碳纤维复合材料层合材可被应用于航天、航海领域的工程结构中，也可被应用于坦克的炮管、机器人手臂、汽车刹车踏板和弹簧等工程结构中；碳纤维复合材料层合材相对于传统层合材的优势在于其强度重量比大、刚度大、不易疲劳破坏、耐腐蚀、具有良好的摩擦特性和易于制造；碳纤维复合材料层合材在工业上应用范围的不断扩大，对于在微观和宏观层面上研究这种复合材料有很大的帮助。在各种实际工程情况下，如何避免结构在低频振动时因振幅过大而导致材料疲劳破坏是机械工程界的研究前沿问题，值得深入研究。 为了避免碳纤维复合材料层合梁(简称层合梁)在实际工程情况中受低频振动时形成共振效应，本文探究了层合梁在不同约束形式下的自由振动问题。利用有限元方法(FEM)中的能量法分析这个问题，利用一阶剪切变形理论(FSDT)分析层合梁的剪切变形。研究中考虑层合梁的约束形式包括：铰支-自由梁(HF)、悬臂梁(CF)、固支梁(CC)、自由梁(FF)、简支梁(CH)和铰支-铰支梁(HH)六种。 利用能量法建立层合梁自由振动的数学模型，模拟分析层合梁在不同约束形式下的自由振动的固有频率；对所建立的数学模型进行求解，带入约束条件，用MATLAB软件求解获得层合梁自由振动的无量纲固有频率；利用DHVTC实验系统对层合梁进行振动实验分析；确定层合梁样本的制备方法，制作实验样本，利用DHVTC实验系统测试在不同约束条件下四层层合梁自由振动的固有频率；将实验结果与有限元模型的数值分析结果进行比较表明：约束条件为悬臂梁和固支梁的层合梁在一阶弯曲模态下的计算结果和实验结果的重合度较高。 将数值分析结果与此领域相关度较高的文献中的结果进行比较，比较选择了四种情况：正交各向异性梁、对称层合梁、非对称层合梁和不同的剪切理论。通过比较证明，本研究结果与参考文献的结果不论在低阶还是高阶模态下差异都很小，对比结果证明了本文所建立数学模型和编制计算机程序的正确性。 利用数值分析结果，分析得出纤维取向角、自由端运动和外形尺寸等参数与层合梁自由振动固有频率之间的联系。当在建立数学模型时考虑横向剪切变形和转动惯量这两个因素时，在相同的外形尺寸和约束条件下，纤维取向角对称和反对称的层合梁具有相似的固有频率；随着长宽比的增大，层合梁纵向振动引起的固有频率也随之增大；随着纤维取向角的增大，层合梁的固有频率随之减小；层合梁的横向振动只受侧向运动影响，且层合梁纵向模态的固有频率在拥有移动端的约束形式中相同。 文中采用数值模拟方法和实验法相结合的方式进行分析研究，为探究层合梁在不同约束形式下的自由振动问题提供了理论支撑，也为用DHVTC方法测试层合梁固有频率做出积极的探索和尝试。 关键词：碳纤维复合材料；层合梁；一阶剪切变形理论；自由振动；梁的约束条件；固有频率

 A composite has been used in engineering structures over the last four decades or so. They could be seen in a variety of applications as in craft wings and fuselage, satellites helicopter blades, wind turbines boats and vessels, tubes and tanks, robot arms, brake pedals and springs etc. Their advantages over traditional materials are widely recognized and these are high strength to weight ratio, and their properties which can be tailored according to need. Other advantages include high stiffness, high fatigue and corrosion resistance, good friction characteristics, and ease of fabrication. The ever growing use of composites in industry has led to tremendous advancements in the understanding of their micro and macro behavior. The knowledge of the few lower natural frequencies of a structure is of utmost importance in order to save it in service from being subjected to unnecessary large amplitude of motion which can cause immediate collapse or ultimate failure by fatigue. In order to avoid the resonance effect of carbon fiber composite laminated beams under low frequency vibration in practical engineering environment, this study developed to solve the problem of prediction of the natural frequencies of free vibration for the carbon fiber-epoxy composite laminated beams. The problem is analyzed and solved by using the energy approach, which is formulated by a finite element model. The shear deformation is formulated by the first-order shear deformation theory. Different boundary conditions for the beams are considered which are: clamped-clamped; hinged-hinged; free-free; clamped-hinged; clamped-free; and hinged-free beams. Two types of laminations were considered which are symmetric [θ/-θ/-θ/θ] and anti-symmetric [θ/-θ/θ/-θ] angle-ply laminated beams. The angle(θ) is the angle of fibers orientation measured from the longitudinal axis of the beam. The energy method which is used to establish the mathematical model of the laminated beam, the natural frequencies of the laminated beam under different constraints are simulated. Shear deformation is formulated by the first-order shear deformation theory. The established mathematical model was solved, and the constraint conditions were introduced. The dimensionless natural frequencies of free vibration of laminated beams were obtained by using MATLAB software. The carbon fiber - epoxy composite laminated beams also are analyzed experimentally using DHVTC experimental system for vibration test with Impulse Technique. Fabrication procedure of the specimens of the carbon fiber-epoxy composite laminated beams was described. The natural frequencies of 4-layered for carbon fiber-epoxy cantilevered and clamp-clamp composite beams have been determined experimentally. The present experimental results were compared with numerical results which obtained by applying a finite element model and the results showed good agreement especially in the first mode. The numerical analysis results were compared with the results in the literature with high relevance in this field, and four cases were selected to verify the results, which are: orthogonal anisotropic beams, symmetric laminated beams, non-symmetric laminated beams and different shear theories. Through comparison, the difference between the results of this study and the results of references is very small in both low order and high order modes. The comparison results prove the correctness of the mathematical model and computer program established in this paper. Based on the numerical analysis results, the relation between the natural frequency of composite laminated beams and the parameters of fiber orientation angle, aspect ratio, type of beam support and the end movement are obtained. With considering the influence of transverse shear deformation and rotational inertia on the free vibration of laminated beams, it was found that the symmetry and anti-symmetric laminated beams have similar natural frequencies under the similar dimensions and end conditions. The natural frequencies due to longitudinal vibration of the composite laminated beams increase as the aspect ratio increased, and the natural frequencies of the composite laminated beams generally decrease as the fiber orientation angle increases. The lateral vibration of the laminated beam is only affected by the lateral motion, and the values of the natural frequencies of longitudinal modes are found to be the same for all beams with movable ends since they are generated by longitudinal movements only. In this study, numerical simulation method and experimental method are used to analyze and study the free vibration of laminated beams under different constraints, which provides theoretical support, and also makes a positive exploration and attempt to test the natural frequency of laminated beams by using DHVTC experimental system. Keywords: Carbon Fiber Composite, Laminated Beam, First Order Shear Deformation Theory, Free Vibration, Beam End Conditions, Natural Frequencies