一维纳米准晶层合梁的非局部振动、屈曲与弯曲研究
Nonlocal Vibration,Buckling and Bending of 1D Layered Quasicrystal Nanobeams
原庆丹 1郭俊宏2
作者信息
- 1. 内蒙古工业大学 理学院 力学系,呼和浩特 010051
- 2. 内蒙古工业大学 理学院 力学系,呼和浩特 010051;内蒙古工业大学 航空学院,呼和浩特 010051
- 折叠
摘要
基于非局部理论,建立了一维纳米准晶层合简支深梁模型,研究了其自由振动、屈曲行为及其弯曲变形问题.采用伪Stroh型公式,导出了纳米梁的控制方程,并通过传递矩阵法获得简支边界条件下纳米准晶层合梁固有频率、临界屈曲载荷及弯曲变形广义位移和广义应力的精确解.通过数值算例,分析了高跨比、层厚比、叠层顺序及非局部效应对一维纳米准晶层合简支梁固有频率、临界屈曲载荷和弯曲变形的影响.结果表明:固有频率和临界屈曲载荷随着非局部参数增大而减小;外层准晶弹性常数更高时,固有频率和临界屈曲载荷更大;叠层顺序对纳米准晶梁的力学行为有较大影响.所得的精确解可为纳米尺度下梁结构的各种数值方法和实验结果提供参考.
Abstract
Based on the nonlocal theory,a 1D layered nano-quasicrystal(QC)simply supported beam model was established to investigate the free vibration,buckling behavior,and bending deformation of nano-QC beams.The pseudo-Stroh formula was used to derive the governing equations for the nanobeam.Using the transfer matrix method,exact solutions of the natural frequency,the critical buckling load,the generalized dis-placement and the generalized stress for bending problems of layered nano-QC beams was obtained under sim-ply supported boundary conditions.The effects of the height-span ratio,the layer thickness ratio,the stacking sequence,and the nonlocal effect on the natural frequency,the critical buckling load and the bending deforma-tion of layered nano-QC simply supported beams were analyzed.The results show that,the natural frequency and the critical buckling load decrease with increasing nonlocal parameter.The bigger the outer-layer quasicrys-tal elastic constant is,the higher the natural frequency and the buckling critical load will be.The stacking se-quence has a significant effect on the mechanical behavior of nano-QC beams.The obtained exact solution pro-vides a reference for various numerical methods and experimental results of nanoscale beam structures.
关键词
纳米准晶/简支梁/自由振动/屈曲/弯曲/非局部效应Key words
nano-quasicrystal/simply supported beam/free vibration/buckling/bending/nonlocal effect引用本文复制引用
基金项目
国家自然科学基金(12072166)
内蒙古自治区科技计划项目(2021GG0254)
内蒙古自治区直属高校基本科研业务费(JY20220075)
出版年
2024
国家科技期刊平台
NSTL
万方数据