中文摘要：

粘滞阻尼器在工程中得到了日益广泛的应用,其出力存在分数指数律的非线性关系。工程中常用的阻尼指数为0.3~0.5,在此情况下,传统的非线性时程分析方法如Newmark积分及新近发展的KR-α方法等,均可能出现不稳定或数值脉冲现象,而经典的能量等效线性化方法则存在迭代求解及精度不高等问题。该文首次分析了该类粘滞阻尼器系统的刚性特征。在此基础上引入向后差分格式,并与耗能等效格式、Newmark积分格式和KR-α方法在精度、稳定性和计算效率等方面进行了对比分析。数值分析结果表明,向后差分法格式既能保证算法的稳定性、又具有足够的精度和效率。

英文摘要：

The fluid viscous dampers （FVDs） have received great appeals in engineering applications. Generally, the output force against the damper velocity is a nonlinear function in the form of fractional-power law. The usual damping exponent in practical applications is usually 0.3-0.5, within which the traditional time-integration methods for nonlinear analysis, such as the Newmark formula and the newly developed KR-α formula, etc., would suffer from instability and spurious numerical pulses; whereas the conventional energy-equivalence based formulas suffers from iteration and relatively low accuracy. In the present paper, the stiff properties of the viscously damped nonlinear systems are systematically analyzed. Then the backward difference formulas （BDFs） are introduced. The advantages of the BDFs over the above mentioned formulas are demonstrated through comparative studies. The accuracy, stability and efficiency of these formulas are examined. Numerical results reveal that the BDFs operate well in guaranteeing the stability of the algorithm, and in gaining high accuracy of solutions of stiff systems.