摘要
应用调制反馈模型给出了一个受迫参数系统响应解的完整数学表达,其响应解可表示为谐波线性组合的三角级数。通过谐波平衡、极限运算方法将响应中谐波分量的所有系数由级数表示,从而给出了一个完整的受迫响应表达,并构建了理论频谱。此外,还定量地确定了参数变量β与主共振频率左偏的关系、图示频率响应中因参数变量β引起的相位跃变等重要响应性质;对受迫响应的相图与标准的龙格-库塔法的结果进行了轨迹一致性比较。研究结果表明:参数振动响应解的三角级数表达在拓宽受迫响应和非线性动力学特性方面具有表达形式简单、分析便捷的优势,可为涉及受迫参数振动理论的研究和工程应用提供参考。
The forecasting model on modulation feedback is used to investigate a forced response of linear system that is governed by an ordinary differential equation with periodic coefficient. The system is excited by both periodic coefficient and external force with the same period. In the developed approach, the forced response is expressed as a linear combination of the harmonic terms. By the application of harmonic balance and limitation operation, all coefficients of harmonic components in the response solution fully approach to a set of series. This approach has been successfully verified by the comparison with the standard Runge-Kutta method. Meanwhile, some important response characteristics, such as the parameter index β effect on shift of main resonance frequency, the parametric index β causing additional phase delay in the frequency response, etc., are discussed through mathematical deduction and computation. Results obtained reveal that the developed approach has an advantage in the complete and analytical solution of forced response and nonlinear dynamic characteristics, and it is very significant for the theoretical research and engineering application concerning the problem of forced parametric vibration.
出处
《应用力学学报》
CAS
CSCD
北大核心
2013年第6期887-893,954,共7页
Chinese Journal of Applied Mechanics
关键词
参数振动
受迫响应
非线性动力学响应
频率响应特性
parametric vibration,forced response,nonlinear dynamic behavior,frequency response characteristic
