Taking a turbine runner blade under hydraulic excitation as the object of this study, the fluid–structure interaction dynamic model of the runner blade was established using the finite element method, and the vibration characteristics and the dynamic stress characteristics of the runner blade have been explored. Based on this, the characteristics of vibration and fatigue of the turbine runner blade were then analyzed using the Pairs fatigue crack growth model, and the fatigue crack growth regularity of the runner blade under hydraulic excitation was discovered. The influence of a fatigue crack on the ultimate strength of a runner blade was then discussed according to the strength theory, and the dynamic characteristics of the ultimate strength of a runner blade under the influence of vibration fatigue have been revealed. Finally, the dynamic characteristics of the ultimate strength of a turbine runner blade under hydraulic excitation were simulated and analyzed using an example from the literature. The results showed that the ultimate strength of turbine runner blades was not only related to their vibration characteristics but also their fatigue characteristics. It was found that with the propagation of a fatigue crack in a runner blade, its ultimate strength decreased continuously.

In this paper, a turbine runner blade under hydraulic excitation was taken as the object of study and the mathematical hydrodynamic pressure model of a turbine runner blade under the rotor-stator interaction was established using quasi-three-dimensional finite element model. The regularity of the distribution of the hydrodynamic pressure was then investigated. First, the quasi-three-dimensional finite element model of a runner blade was established using the quasi-three-dimensional theory. Next, according to the pressure distribution from the numerical simulation, the mathematical mean pressure model of a node was established using the relative pressure difference method; the pressure fluctuation was then established taking the rotor-stator interaction into consideration. Then, based on the mean pressure and the pressure fluctuation of a node, the mathematical hydrodynamic pressure model for any position of a runner blade was obtained. Finally, the feasibility of the mathematical model was verified by an example analysis, and the internal relationship between the hydrodynamic pressure and its hydraulic parameters and the structural parameters of the blade was revealed, which provides a theoretical basis for further study of the dynamic characteristics of turbine runner blades under the rotor-stator interaction.

Based on the fast Fourier wave superposition spectrum method, a new equivalent source method (ESM) with a sparse sampling technique is proposed. First, the equivalent source intensities are expanded on a rectangular virtual surface using a bidirectional Fourier series, resulting in a semi-analytic and half-numerical acoustic pressure expression. The Fourier coefficients result in good sparsity for continuous acoustic pressures from structural vibration sources, and the proposed sparse sampling method can further reduce correlation in the measurement matrix. Better results can be obtained by solving the l₁ norm optimization problem. Finally, the method was verified using several examples. The proposed method offers two main advantages compared with the traditional compressive equivalent source method: (1) the unknown source intensity vector is expanded into a bidirectional Fourier series, thereby transforming an unknown source intensity vector into a sparse Fourier coefficient vector, which has better sparsity; (2) the proposed method constructs a random sampling matrix, which is expanded into a sparse sampling matrix by random distribution, thereby improving the reconstruction accuracy of planar near-field acoustic field compared with the traditional random position sampling method reducing correlation in the transfer matrix.