复合材料层合板动力学建模与内共振研究
发布时间：2018-11-18 10:49
【摘要】：复合材料层合结构是复合材料应用的基本结构之一,其动力学模型的建立与振动特性的研究具有重要的实际意义。目前,对于受主参激共振与内共振联合作用的复合材料层合板振动特性的研究相对较少,本文建立受面内力主参激共振与内共振联合作用的复合材料层合板的动力学方程。以此为基础,选取正交各向异性的石墨/环氧层合板为研究对象,研究不同激励参数及不同结构参数对系统内共振的影响。并对复合材料层合板的横向振型函数进行三阶模态假设,研究阻尼系数对系统幅频特性的影响,具体如下:首先,采用经典剪切变形理论和von Kármán非线性形变理论,建立受面内力参数激励的复合材料层合板动力学方程,并对前两阶模态进行Galerkin截断。其后,采用多尺度法进行近似求解,以石墨/环氧层合板作为研究对象,绘制单自由度主共振,两自由度主参激共振与1:3内共振联合作用下系统的幅频特性曲线。通过改变系统的结构参数,观测系统参数的微小改变,对幅频特性产生的巨大影响。其次,以建立的复合材料层合板的动力学方程为基础,假设其横向振型函数为三阶模态形式,进行三模态的Galerkin截断,采用多尺度法近似求解并绘制了系统1:3:9内共振条件下系统的幅频特性曲线,观察阻尼系数的变化对于系统响应幅值的影响。最后,以四边简支边界条件下的酚醛电木板作为研究对象,采用理论计算与实验对比的方式验证了确定尺寸下的酚醛电木板,固有频率满足产生1:3内共振的基本条件,进一步验证了前文理论建模的准确性。
[Abstract]:Composite laminated structure is one of the basic structures used in composite materials. The establishment of its dynamic model and the study of its vibration characteristics are of great practical significance. At present, there are relatively few studies on the vibration characteristics of composite laminates subjected to the combination of principal parametric resonance and internal resonance. In this paper, the dynamic equations of composite laminated plates acting on the combination of principal parametric resonance and internal resonance are established. On this basis, the orthogonal anisotropic graphite / epoxy laminates were selected as the research object to study the effects of different excitation parameters and different structural parameters on the internal resonance of the system. The effects of damping coefficient on the amplitude-frequency characteristics of composite laminated plates are studied by using the third-order modal hypothesis. Firstly, the classical shear deformation theory and von K 谩 rm 谩 n nonlinear deformation theory are used. The dynamic equations of composite laminated plates excited by in-plane force parameters are established and the first two modes are truncated by Galerkin. Then, the multi-scale method is used to approximate the solution. The single degree of freedom principal resonance, two degree of freedom principal parametric resonance and 1:3 internal resonance are combined to draw the amplitude-frequency characteristic curve of the system, taking the graphite / epoxy laminated plate as the object of study. By changing the structural parameters of the system and observing the minor changes of the system parameters, the amplitude and frequency characteristics are greatly affected. Secondly, based on the dynamic equation of composite laminated plate, the transverse mode function is assumed to be a third-order mode form, and the three-mode Galerkin truncation is performed. The amplitude-frequency characteristic curve of the system under the condition of 1:3:9 internal resonance is approximately solved and drawn by the multi-scale method. The influence of the change of damping coefficient on the response amplitude of the system is observed. Finally, the phenolic electric plank with four edges simply supported boundary condition is taken as the research object. The theoretical calculation and experimental comparison are used to verify that the natural frequency of the phenolic electric board with certain size satisfies the basic condition of producing resonance within 1:3. Furthermore, the accuracy of the previous theoretical modeling is verified.
【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB33
本文编号：2339824
[Abstract]:Composite laminated structure is one of the basic structures used in composite materials. The establishment of its dynamic model and the study of its vibration characteristics are of great practical significance. At present, there are relatively few studies on the vibration characteristics of composite laminates subjected to the combination of principal parametric resonance and internal resonance. In this paper, the dynamic equations of composite laminated plates acting on the combination of principal parametric resonance and internal resonance are established. On this basis, the orthogonal anisotropic graphite / epoxy laminates were selected as the research object to study the effects of different excitation parameters and different structural parameters on the internal resonance of the system. The effects of damping coefficient on the amplitude-frequency characteristics of composite laminated plates are studied by using the third-order modal hypothesis. Firstly, the classical shear deformation theory and von K 谩 rm 谩 n nonlinear deformation theory are used. The dynamic equations of composite laminated plates excited by in-plane force parameters are established and the first two modes are truncated by Galerkin. Then, the multi-scale method is used to approximate the solution. The single degree of freedom principal resonance, two degree of freedom principal parametric resonance and 1:3 internal resonance are combined to draw the amplitude-frequency characteristic curve of the system, taking the graphite / epoxy laminated plate as the object of study. By changing the structural parameters of the system and observing the minor changes of the system parameters, the amplitude and frequency characteristics are greatly affected. Secondly, based on the dynamic equation of composite laminated plate, the transverse mode function is assumed to be a third-order mode form, and the three-mode Galerkin truncation is performed. The amplitude-frequency characteristic curve of the system under the condition of 1:3:9 internal resonance is approximately solved and drawn by the multi-scale method. The influence of the change of damping coefficient on the response amplitude of the system is observed. Finally, the phenolic electric plank with four edges simply supported boundary condition is taken as the research object. The theoretical calculation and experimental comparison are used to verify that the natural frequency of the phenolic electric board with certain size satisfies the basic condition of producing resonance within 1:3. Furthermore, the accuracy of the previous theoretical modeling is verified.
【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB33
【参考文献】
相关期刊论文 前1条
1 丁皓江,陈伟球,徐荣桥;横观各向同性层合矩形板弯曲、振动和稳定的三维精确分析[J];应用数学和力学;2001年01期
，本文编号：2339824
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