In this paper, we implement a new approach coupled with the iteration method. This procedure is obtained by combining He’s frequency-amplitude formulation and He’s energy balance method into a new iteration procedur...In this paper, we implement a new approach coupled with the iteration method. This procedure is obtained by combining He’s frequency-amplitude formulation and He’s energy balance method into a new iteration procedure such that excellent approximate analytical solutions, valid for small as well as large values of amplitude, can be determined for nonlinear oscillators. This study has clarified the motion equation of nonlinear oscillators by the iteration method to obtain the relationship between amplitude and angular frequency. We compare the approximate periods obtained by our procedure with the numerical solution and with other methods like energy balance method and variational iteration method. The results show that the approximations are of extreme accuracy.展开更多
为了研究RLC电路弹簧耦合系统的非线性振动,用统一的能量法考虑机电耦合系统的电场能、磁场能和机械能,应用拉格朗日-麦克斯韦方程建立起一个受到简谐激励的RLC电路弹簧耦合系统的数学模型,该机电耦合系统具有平方非线性。根据线性振动...为了研究RLC电路弹簧耦合系统的非线性振动,用统一的能量法考虑机电耦合系统的电场能、磁场能和机械能,应用拉格朗日-麦克斯韦方程建立起一个受到简谐激励的RLC电路弹簧耦合系统的数学模型,该机电耦合系统具有平方非线性。根据线性振动理论对系统运动微分方程组进行分析,得到了一个受简谐激励的M ath ieu方程,通过积分变换,得到了M ath ieu方程的级数形式解。分别用龙格库塔法和级数法计算了在无外激励的情况下,有阻尼和无阻尼时系统分别对应的时间响应,通过M atlab软件进行模拟分析,发现二者得到的响应曲线吻合,证明了级数法对分析类似系统是个很有效的手段。展开更多
文摘In this paper, we implement a new approach coupled with the iteration method. This procedure is obtained by combining He’s frequency-amplitude formulation and He’s energy balance method into a new iteration procedure such that excellent approximate analytical solutions, valid for small as well as large values of amplitude, can be determined for nonlinear oscillators. This study has clarified the motion equation of nonlinear oscillators by the iteration method to obtain the relationship between amplitude and angular frequency. We compare the approximate periods obtained by our procedure with the numerical solution and with other methods like energy balance method and variational iteration method. The results show that the approximations are of extreme accuracy.
文摘为了研究RLC电路弹簧耦合系统的非线性振动,用统一的能量法考虑机电耦合系统的电场能、磁场能和机械能,应用拉格朗日-麦克斯韦方程建立起一个受到简谐激励的RLC电路弹簧耦合系统的数学模型,该机电耦合系统具有平方非线性。根据线性振动理论对系统运动微分方程组进行分析,得到了一个受简谐激励的M ath ieu方程,通过积分变换,得到了M ath ieu方程的级数形式解。分别用龙格库塔法和级数法计算了在无外激励的情况下,有阻尼和无阻尼时系统分别对应的时间响应,通过M atlab软件进行模拟分析,发现二者得到的响应曲线吻合,证明了级数法对分析类似系统是个很有效的手段。
