武汉科技大学学报(自然科学版)
武漢科技大學學報(自然科學版)
무한과기대학학보(자연과학판)
JOURNAL OF WUHAN UNIVERSITY OF SCIENCE AND TECHNOLOGY(NATURAL SCIENCE EDITION)
2013年
6期
428-430,438
,共4页
李明%郑慧明%罗侠
李明%鄭慧明%囉俠
리명%정혜명%라협
单壁碳纳米管%固支梁%非局部弹性理论%能量法%频率近似值
單壁碳納米管%固支樑%非跼部彈性理論%能量法%頻率近似值
단벽탄납미관%고지량%비국부탄성이론%능량법%빈솔근사치
SWCNTs%clamped-clamped beam%nonlocal elastic theory%energy method%approximate value of frequency
以非局部弹性理论为基础,同时考虑碳纳米管小尺度效应,采用欧拉-伯努利梁模型建立有外加预应力情况下单层碳纳米管的动力学控制方程,并给出其振动频率精确解,进而基于能量法给出单层碳纳米管振动频率近似解,最后通过具体算例将其精确解与近似解进行比较。结果表明,外加预应力的大小、碳纳米管模态数以及小尺度参数均影响单层碳纳米管振动频率预测值的准确性。
以非跼部彈性理論為基礎,同時攷慮碳納米管小呎度效應,採用歐拉-伯努利樑模型建立有外加預應力情況下單層碳納米管的動力學控製方程,併給齣其振動頻率精確解,進而基于能量法給齣單層碳納米管振動頻率近似解,最後通過具體算例將其精確解與近似解進行比較。結果錶明,外加預應力的大小、碳納米管模態數以及小呎度參數均影響單層碳納米管振動頻率預測值的準確性。
이비국부탄성이론위기출,동시고필탄납미관소척도효응,채용구랍-백노리량모형건립유외가예응력정황하단층탄납미관적동역학공제방정,병급출기진동빈솔정학해,진이기우능량법급출단층탄납미관진동빈솔근사해,최후통과구체산례장기정학해여근사해진행비교。결과표명,외가예응력적대소、탄납미관모태수이급소척도삼수균영향단층탄납미관진동빈솔예측치적준학성。
Based on nonlocal elastic theory and with the size effect of carbon nanotubes considered ,this paper used Euler-Bernoulli beam theory (EBT ) to establish the dynamic governing equation of single-walled carbon nanotubes (SWCNTs) with clamped-clamped boundary under prestress .It gave the ex-act solution to the vibration frequency of SWCNTs ,which was then compared with the approximate solution derived by the energy method .It is found that the accuracy of SWCNTs vibration frequency prediction is influenced by the value of prestress ,modal number and small scale parameters of SWC-NTs .