In this paper, the response solutions of the damped fluid-conveying pipe system with elastic torsion constraints at both ends are analyzed. The pipe system considering gyroscopic effect induced by internal flow and damping effect is a typical damped gyroscopic system. This system cannot be decoupled in the modal space by the traditional modal analysis, and then the semi-analytical response solutions cannot be obtained by the classical modal superposition method. In order to remedy this problem, this paper proposes a new method based on complex modal superposition method and state-space method to give the semi-analytical response solutions of the damped fluid-conveying pipe system. The adjoint system is introduced through the concept of adjoint operator, and the orthogonality conditions of the damped fluid-conveying pipe system are derived in the state-space by using the eigenvalue relationship between the original system and the adjoint system. The Laplace transformation method is used to solve the eigenvalue problems of the original system and the adjoint system, and the implicit function equations about the eigenvalues and analytical eigenfunctions are obtained. According to the obtained orthogonality conditions, the semi-analytical response solutions of the system under arbitrary initial conditions and excitations are given, and the obtained solutions include transient and steady-state response solutions. In the numerical discussion part, the reliability and accuracy of the present method are verified. This research has positive significance for the dynamic analysis of fluid-conveying pipe systems, and the obtained orthogonality conditions have potential value for the nonlinear dynamics research.

中文翻译：

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基于复模态叠加法的阻尼流体输送管道系统受迫振动和自由振动半解析解

本文分析了两端具有弹性扭转约束的阻尼流体输送管道系统的响应解。考虑内流引起的陀螺效应和阻尼效应的管道系统是典型的阻尼陀螺系统。该系统无法通过传统的模态分析在模态空间中解耦，进而无法通过经典的模态叠加方法获得半解析响应解。为了解决这个问题，本文提出了一种基于复模态叠加法和状态空间法的新方法，给出阻尼流体输送管道系统的半解析响应解。通过伴随算子的概念引入伴随系统，利用原系统与伴随系统的特征值关系，在状态空间中导出阻尼流体输送管道系统的正交条件。采用拉普拉斯变换方法求解原系统和伴随系统的特征值问题，得到特征值的隐函数方程和解析特征函数。根据获得的正交条件，给出了系统在任意初始条件和激励下的半解析响应解，获得的解包括瞬态响应解和稳态响应解。数值讨论部分验证了该方法的可靠性和准确性。该研究对于流体输送管道系统的动力学分析具有积极意义，所获得的正交条件对于非线性动力学研究具有潜在价值。