功能梯度一维六方准晶层合梁的自由振动和弯曲变形研究  

Study on Free Vibration and Bending Deformation of Functionally Graded One-Dimensional Hexagonal Quasicrystal Laminated Beams

作　　者：高得旺 郭俊宏 王浩田 孙托娅 Dewang Gao;Junhong Guo;Haotian Wang;Tuoya Sun(Department of Mechanics,College of Science,Inner Mongolia University of Technology,Hohhot,O10o51;School of Aeronautics,Inner Mongolia University of Technology,Hohhot,O10o51)

机构地区：[1]内蒙古工业大学理学院力学系,呼和浩特010051 [2]内蒙古工业大学航空学院,呼和浩特010051

出　　处：《固体力学学报》2024年第6期808-819,共12页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(12072166,21462007);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项目(JY20220075);内蒙古自然科学基金重点项目(No.2024ZD21);内蒙古自治区研究生科研创新项目(B20231101Z)资助。

摘　　要：本文利用伪Stroh公式,研究具有功能梯度的一维六方准晶层合梁的自由振动和弯曲问题.建立准晶层合简支梁模型,采用传递矩阵法,推导出简支边界条件下梁自由振动的固有频率及弯曲变形位移的精确解,并与已有结果对比,验证本文模型和方法的准确性和有效性.通过数值算例,分析两种不同叠层顺序下层合梁的高跨比、层厚比和功能梯度系数对一维准晶层合简支梁固有频率和弯曲变形的影响规律.结果表明,固有频率随功能梯度系数增大而增大;两种叠层顺序下随功能梯度系数的增大,声子场位移逐渐减小而相位子场位移逐渐增大;功能梯度系数和叠层顺序对层合梁的应力有很大影响,其中对准晶特有的相位子场应力影响更大.本文给出的精确解可为研究准晶梁的各种数值方法和实验结果提供理论参考.The pseudo-Stroh formulism can transform the governing equations of multi-field coupling materials such as quasicrystals into a linear eigensystem,enabling the exact solution of multilayered structures with simply-supported boundary conditions.This provides an important reference for various numerical and experimental methods of quasicrystal beams in engineering practice.In this paper,the free vibration and bending problems of one-dimensional(1D) hexagonal quasicrystal(QC) laminated beams with functional gradients are investigated using the pseudo-Stroh formula.A simply-supported QC laminated beam is modeled,and the transfer matrix method is used to derive the exact solutions for natural frequency of free vibration and bending deformation displacements of the beam under simply-supported boundary conditions.The obtained results are compared with the existing ones to verify the accuracy and precision of the presented model.Numerical examples are provided to show the effects of high span ratio,layer thickness ratio,and functional gradient coefficient on the natural frequency,bending deformation,and mode shape of simply-supported 1D QC laminated beams under two different stacking sequences.The results show that natural frequency increases with the increase of functional gradient coefficient.Phonon displacement decreases while phason displacement increases with the increase of functional gradient coefficient under the two stacking sequences.Functional gradient coefficient and stacking sequence minimally affect phonon displacement modes but significantly impact phason displacement modes.Moreover,they notably affect phason stresses compared to phonon stresses in QC laminated beams.Thus,the optimal natural frequency and deformation displacement of a QC beam can be achieved by adjusting geometric size,stacking sequence,and functional gradient coefficient of the layered beam.These findings can provide theoretical references for various numerical methods and experimental studies on QC beams.

关 键 词：准晶 功能梯度 简支梁 自由振动 弯曲变形 

分 类 号：O327[理学—一般力学与力学基础]