利用常微分方程组理论在较一般条件下求出了线性有阻尼多自由度振动系统对任意外激励的精确响应。

Exact response of damped linear vibrating systems to arbitrarily excitation is obtained according to theory of ordinary differential equations.

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求解有阻尼多自由度结构系统的振动微分方程，实模态分析法是得到广泛应用的一种有效方法。

The dynamic response of the damping multi-DOF structural system is usually calculated by the real modal analysis method.

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并从实际出发，考虑砧下垫层的弹性作用及垫层和土壤的阻尼作用，建立了锻锤振动系统的双自由度有阻尼振动力学模型。

In the last part of this paragraph, a calculation model for forging hammer foundation vibration system with dual-freedom is presented.

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