Trigonometric Series Approach for Forced Parametric Vibration Response
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摘要: 基于调制反馈方法,对参数周期与激励力周期不相同情况下,研究其参数系统受迫振动响应三角级数解.采用谐波的线性组合形式从数学上表达受迫振动响应解,然后通过运用谐波平衡,将参数振动方程转化成无限阶线性代数方程组,解出其谐波的系数.上述方法的特点在于:1) 用三角级数来表达振动受迫响应,十分便于参数振动的频域分析,剖析受迫响应性质;2) 从解的表达可直接推出组合谐波共振条件; 3) 采用标准的RungeKutta算法得到的相图证实上述方法结果的精确性.研究结果表明:该方法适用于参数振动完整受迫响应解的数学表达与分析.Abstract: Modulation feedback method was used to predict the forced response of a linear system that was governed by an ordinary differential equation with periodic coefficients. The system was excited by both periodic coefficients and external force terms that had different periods. In the method, the forced response is expressed as a special trigonometric series. By applying harmonic balance and limitation operation, all coefficients of the harmonic components in the forced response solution are fully approached. The investigation result shows that the new approach has an advantage in the complete and analytical solution of forced response and in the expression of nonlinear dynamic characteristics, and it is very significant for the theoretical research and engineering application in dealing with the problem of forced parametric vibration.
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Key words:
- parametric vibration /
- forced response /
- trigonometric series
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