In this paper, the nonlinear damping and forced response behaviors of laminated composite cylindrical shells considering the internal damping of composite materials are investigated. Based on Donnell nonlinear shell theory, the dynamic governing equations of composite cylindrical shells with geometrical nonlinearity are established by using the Hamilton principle, in which the inherent material damping is taken into account by complex modulus method. The dependence of nonlinear damping on vibration amplitude and amplitude–frequency response are analytically obtained by the Galerkin method in conjunction with harmonic balance method. By comparing the results of natural frequency and modal damping with those in the literature, the correctness of the above theoretical analysis is verified. Furthermore, the effects of the circumferential wave number, lamination schemes, vibration amplitude and geometric configuration on the nonlinear damping and forced responses of the composite cylindrical shell with unidirectional, angle-ply and cross-ply laminations are analyzed. The results show that the damping dissipation capacity of the composite cylindrical shell is amplitude-dependent, and the effect of the amplitude on the nonlinear damping characteristics gradually decreases with the increase of the length-to-radius ratio. The ply angle not only affects the value of the resonance peak, but also significantly changes the degree of the soft and hard spring characteristics of the composite cylindrical shell. With the increase of internal material damping, the amplitude-frequency curve of the composite cylindrical shell changes from the coexistence of hard and soft characteristics to the only soft characteristics.

中文翻译：

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具有固有材料阻尼的叠层复合圆柱壳的非线性阻尼和受迫响应

本文研究了考虑复合材料内部阻尼的叠层复合圆柱壳的非线性阻尼和受迫响应行为。基于Donnell非线性壳理论，利用Hamilton原理建立了具有几何非线性的复合圆柱壳的动力控制方程，其中采用复模量法考虑了材料固有阻尼。通过伽辽金法结合谐波平衡法解析得到非线性阻尼对振幅和幅频响应的依赖性。通过将固有频率和模态阻尼结果与文献中的结果进行比较，验证了上述理论分析的正确性。此外，圆周波数的影响，分析了单向叠片、角叠片和交叉叠片复合圆柱壳的非线性阻尼和受迫响应的叠片方案、振动幅度和几何构型。结果表明，复合圆柱壳的阻尼耗散能力与幅值相关，且幅值对非线性阻尼特性的影响随着长径比的增大而逐渐减小。帘布层角度不仅影响共振峰的值，而且显着改变复合圆柱壳软硬弹簧特性的程度。随着内部材料阻尼的增加，