc. on the dynamic stabilities, which provides reference basis for dynamic analysis and design in structure engineering.
2012, Vol. 31 
