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This paper proposes a new theoretical method to investigate the thermal behaviors of the inter-shaft bearing considering the nonlinear dynamic characteristics of a dual-rotor system by combining heat transfer and nonlinear dynamics. The nonlinearities of the inter-shaft bearing, including the Hertzian contact and the radial clearance, are considered during the dynamic modeling for the system. The dynamic load of the inter-shaft bearing is defined according to the nonlinear dynamic responses of the system. Therefore, some fundamental nonlinear phenomena, i.e., jump and bi-stable phenomena happen to the dynamic load. It makes the dynamic load more appropriate to describe the actual load of the inter-shaft bearing than the static load. Furthermore, a steady-state heat transfer model for the inter-shaft bearing subjected to the dynamic load can be set up with the help of Palmgren’s empirical formula. The variation of temperatures with the rotation speed is obtained by using the Gauss–Seidel iteration. Temperatures of the inter-shaft bearing also show nonlinear thermal behaviors, i.e., jump and bi-stable phenomena. It implies the nonlinear dynamic behaviors of the system have a great impact on the thermal behaviors of the inter-shaft bearing. Moreover, an exhaustive parametric analysis for temperatures and nonlinear thermal behaviors of the inter-shaft bearing affected by dynamic parameters (including the rotation speed ratio, unbalances of rotors, the radial clearance, the stiffness and the roller number of the inter-shaft bearing) and thermal parameters (including the lubricant viscosity and the ambient temperature) is carried out. The results show that the rotation speed ratio has a significant influence on both temperatures and nonlinear thermal behaviors, other dynamic parameters mainly affect nonlinear thermal behaviors, while thermal parameters only affect temperatures. This unique discovery indicates the thermal behaviors of the inter-shaft bearing could be much more complex because of the nonlinear dynamic characteristics of the dual-rotor system. The obtained results will contribute to a better understanding of the nonlinear thermal behaviors of bearings and profoundly reveal the mechanism of the nonlinear thermal behaviors of bearings.

A series of work for distributed dynamic load identification is investigated in this paper considering unknown-but-bounded uncertainties in the aircraft structure. To facilitate the analysis, the complicated rudder structure is simplified to a plate structure based on the robust equivalence principle of mechanical property under multi-cases of flight environments. Aiming at the plate structure, a time domain–based model for distributed dynamic load identification is established through the acceleration response measured by sensors. Among them, the spatial distributed load is approximated by Chebyshev orthogonal polynomials at each sampling time, and load boundaries can be calculated by the Taylor-expansion-based uncertain propagation analysis. As keys to improve the reliability of recognition results, the optimization process for sensor placement is constructed by the particle swarm optimization algorithm, taking the robustness evaluation index and sensor distribution index into consideration. The validity and the feasibility of the proposed methodology are demonstrated by several numerical examples, and the results reveal that designer can make a rational tradeoff choice among the cost of sensor placement and the performance of load identification in a systematic framework.

The exploitation of mineral resources is gradually shifting from shallow to deep targets. However, the corresponding basic theoretical research has not determined the differences in rock-mining engineering at different depths. In this paper, longitudinal wave velocity measurements, uniaxial compression tests, and dynamic impact tests were conducted on granite from various burial depths to reveal the static and dynamic mechanical properties of the rocks. The initial damage variables of the rock specimens decrease after a rapid increase with increasing burial depth. The stress–strain curves of the deep rocks for various strain rates can be divided into two modes. The relationships between the secant modulus, peak stress, elastic modulus, and burial depth basically follow a quadratic function. The rock failure patterns observed in the uniaxial compression tests are basically tensile. In the dynamic loading experiments at various strain rates, the failure pattern of the rock changes with burial depth, when the strain rate is small, from local instability to overall instability and back to local instability; while the strain rate increases, the failure pattern transforms into overall instability. In the dynamic impact experiments with different confining pressures, the rock only undergoes shear failure due to the restriction of the lateral deformation from the confining pressure. These research achievements could provide significant theoretical support for rockburst prevention at greater mining depths.

In deep mine, coal is usually subjected to coupled high gas pressure and static compressive stress. The coal may be also subjected to dynamic loading due to the sudden fracture of hard roof during mining. In our previous study, the behaviour of gas-containing coals with initial gas pressure was investigated subjected to uniaxial static compression. In this study, the dynamic compressive behaviour of gas-containing coals with gas pressure and static axial preloading is investigated using a modified Split Hopkinson Pressure Bar (SHPB) system. The dynamic behaviours of gas-containing coals under SHPB tests are studied by varying initial gas pressure and axial static preloading. The testing results include strain measurements and energy dissipation. In addition, the wave impedance method is used to quantify damage of gas-containing coals under coupled gas-static-dynamic load. It is found that the dynamic compressive strength of gas-containing coal under coupled load decreases with the increasing initial gas pressure. The gas-containing coal with higher gas pressure and axial static preloading is more vulnerable to dynamic loading. The findings can be applied to mining design or support design in deep mining of high-gas-containing coal seam.

The determination of structural dynamic characteristics can be challenging, especially for complex cases. This can be a major impediment for dynamic load identification in many engineering applications. Hence, avoiding the need to find numerous solutions for structural dynamic characteristics can significantly simplify dynamic load identification. To achieve this, we rely on machine learning. The recent developments in machine learning have fundamentally changed the way we approach problems in numerous fields. Machine learning models can be more easily established to solve inverse problems compared to standard approaches. Here, we propose a novel method for dynamic load identification, exploiting deep learning. The proposed algorithm is a time-domain solution for beam structures based on the recurrent neural network theory and the long short-term memory. A deep learning model, which contains one bidirectional long short-term memory layer, one long short-term memory layer and two full connection layers, is constructed to identify the typical dynamic loads of a simply supported beam. The dynamic inverse model based on the proposed algorithm is then used to identify a sinusoidal, an impulsive and a random excitation. The accuracy, the robustness and the adaptability of the model are analyzed. Moreover, the effects of different architectures and hyperparameters on the identification results are evaluated. We show that the model can identify multi-points excitations well. Ultimately, the impact of the number and the position of the measuring points is discussed, and it is confirmed that the identification errors are not sensitive to the layout of the measuring points. All the presented results indicate the advantages of the proposed method, which can be beneficial for many applications.

This paper aims to study the fracture characteristics of blunt indenter impacting formation under static and harmonic dynamic loads by carrying out a series of FE numerical simulations. The methodology of globally embedding cohesive elements with zero-thickness is introduced based on its constitutive response. Subsequently, the secondary development of FE simulation is carried out, and the 3D simulation of random initiation and propagation of formation without preset crack under compressive loads is realized. Two key parameters (amplitude and frequency) of dynamic load are considered, three fracture characteristic parameters (crack element number, crack area and crack volume) of formation are discussed, and the process and morphology of formation fracture and the impact velocity and displacement of blunt indenter under static–dynamic loads are investigated, respectively. Based on the analysis undertaken, it can be concluded that the harmonic dynamic load can promote crack propagation and connection. The amplitude of harmonic dynamic load is beneficial to the formation fracture, and the influence of loading frequency on it still needs to be further discussed. The impact velocity of blunt indenter changes in a harmonic form and the impact displacement increases in a fluctuating form under static–dynamic loads. The research results are of great significance for optimizing drilling parameters and designing speed-increasing tools.HighlightsThe methodology of globally embedding cohesive element with zero-thickness is introduced based on constitutive response.The secondary development of FE simulation is conducted, which can realize random initiation and propagation of formation without preset crack under compressive loads and extract fracture characteristic parameters.The 3D simulation model of blunt indenter impacting formation is proposed and the fracture process of formation under static and static-dynamic loads is compared.Two key parameters (amplitude and frequency) of harmonic dynamic load are considered and three fracture characteristic parameters (crack element number, crack area and crack volume) of formation are discussed.The process and morphology of formation fracture and the impact velocity and displacement of blunt indenter under static-dynamic loads are investigated.

Underground rock is often subjected to the coupled action of acid sulfate, chloride ion corrosion, and external dynamic disturbance: the degree of corrosion and dynamic load can significantly affect the pore structure and mechanical behavior of rock. To quantify the microscopic pore structure changes and macro-dynamic behavior characteristics of acidified corroded sandstone, first, a mixed acidic solution of NaHSO4 and HCl with different pH values was used for immersion corrosion of sandstone; second, the pore structure of sandstone before and after corrosion was quantitatively evaluated by nuclear magnetic resonance (NMR), dynamic loading tests of corroded sandstone were conducted on an SHPB experimental system and scanning electron microscopy (SEM) was used to observe the morphology of corroded sandstone section; and finally, the mechanism of water–rock interaction and damage and fracture of acid-corroded sandstone were analyzed. The results show that, after acidizing corrosion of sandstone, the macropores increase significantly in number and volume, the boundary of the pore structure tends to be fuzzy; the effective porosity, the number of effective pores, and the total porosity increase significantly; the residual porosity, the number of residual pores, and T2 cut-off value decrease. The proportion accounted for by the elastic stage in stress–strain curves of corroded sandstone is lowered; the proportion accounted for by the plastic yield stage is increased; and post-peak rebound is diminished. With the decrease of pH value, the peak stress on acid-corroded sandstone decreases and the peak strain increases. The peak stress on corroded sandstone is negatively correlated with effective porosity and the number of effective pores, but positively correlated with residual porosity, the number of residual pores, and the T2 cut-off value. The reaction of acidic solution with sandstone minerals causes the free fluid space to increase, the bound fluid space decreases, and the number of pores increases, resulting in a decrease in the dynamic strength of acidified sandstone. The fracture of original sandstone after impact failure has no obvious directionality, and the failure mode of grain is the coexistence of intergranular fracture and trans-granular fracture. The fracture of sandstone after acidizing corrosion is obviously directional after impact damage, and the fracture form is single, which is intergranular fracture. The research results can provide a certain reference for the protection of rock engineering under acidic water chemical environment.

The stability control of surrounding rock for large or super-large section chamber is a difficult technical problem in deep mining condition. Based on the in-site geological conditions of Longgu coal mine, this paper used the dynamic module of FLAC3D to study the response characteristics of deep super-large section chamber under dynamic and static combined loading condition. Results showed that under the static loading condition, the maximum vertical stress, deformation and failure range are large, where the stress concentration coefficient is 1.64. The maximum roof-to-floor and two-sides deformations are 54.6 mm and 53.1 mm, respectively. Then, under the dynamic and static combined loading condition: (1) The influence of dynamic load frequency on the two-sides is more obvious; (2) The dynamic load amplitude has the greatest influence on the stress concentration degree, and the plastic failure tends to develop to the deeper; (3) With the dynamic load source distance increase, the response of surrounding rock is gradually attenuated. On this basis, empirical equations for each dynamic load conditions were obtained by using regression analysis method, and all correlation coefficients are greater than 0.99. This research provided reference for the supporting design of deep super-large section chamber under same or similar conditions.

The deep fissured rock mass is affected by coupled effects of initial ground stress and external dynamic disturbance. In order to study the effect of internal flaw on pre-stressed rock mechanical responses and failure behavior under impact loading, intact granite specimens and specimens with different flaw inclinations are tested by a modified split Hopkinson pressure bar (SHPB) and digital image correlation (DIC) method. The results show that peak strain and dynamic strength of intact specimens and specimens with different flaw angles (α) decrease with the increase of axial static pressure. The 90° flaw has weak reduction effect on peak strain, dynamic strength and combined strength, while 45° and 0° flaws have remarkable reduction effect. Specimens with 90° flaw are suffered combined shear and tensile failure under middle and low axial static pre-stresses, and suffered shear failure under high axial static pre-stresses. Specimens with 45° and 0° flaws are suffered oblique shear failure caused by pre-existing flaw under different axial static pre-stresses. Besides, based on digital image correlation method, it is found that micro-cracks before formation of macro fractures (include shear and tensile fractures) belong to tensile cracks. Tensile and shear strain localizations at pre-existing flaw tip for specimen with 45° and 0° flaws are produced much earlier than that at other positions.

In order to study the influencing factors of static and dynamic loads on short blunt body balanced wing structures in the external atmospheric environment, and to avoid and prevent structural overload and damage, this paper conducted load tests on short blunt body structures and conducted load correlation analysis. This article establishes a dynamic load testing method for internal excitation and measurement, which is more suitable for dynamic load measurement of small structures compared to traditional wind tunnel testing techniques. On this basis, the influencing factors of dynamic loads were studied. By measuring and changing the Mach number, angle of attack, model frequency, and aerodynamic damping data of the model flight, the influence of the above variables on the static and dynamic loads of the model was obtained. The experimental results indicate that the established measurement technique can accurately and effectively obtain static and dynamic test results of the structure. Pneumatic damping is negatively correlated with dynamic loads, with a correlation coefficient of around -0.8. The Mach number and angle of attack are positively correlated with dynamic loads, with a correlation coefficient of around 0.98. This article establishes a new wind tunnel testing and measurement method, analyzes the influencing factors of dynamic loads, and is of great significance for dynamic load measurement and the design of new aircraft.