Free vibration analysis of nonlocal strain gradient beams made of functionally graded material

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• 作者：Li Li ; ^{lili_em@hust.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{lili_em@126.com" class="auth_mail" title="E-mail the corresponding author} ; Xiaobai Li ; Yujin Hu
• 关键词：Functionally graded material ; Vibration ; Nonlocal strain gradient theory ; Strain gradient theory ; Nonlocal continuum theory
• 刊名：International Journal of Engineering Science
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：102
• 期：Complete
• 页码：77-92
• 全文大小：724 K

文摘

A size-dependent Timoshenko beam model, which accounts for through-thickness power-law variation of a two-constituent functionally graded (FG) material, is derived in the framework of the nonlocal strain gradient theory. The equations of motion and boundary conditions are deduced by employing the Hamilton principle. The model contains a material length scale parameter introduced to consider the significance of strain gradient stress field and a nonlocal parameter introduced to consider the significance of nonlocal elastic stress field. The influence of through-thickness power-law variation and size-dependent parameters on vibration is investigated. It is found that through-thickness grading of the FG material in the beam has a great effect on the natural frequencies and therefore can be used to control the natural frequencies. The vibration frequencies can generally increase with the increasing material length scale parameter or the decreasing nonlocal parameter. When the material characteristic parameter is smaller than the nonlocal parameter, the FG beam exerts a stiffness-softening effect. When the material characteristic parameter is larger than the nonlocal parameter, the FG beam exerts a stiffness-hardening effect.