本文選題：柔性約束 + 相對(duì)剛度　； 參考：《應(yīng)用數(shù)學(xué)和力學(xué)》2017年08期

【摘要】：研究了一端固定、一端彈簧約束滑動(dòng)固定的壓桿在Euler臨界載荷作用下的穩(wěn)定性.將系統(tǒng)的勢(shì)能表示為轉(zhuǎn)角的泛函,將擾動(dòng)量展開成Fourier級(jí)數(shù),將勢(shì)能的二階變分表示成一個(gè)二次型,得到在臨界狀態(tài)下勢(shì)能的二階變分半正定,并求得臨界載荷與屈曲模態(tài).進(jìn)一步研究臨界狀態(tài)下高階變分的正定性,包括四階和六階變分的正定性.結(jié)果表明,與剛性約束不同的是,柔性約束壓桿臨界狀態(tài)的穩(wěn)定性與約束的剛度有關(guān),有穩(wěn)定與不穩(wěn)定之分,并給出了臨界狀態(tài)是穩(wěn)定和不穩(wěn)定的情況下柔性約束相對(duì)剛度的范圍.
[Abstract]:The stability of the compression bar with one end fixed and one end spring bound sliding fixed under the Euler critical load is studied.The potential energy of the system is expressed as a functional of the rotation angle, the perturbation quantity is expanded into a Fourier series, the second order variation of the potential energy is expressed as a quadratic form, the second order variational semidefinite of the potential energy is obtained under the critical state, and the critical loads and buckling modes are obtained.In this paper, we further study the positive definiteness of higher order variational in critical state, including the positive definiteness of fourth and sixth order variations.The results show that, unlike rigid constraints, the stability of the critical state of a flexible compression bar is related to the stiffness of the constraint, and there is a difference between stability and instability.The range of relative stiffness of flexible constraint is given when the critical state is stable and unstable.
【作者單位】： 北京交通大學(xué)土木建筑工程學(xué)院力學(xué)系;
【基金】：高等學(xué)校博士學(xué)科點(diǎn)專項(xiàng)科研基金(20120009110019)
【分類號(hào)】：O342

【相似文獻(xiàn)】

相關(guān)期刊論文 前4條

1 計(jì)三有,孫國(guó)正,沈成武,蔣瓊珠;散粒體臨界狀態(tài)下的變形規(guī)律[J];武漢交通科技大學(xué)學(xué)報(bào);1998年06期

2 張萍,蘇巖;關(guān)于水面形狀的分析[J];沈陽(yáng)大學(xué)學(xué)報(bào);2004年04期

3 凌國(guó)平,凌國(guó)燦;繞旋轉(zhuǎn)圓柱流動(dòng)渦尾流結(jié)構(gòu)和臨界狀態(tài)特性[J];力學(xué)學(xué)報(bào);1997年01期

4 張維志;等溫管道層流與紊流臨界狀態(tài)值的分析[J];油氣儲(chǔ)運(yùn);1995年02期

相關(guān)會(huì)議論文 前1條

1 尹益輝;陳剛;陳裕澤;韋日演;;熱力聯(lián)合作用下圓板屈曲臨界狀態(tài)分析[A];中國(guó)工程物理研究院科技年報(bào)（2000）[C];2000年

，

本文編號(hào)：1741047