周期荷載作用下組合壓桿動(dòng)力穩(wěn)定性分析
趙洪金1,劉超1,2,董寧娟3
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(1 西安建筑科技大學(xué)土木工程學(xué)院,西安710055; 2 西安建筑科技大學(xué)理學(xué)院,西安710055;3 中國飛機(jī)強(qiáng)度研究所,西安710065)[摘要]通過能量法和Hamilton原理分別建立了綴條式和綴板式組合壓桿在縱向周期荷載作用下的動(dòng)力偏微分方程,利用Galerkin方法將其轉(zhuǎn)化為二階常微分Mathieu型參數(shù)振動(dòng)方程,求得周期解所包圍的動(dòng)力不穩(wěn)定區(qū)域,探討了兩種組合壓桿發(fā)生參數(shù)振動(dòng)的動(dòng)力穩(wěn)定性問題,分析了桿件長細(xì)比、綴條面積、綴板剛度等參數(shù)對(duì)組合壓桿動(dòng)力穩(wěn)定性的影響,為結(jié)構(gòu)工程動(dòng)力分析與設(shè)計(jì)提供參考依據(jù)。[關(guān)鍵詞]參數(shù)振動(dòng);動(dòng)力穩(wěn)定性;組合壓桿;周期荷載中圖分類號(hào):TU311.2文獻(xiàn)標(biāo)識(shí)碼:A文章編號(hào):1002-848X(2011)02-0068-03Dynamic stability of compressed built-up members subject to periodic loadZhao Hongjin1, Liu Chao1,2, Dong Ningjuan3(1 School of Civil Engineering, Xian University of Architecture & Technology, Xian 710055, China;2 School of Science, Xian University of Architecture & Technology, Xian 710055, China;3 Aircraft Strength Research Institute of China, Xian 710065, China)Abstract:Through the energy method and Hamilton principle, parametric vibration equations of sewed bar and sewed slab compressed built-up members subject to periodic load were established respectively. Galerkins method was used to convert the partial differential equations into the ordinary differential Mathieu equations and dynamic instability regions surrounded by periodic solutions were obtained. Dynamic stability problems of parametric vibration were discussed about two kinds of compressed built-up members. The influences of slenderness ratio, area of sewed bars and stiffness of sewed slabs on the dynamic stabilites of axial compression lattice column were discussed, which can provide references for dynamic analysis and design in structure engineering.Keywords:parametric vibration; dynamic stability; compressed built-up member; periodic load作者簡介:趙洪金,博士研究生,Email:zhq-2005@163.com。參考文獻(xiàn)[1]龍馭球,包世華.結(jié)構(gòu)力學(xué)教程(Ⅱ)[M].北京:高等教育出版社,2002.[2]胡雋,王元豐.組合壓桿大撓度屈曲分析[J].北方交通大學(xué)學(xué)報(bào),2002,24(1):28-32.[3]李國躍,呂鳳梧.雙肢綴板鋼格構(gòu)立柱的整體穩(wěn)定分析[J].土木工程學(xué)報(bào),2002,35(4):17-19.[4]符·華·鮑洛金. 彈性體系的動(dòng)力穩(wěn)定性[M].林硯田,等譯. 北京:高等教育出版社,1960.[5]孫強(qiáng).變截面桿的動(dòng)力穩(wěn)定性研究[J].四川建筑科學(xué)研究,1999,11(2):17-19.
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