不同拉压特性结构振动分析的双线性近似方法  

BILINEAR METHOD FOR VIBRATION ANALYSIS OF A STRUCTURE WITH DIFFERENT TENSION AND COMPRESSION BEHAVIOR

作　　者：赵荣国[1] 徐友钜[2] 陈忠富[2] 胡绍全[2] 黄西成[2] 

机构地区：[1]湘潭大学土木工程与力学学院,湘潭411105 [2]中国工程物理研究院结构力学研究所,绵阳621900

出　　处：《振动与冲击》2005年第1期4-7,17,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(10232040)

摘　　要：对拉压特性不同的双模量结构的非线性自由振动进行了研究。给出了恢复力-位移曲线由三段斜率不 同的直线构成的单自由度系统自由振动频率的精确解。应用双线性近似方法讨论了有间隙双模量结构和无间隙双模量 结构非线性自由振动频率的近似求解问题。结果表明,不管恢复力-位移表达式多么复杂,应用双线性近似方法都可以 方便地求得结构的等效线性刚度,进而获得结构固有频率的近似解。通过近似计算结果与精确解之间的比较,验证了双 线性近似方法对于工程中大量存在的一类具有不同拉压特性的结构进行振动分析的实用性。Some aspects of nonlinear free vibration of bimodular structures behaving dissimilarly in tension and in compression are studied. The exact solutions of frequency of nonlinear free vibration for a single degree of freedom system with restoring force described by three straight lines with different slopes are given. The bilinear approximation method is applied to solve the frequency of nonlinear free vibration for both bimodular system with gaps and that without gap. The result shows that no matter how complex the expression of restoring force-displacement is, the equivalent linear stiffness of the system can be easily obtained by using the bilinear approximation method, and then, the approximate solution of natural frequency of the system can be achieved. The practicability of the bilinear approximation method for a class of structure with different tension and compression behavior in the engineering field is verified by the comparison between exact solutions and approximation ones.

关 键 词：近似方法 双线性 精确解 近似解 双模 结构振动 表达式 拉压 刚度 位移 

分 类 号：TU391[建筑科学—结构工程] O211.61[理学—概率论与数理统计]