惯容减震系统性能成本控制解析设计方法

Performance-cost design method of inerter system based on closed-form formulae

惯容减震系统是具备惯性与耗能增效特性的结构吸振减震装置。惯容的增效特性可能会产生较大的惯性控制力,导致实际应用时制造安装成本较高。为此,针对现有惯容减震系统设计时的成本控制考虑不足及计算繁琐问题,以结构性能、成本(控制力)同时作为直接的设计控制目标,从随机响应角度推导简洁实用的参数设计公式。在惯容减震单自由度结构随机振动响应解析解的基础上,研究结构响应和控制力的变化规律,发现其性能优化和成本优化的平衡点。根据响应极值条件,推导了白噪声激励下惯容减震系统考虑“性能-成本”控制原则的关键参数计算公式。通过算例设计分析,验证了设计公式的正确性和设计过程的简便性,且采用文中所推导解析公式进行惯容减震系统设计,可在保证性能需求的同时,避免过大的控制成本;公式设计结果能适用于不同类型地震激励和考虑固有阻尼比的情况。

An inerter system is a structural vibration absorbing device with functions of inertia enhancement and damping enhancement.The enhancement functions of inerter system may produce large inertial control force,which leads to high manufacturing and installation costs in practical applications.Therefore,in view of the problems that the cost control for the design of an inerter system has not been paid enough attention to in existing researches and the calculation procedure is complicated,a set of concise and practical parameter design formulae for inerter systems was derived from the aspect of stochastic response,taking both structural performance and cost(control force)as the direct control objectives.Based on the expressions of the closed-form stochastic response of a single-degree-of-freedom structure with an inerter system,the variation patterns of structural response and control force were studied,and the balance point between performance optimization and cost optimization was discovered.The corresponding response extremum conditions of performance-cost control principle led to the closed-form formulae for the calculation of the key parameters of inerter systems under white noise excitations.The correctness of the design formulae and the simplicity of the design method were verified through case design and performance check.Meanwhile,it has been proved that the excessive control cost of the inerter system can be avoided on the premise of ensuring performance requirements by adopting the closed-form formulae derived in this paper.The formulae hold true for the situations of various types of seismic excitation and the involvement of inherent damping.