CAJ | 학술논문

依据薄板大幅振动的Von Karman方程的动态比拟，通过Galerkin法得到控制屈曲薄板振动的参数激励型非线性动力学模型．通过引入变换，证实了参数激励屈曲薄板振动系统为一带有平方和立方非线性的参数激励和外激励联合作用的系统．对该系统的摄动分析表明，系统具有出现 2倍超谐振动的参数域．研究了系统平方非线性因素对系统的调节作用，并运用仿真方法讨论了系统的2倍超谐振动及其对屈曲薄板振动性能的影响．对系统2倍超谐振动的试验研究证实了理论分析和数值仿真结果，并给出了系统2倍超谐振动的特征．
의거박판대폭진동적Von Karman방정적동태비의，통과Galerkin법득도공제굴곡박판 진동적삼수격려형비선성동역학모형．통과인입변환，증실료삼수격려굴곡박판진동계통위일대유 평방화립방비선성적삼수격려화외격려연합작용적계통．대해계통적섭동분석표명，계통구유출현 2배초해진동적삼수역．연구료계통평방비선성인소대계통적조절작용，병운용방진방법토론료계 통적2배초해진동급기대굴곡박판진동성능적영향．대계통2배초해진동적시험연구증실료이론 분석화수치방진결과，병급출료계통2배초해진동적특정．
Based on the dynamic analog of the Karman large-deflection equations, a nonlinear dynamic model of a buckled rectangular plate subjected to parametric excitation was proposed by the Galerkin discretization procedure. By introducing a mathematical transformation into the dynamic system of the buck led plate, it was proved that the normal mathematical expression of the dynamic system in the form of parametric and external excitation is incorporated with quadratic and cubic nonlinear terms. It was shown by perturbation analysis that the system has a parametric area in which 2-times superharmonic response takes place. The influence of the quadratic nonlinearities on dynamic responses of the system was investigated. The 2-times superharmonic resonance and its effect on the dynamic behaviors of the bucled plate were analyzed and discussed. Numerical results for the 2-times super-resonance obtained from perturbation solution were presented and compared with experimental results. The characteristic of the 2-time superresonance was given out by the experiment.