A new model is presented for studying the effects of crack parameters on the dynamics of a cracked beam structure. The model is established by the finite element displacement method. In particular, the stiffness matrix of the cracked beam element is firstly derived by the displacement method, which does not need the flexibility matrix inversion calculation compared with the previous local flexibility approaches based on the force method. Starting with a finite element model of cracked beam element, the equation of strain energy of a cracked beam element is formed by the displacement method combined with the linear fracture mechanics. Then, based on the finite element method, the dynamic model of the cracked beam structure is obtained. The results show that the dynamic model discovers the internal relation between the dynamic characteristics of cracked beam structure and structural parameters, material parameters, and crack parameters. Finally, an example is presented to validate the proposed dynamic model.

Considering the complex vibration phenomenon of turbine runner blades under the flow excitation, the nonlinear coupling dynamic equation, which contains hydraulic parameters and blade structure parameters, is established by the finite element method, based on geometrical nonlinearity and fluid–structure interaction of runner blades. According to the dynamic equation, the dynamic response of turbine runner blades under the flow excitation is simulated and analyzed through an example and is compared with the experimental results. The research shows that the proposed equation can well reflect the relation between the dynamic performance of turbine runner blades and its hydraulic parameters, structural parameters, and material parameters. Therefore, the equation provides a necessary theoretical basis for further study on deep-seated problems such as the dynamic characteristics of runner blade and the mechanism of vibration fatigue of runner blade.

The rotary platform is the load‐bearing substrate of a hydraulic excavator. The dynamic characteristics of the rotary platform directly affect the reliability and safety of the whole machine of a hydraulic excavator. In this work, the characteristics of the main external excitations acting on the hydraulic excavator such as the engine excitation, pressure pulsation excitation of the piston pump, inertial excitation of the working device, and road excitation are analyzed. The vibration transmission paths under the action of external excitations are ascertained. A vibration test method for the rotary platform of the hydraulic excavator is proposed. The vibration characteristics of the rotary platform under complex working conditions are researched, and the internal relationships between the vibration characteristics of the rotary platform and the engine excitation, pressure pulsation excitation of the piston pump, and road excitation are analyzed experimentally. The results show that the rotary platform is subjected to different excitations when it is under different working conditions. Moreover, the internal relationships between the dynamic characteristics of the rotary platform and the external excitation characteristics can be discovered by analyzing the vibration signals of the rotary platform, and the dynamic characteristics of the whole machine of the hydraulic excavator can be deeply studied based on the vibration characteristics of the rotary platform.

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.