轴向变形对拱自振频率影响的样条有限点法
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摘要
提出用样条有限点法计算拱的横向振动和纵向振动的最小频率。用3次B样条函数的线性组合模拟拱自振时的位移振型函数,根据Hamilton原理推导出了拱结构自由振动频率方程。通过实例验证了样条有限点法计算效率高、精度高、计算格式简单,较有限元法具有很大优越性。计算分析了轴向变形对横向振动最小频率的影响,提出了临界矢跨比的概念。考虑轴向变形时不仅频率系数的大小发生了变化,同时它的变化规律也与原来不同。当结构的矢跨比小于临界矢跨比时,横向振动最小频率较不计轴向变形时减小,随着矢跨比的增大逐渐增大;当结构的矢跨比大于临界矢跨比时,横向振动最小频率较不计轴向变形时增大,随着矢跨比的增大逐渐减小。由此给出了目前广泛使用的横向振动最小频率曲线的适用范围,同时建立了纵向振动频率计算用曲线。
A spline finite point method is presented for studying the natural frequency of arch structures.The displacement mode shape function of the arch free vibration is simulated with a linear combination of cubic B–spline.The free vibration frequency equation of arch structures is derived according to Hamilton principle.The spline finite point method is verified by examples.The results show that the method is efficient and accurate.This method is better than finite element method.The influence of the axial deformation on the natural frequency is analyzed.The concept of the critical rise span ratio is put forward.Not only the value of the frequency coefficient is changed,but also its variation law is considered.When the arch rise span ratio is less than the critical rise-span,the axial deformation makes the natural frequency decrease.The lateral frequency coefficient increases as the rise span ratio increases.When the arch rise span ratio is greater than the critical rise-span,the axial deformation makes the natural frequency increase.The lateral frequency coefficient decreases as the rise span ratio increases.
A spline finite point method is presented for studying the natural frequency of arch structures.The displacement mode shape function of the arch free vibration is simulated with a linear combination of cubic B–spline.The free vibration frequency equation of arch structures is derived according to Hamilton principle.The spline finite point method is verified by examples.The results show that the method is efficient and accurate.This method is better than finite element method.The influence of the axial deformation on the natural frequency is analyzed.The concept of the critical rise span ratio is put forward.Not only the value of the frequency coefficient is changed,but also its variation law is considered.When the arch rise span ratio is less than the critical rise-span,the axial deformation makes the natural frequency decrease.The lateral frequency coefficient increases as the rise span ratio increases.When the arch rise span ratio is greater than the critical rise-span,the axial deformation makes the natural frequency increase.The lateral frequency coefficient decreases as the rise span ratio increases.
引文
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[2]陈宝春,韦建刚.钢管混凝土(单圆管)拱肋刚度对其动力特性的影响[J].地震工程与工程振动,2004,24(3):50-55.CHEN Baochun,WEI Jiangang.Effect of rigidities of concrete filled steel tubular(single tube)arch rib on its dynamic characteristics[J].Journalof Earthquake Engineering and Engineering Vibration,2004,24(3):50-55.(in Chinese)
[3]薛祖卫.抛物线拱的反对称和对称的固有振动[J].土木工程学报,1963,9(5):121-124.XUE Zuwei.Parabolic arch of the antsymmetric and symmetric vibration inherent[J].Civil Engineering Technology,1963,9(5):121-124.(inChinese)
[4]李宝,刘洪兵,张春燕.重力影响条件下拱的振动分析[J].低温建筑技术,2005,103(1):52-54.LI Bao,LIU Hongbing,ZHANG Chunyan.Vibration analysis of arch under the influence of gravity load[J].Low Temperature Architecture Tech-nology,2005,103(1):52-54.(in Chinese)
[5]钱七虎.拱型结构的自振频率计算及轴向变形对自振频率的影响[C].钱七虎院士论文选集,1999,153-160.QIAN Qihu.Arch natural frequency calculation and affection of the axial deformation on the natural frequencey[C].Qian Qihu Academician Tech-nolog,1999,153-160.(in Chinese)
[6]Anil K.Chopra..Dynamics of structures theory and application to earthquake engineering[M].USA:Pearson Education Inc.2000.
[7]OZ H R,Das M T.In plane vibration of circular curved beams with a transverse open crack[J].Matnematical and Computional Applications,2006,11(1):1-10.
[8]刘晶波,杜修力.结构动力学[M].北京:机械工业出版社,2005:27-28.LIU Jingbo,DU Xiuli.Structural dynamics[M].Beijing:Machinery Industry Press,2005,27-28.(in Chinese)
[9]魏德敏.拱的非线性理论及其应用[M].北京:科学出版社,2004:59-68.WEI Demin.Arch nolinear theory and application[M].Beijing:Science Press,2004.
[10]秦荣.计算结构力学[M].北京:科学出版社,2001.QIN Rong.Computational structural mechanics[M].Beijing:Science Press,2001.(in Chinese)
[11]刘古岷.应用结构稳定计算[M].北京:科学出版社,2004.LIU Gumin.Application of structural stabilisty calculation[M].Beijing:Science Press,2004.(in Chinese)
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