考虑表面效应的纳米圆形薄板振动-中国石油大学学报.PDFVIP

2017年摇 第41卷摇 摇 摇 摇 摇 摇 中国石油大学学报(自然科学版)摇 摇 摇 摇 摇 摇 摇 摇 Vol.41摇 No.5 摇 第5期摇 摇 摇 摇 摇 摇 摇 摇 Journal of China University of Petroleum摇 摇 摇 摇 摇 摇 摇 摇 Oct.2017 摇 摇 文章编号:1673鄄5005(2017)05鄄0153鄄06摇 摇 摇 doi:10.3969/ j.issn.1673鄄5005.2017.05.019 考虑表面效应的纳米圆形薄板振动 赵德敏,龚宇龙 (中国石油大学储运与建筑工程学院,山东青岛266580) 摘要:基于Gurtin的表面弹性理论考虑表面弹性和残余表面应力,建立周边固支的轴对称纳米圆板的振动微分方程。 研究残余表面应力对纳米板振动频率和主振型的影响。 结果表明:前四阶固有频率分别随着残余表面应力参数的增大 而减小;但残余表面应力对一阶固有频率和主振型影响最大,随着振动阶数的增大,残余表面应力对固有频率和主振型 的影响逐渐减小;同时对于一阶固有频率,板的厚度越薄或者板的半径越大,受残余表面应力的影响越大。 关键词:纳米圆板振动;表面弹性;残余表面应力;固有频率;主振型 中图分类号:O326摇 摇 摇 文献标志码:A 引用格式:赵德敏,龚宇龙.考虑表面效应的纳米圆形薄板振动[J]. 中国石油大学学报(自然科学版),2017,41(5): 153鄄158. ZHAO Demin,GONGYulong. Surfaceeffectsonvibrationof circularthinnano鄄plate[J]. Journalof ChinaUniversityof Pe鄄 troleum (Edition of Natural Science),2017,41(5):153鄄158. Surface effects on vibration of circular thin nano鄄plate ZHAO Demin,GONG Yulong (College of Pipeline and Civil Engineering in China University of Petroleum,Qingdao266580,China) Abstract:Based upon Gurtins theory of surface elasticity,the surface elasticity andresidual surface stressareboth consid鄄謖 ered,andthevibrationmodel of athinaxi鄄symmetricplateat nano鄄scalewithclampedboundary conditionisdeveloped. The influences of the residual surface stress effect onthefirstfour order naturalfrequenciesandvibration modeswerepresented. The results reveal that thefirst order natural frequency decreases with the increase of the residual surface stress parameter. Moreover,the residual surface stress effect exerts more important effect on the first natural frequency than others,and with the vibrationorderincreases,theeffectbecomesweaker. Thefirstfourordervibrationmodesforvarioussurfaceeffectparam鄄 eters are also given