复振型叠加方法合理振型数量的确定

Determination of reasonable mode number for complex modal superposition approach

针对适用于非经典阻尼体系的复振型叠加方法,基于理论推导,得到了评价振型贡献程度的复振型质量参与系数,并给出了两种等效的表达形式,可作为评估非经典阻尼系统所需振型数量的一种方法。同时,根据复振型退化为实振型的条件(即实部与虚部成比例关系),论证了实、复振型质量参与系数法的统一性。实、复振型质量参与系数基于相同的原理和假定,具有相同的物理意义,易于工程设计人员掌握和使用。采用典型的减隔震系统数值算例和安装黏滞阻尼器的9层钢结构Benchmark模型对复振型质量参与系数方法进行了验证,结果表明该方法能够有效估计所需振型数量。但是由于实、复振型质量参与系数法是基于基底剪力推导而得到,当用于评估加速度响应所需振型时,其数量往往偏小。

Based on theoretical derivation,complex modal mass participation ratio is gained,which can be applied to complex modal superposition approach for non-classical damping systems.In this paper two equivalent expressions of complex modal mass participation ratios are developed and both of them can be used to determine the reasonable mode number.In addition,the modal mass participation ratios of real and complex modes are unified according to the condition of complex modes degenerating to real modes(i.e.,the real part is proportional to the imaginary part).There is no further assumption involved in the new proposed modal mass participation ratio except those have been adopted in the real modal mass participation ratio and have the same physical meanings.Thus it is easy for design engineers to master and apply.A typical isolated and response controlled buildings and a nine-story steel benchmark model with viscous dampers are taken as numerical examples,to demonstrate the significant effectiveness of the complex modal mass participation ratio to evaluate reasonable mode number.It should be noted that the mode number determined by the modal mass participation ratio to evaluate the acceleration response is smaller than that required to reach acceptable accuracy level,since the modal mass participation ratio is derived based on the base shear.