CAJ | 학술논문

研究在拱受外激励作用下斜拉索拱结构中索拱之间1∶1内共振问题.当拱的某阶频率接近索的某阶频率时,可导致索拱之间出现1∶1内共振,利用已建立的斜拉索拱非线性动力学耦合面内运动微分方程,采用Galerkin方法把斜拉索拱的面内运动方程进行离散,然后利用多尺度法对离散的运动方程进行摄动得到拱主共振情况下的平均方程,研究在拱受到外激励作用下拱振动对索振动产生的影响,同时对斜拉索拱内共振时的稳定、分叉及混沌情况进行了分析.结果表明:拱受到外激励产生共振后,通过索拱之间的内共振容易激发对柔性索的振动,导致索出现较大的幅值.能量在索拱之间相互传递,原本静止的索也可能出现共振,共振频域区间内索拱振动将出现跳跃、分叉及混沌等复杂的非线性动力学行为.
연구재공수외격려작용하사랍색공결구중색공지간1∶1내공진문제.당공적모계빈솔접근색적모계빈솔시,가도치색공지간출현1∶1내공진,이용이건립적사랍색공비선성동역학우합면내운동미분방정,채용Galerkin방법파사랍색공적면내운동방정진행리산,연후이용다척도법대리산적운동방정진행섭동득도공주공진정황하적평균방정,연구재공수도외격려작용하공진동대색진동산생적영향,동시대사랍색공내공진시적은정、분차급혼돈정황진행료분석.결과표명:공수도외격려산생공진후,통과색공지간적내공진용역격발대유성색적진동,도치색출현교대적폭치.능량재색공지간상호전체,원본정지적색야가능출현공진,공진빈역구간내색공진동장출현도약、분차급혼돈등복잡적비선성동역학행위.
The internal resonance of cable-stayed arch under external excitation on arch with one-to-one internal resonance was investigated.The frequency of the cables and the frequency of the arch were studied, resulting in a one-to-one internal resonance, The coupling nonlinear dynamic equations of the cable-stayed arch derived by using Hamilton principle were used. First, the Galerkin method was used to discrete the nonlinear equation of planar motion. Then, the method of multiple scales was applied to perturb the discrete equations of motion, and the averaged equation under the primary resonances of arch was obtained. The impact of the vibration of the arch over the vibration of cables under external excitation on the arch was studied, and the equilibrium solution, the period solution and chaotic solution of averaging equations were examined. Numerical calculation results have shown that, after the resonance of the arch appears under the external excitation,the resonance of cables is easily excited through the internal resonance between cables and arch, resulting in a larger amplitude of cables. The energy is transferred between the cables and the arch, and the cable-stayed arch show complicated nonlinearity dynamic behavior, such as leap, bifurcation and chaos within the resonance frequency region.