The invention discloses a free vibration semi-analytical calculation method for a liquid filling functional gradient pipeline on an elastic foundation, and relates to the technical field of
solid mechanics and fluid-
solid coupling vibration analysis. The method comprises the following steps: acquiring materials, geometry and boundary parameters of a pipeline, a fluid and a foundation, establishing a fluid-
solid coupling model based on a three-dimensional elastic theory, simulating foundation support by adopting a two-parameter Pasternak model, and deducing a
control equation and boundary conditions of a pipeline structural domain and a fluid domain; discretizing a pipeline
reference surface and a fluid boundary through a two-dimensional high-order spectrum unit, and converting an equation into a standard coordinate
system in combination with proportional boundary coordinate transformation; proportional boundary finite element control equations of a structural domain and a fluid domain are deduced respectively and converted into a first-order
differential equation set, then a fine integration method and an eigenvalue
decomposition method are adopted for solving, and then based on a fluid-solid
coupling condition
coupling equation, the equation is converted into a generalized eigenvalue problem for solving the inherent frequency and the vibration mode. According to the method, only precision, efficiency and discrete boundaries are considered, and support is provided for pipeline design optimization and safety evaluation.