CAJ | 학술논문

为研究Winkler地基上材料非线性矩形薄板受简谐激励的非线性振动,应用弹性力学理论建立其动力学方程,并由Galerkin方法将其转化为非线性振动方程.应用非线性振动的多尺度法求得系统1/3次亚谐共振的近似解,并进行数值计算.分析激励、几何参数、阻尼系数、非线性参数对共振响应曲线的影响.
위연구Winkler지기상재료비선성구형박판수간해격려적비선성진동,응용탄성역학이론건립기동역학방정,병유Galerkin방법장기전화위비선성진동방정.응용비선성진동적다척도법구득계통1/3차아해공진적근사해,병진행수치계산.분석격려、궤하삼수、조니계수、비선성삼수대공진향응곡선적영향.
Based on the elastic theory,nonlinear dynamical equations of externally excited thin rectangular plate on Winkler foundation considering nonlinearity were established in order to study the nonlinear vibration. Then the corresponding nonlinear vibration equation was obtained by Galerkin's method. By means of the method of multiple scales for nonlinear vibration, the first approximate solution of 1/3 subharmonic resonance of the system was obtained, and numerical analysis of the influence of excitation, geometry parameter, damping, and nonlinearity parameter on the system were carried out.