基于振型的工程结构概念设计

Mode-based Concept Design of Engineering Structure

结构概念设计从整体上指导结构的外形尺寸和各杆件之间相对刚度的比例,决定了结构在外界荷载作用下的整体效应。任何对结构的作用都会以位移的形式予以表现,通过位移,可建立内力和应力的方程式,反应结构的受力状态,判断结构的承载力。结构频率和振型是结构的固有特性,频率反映了结构整体刚度和质量的相对关系,振型表征了结构在外界荷载作用下最易发生变形的状态及先后顺序,任何作用效应都能以振型为空间坐标基进行展开。通过基于振型的位移展开,并利用振型方向因子为定量化指标,可清楚了解不同方向上的位移效应及所占比重,这样定量化后有利于设计者提高对结构有利的作用效应,降低不利的作用效应,加强不利振型杆件的构造设计。因此,对结构振型分析,可从整体本质上把握结构的力学性能,更好地指导结构概念设计和构造设计。

The shape of the whole structure and the proportion stiffness between different elements are decided by concept design, at the same time, the response of the action is also judged. Any response is displayed by means of displacement, and through the displacement, the inner force and stress of structure is correlated. The inner force and stress can describe the state of the structure under the outer action, estimating the bearing capacity of the structure. Frequency and mode is the inherent property of structure. Frequency is the proportion between mass and stiffness and the mode is the most easy deformed shape state and sequence, and any action response can be decomposed by mode matrix. Through the mode expansion, utilizing the mode direction factor as quantified index, each direction response and proportion can be clarified; the designer can elevate the good response and cut down the bad response. So the designer can weight the whole structure property by the mode analysis, and guide the concept design and mechanical design.