Abstract Slightly curved pipes are prevalent in many industries including oil installations especially in the Delta regions of the world. The aim of this paper therefore is to investigate the nonlinear dynamics of these pipes conveying fluids under the influence of thermal loadings. These investigations are for three different boundary conditions, namely simply supported ends, clamped-clamped ends and clamped-simply supported ends respectively. To derive the governing equations, small strains of initial curvature, temperature, tension, pressure, longitudinal and transverse strains are considered. Furthermore, strains due to curvature change during bending which are hitherto neglected in most of the previous works on slightly curved pipes are added. The strain due to initial curvature accounts for the geometric imperfection. Two coupled nonlinear differential equations in both longitudinal and transverse directions are obtained and solved using eigenfunction expansion method, up to four modes. Linear natural frequencies were obtained, and is shown that for various boundary conditions, it increases as the initial curvature increases and decreases as thermal loading increases. The nonlinear results obtained show that the amplitude of the pipe motion becomes larger due to the obvious effect of thermal loading. Nonlinear results for both vanishing and non-vanishing longitudinal displacements are presented.

中文翻译：

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热载荷下各种边界条件对微弯管非线性动力学的影响

摘要 微弯管在包括石油装置在内的许多行业中普遍存在，特别是在世界三角洲地区。因此，本文的目的是研究这些管道在热载荷影响下输送流体的非线性动力学。这些研究分别针对三种不同的边界条件，即简支端、夹紧端和夹紧简支端。为了导出控制方程，考虑了初始曲率、温度、张力、压力、纵向和横向应变的小应变。此外，增加了由于弯曲过程中曲率变化引起的应变，这些应变迄今为止在大多数先前关于略微弯曲的管道的工作中被忽略。由于初始曲率引起的应变解释了几何缺陷。使用特征函数展开方法获得并求解纵向和横向的两个耦合非线性微分方程，最多四种模式。获得了线性固有频率，并表明对于各种边界条件，它随着初始曲率的增加而增加，随着热载荷的增加而减少。获得的非线性结果表明，由于热载荷的明显影响，管道运动的幅度变大。呈现了消失和非消失纵向位移的非线性结果。它随着初始曲率的增加而增加，随着热负荷的增加而减少。获得的非线性结果表明，由于热载荷的明显影响，管道运动的幅度变大。呈现了消失和非消失纵向位移的非线性结果。它随着初始曲率的增加而增加，随着热负荷的增加而减少。获得的非线性结果表明，由于热载荷的明显影响，管道运动的幅度变大。呈现了消失和非消失纵向位移的非线性结果。