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 1 D Layered Quasicrystal Nanobeams

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.

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 displacement and the generalized stress for bending problems of layered nano-QC beams was obtained under simply 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 deformation 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 quasicrystal elastic constant is,the higher the natural frequency and the buckling critical load will be.The stacking sequence has a significant effect on the mechanical behavior of nano-QC beams.The obtained exact solution provides a reference for various numerical methods and experimental results of nanoscale beam structures.