This paper investigates the nonlinear vibration isolation problem of simply supported beam bridge structures under displacement excitation, employing the Incremental Harmonic Balance Method (IHBM) to derive an approximate analytical solution for the nonlinear vibration response of the beam. The research focuses on a coupled system consisting of a quasi-zero stiffness (QZS) isolator, constructed using a three-spring system, and a simply supported beam bridge. Based on the classical Euler-Bernoulli beam theory, the governing equations of motion under displacement excitation are established and systematically solved using the IHBM, with the entire analytical process thoroughly derived. The study transforms the final solution into a linear matrix equation using generalized coordinates, achieving a procedural and standardized computational process. To validate the reliability of the IHBM approximate analytical results, the study compares the IHBM computational results with numerical solutions obtained using the fourth-order Runge-Kutta method (ODE45). The results demonstrate that the IHBM method exhibits significant advantages in computational stability and result completeness. Additionally, through parametric analysis, the study explores the influence of key isolator parameters on system amplitude, further confirming the effectiveness and engineering practicality of the IHBM in nonlinear vibration isolation research. The research outcomes provide new theoretical foundations and methodological references for the nonlinear vibration isolation analysis of simply supported beam structures, offering important guidance for engineering practice.

With the rapid acceleration of population aging in China, the demand for feeding assistance among individuals with disabilities is becoming increasingly urgent. However, current feeding robots face several limitations such as poor adaptability to complex environments and safety concerns due to rigid structures. In this paper, a new six-degree-of-freedom feeding robot was developed that integrates obstacle avoidance path planning and compliance control. The robotic arm was designed employing a Bi-directional Rapidly-exploring Random Tree (Bi-RRT) algorithm to generate collision-avoidance trajectories, while inverse kinematics was solved using the Denavit-Hartenberg (D-H) parameter. At the control level, an impedance model-based compliance control strategy was introduced, and its compliant behavior under sudden external forces was verified through dynamic simulations. Prototype experiments demonstrated that the robot could effectively avoid obstacles and respond compliantly to external interference. While the robot achieved a 100% feeding success rate with solid and semi-liquid foods, it occasionally experienced spillage when feeding liquids due to structural limitations of the end-effector. This paper provides both a theoretical framework and practical guidance for enhancing the safety and environmental adaptability of feeding robots. Future work will focus on optimizing the end-effector design to further improve performance with liquid foods.

Optimization of the natural frequencies of exponential functionally graded plates is a critical issue in the engineering field, playing a vital role in enhancing the dynamic performance of plate structures. In response to this challenge, this paper presents an innovative optimization approach that synergistically integrates the smoothed finite element method (SFEM) with surrogate models, aiming to address the problem with both high efficiency and precision. Based on the first order shear deformation theory, a SFEM is established for free vibration analyses of functionally graded plates. During the computation of the system stiffness matrix, gradient smoothing operations are applied to bending strains within smoothed domains, effectively improving computational accuracy. To overcome the shear locking phenomenon, different interpolation forms are adopted to treat bending strains and shear strains separately. For natural frequency optimization, a series of sample points are selected, and their corresponding natural frequencies are calculated using the SFEM. Subsequently, a surrogate model is established to map the relationship between the gradient index and the natural frequencies. The golden section method is employed to determine the optimal gradient index that achieves preset natural frequency targets. Numerical examples demonstrate that the surrogate model based on piecewise cubic Hermite interpolation exhibits high computational accuracy. Moreover, the surrogate model-based optimization significantly reduces the number of SFEM frequency calculations required, substantially enhancing optimization efficiency. This approach provides an efficient and practical method for optimizing natural frequencies of exponential functionally graded plates.

A study is conducted on the nonlinear dynamics of inclined flow pipes reinforced with graphene composite materials conveying fluid under two-phase flow conditions. Based on the von Karman nonlinear strain-displacement relationship and Hamilton's principle, the dynamic equations for inclined two-phase flow pipelines are established. The nonlinear dynamic model was solved using Galerkin method and fourth-order Runge-Kutta method to analyze the influence of the distribution pattern, weight fraction, and gas volume fraction of graphene platelets on the natural frequency and nonlinear dynamics of pipes conveying fluid. The experimental results show that the vibration amplitude of graphene reinforced pipes with V-shaped distribution is the smallest, followed by X-shaped distribution and A-shaped distribution. In addition, increasing the gas volume fraction can help alleviate fluid-induced vibration phenomena in pipelines. The above conclusion provides a theoretical basis for the application of graphene-reinforced inclined two-phase flow pipelines in practical engineering.

Split-sleeve cold expansion technology is a critical process for improving the fatigue life of aerospace structural components. However, the influence of its parameter variations on fatigue performance remains insufficiently studied. This paper systematically investigates the sensitivity of initial hole diameter, thickness of split-sleeve, and diameter of the extrusion zone of the mandrel on the fatigue life of 7050-T7451 aluminum alloy through integrated fatigue testing, finite element simulation, and machine learning methods. Based on the S-N curve model of 7050-T7451 aluminum alloy and the critical distance line method, a fatigue life prediction model for cold-expanded holes was established. The model was then used to generate datasets for training an intelligent fatigue life prediction model. Leveraging 400 000 data points obtained from the intelligent model, Sobol global sensitivity analysis was conducted to quantify the independent and interactive contributions of these parameters to fatigue life. Results indicate that the initial hole diameter has the most significant impact on fatigue life, dominating both independent effects and synergistic interactions, while the influence of Thickness of split-sleeve and mandrel diameter primarily manifests through interactive mechanisms. The study proposes prioritizing tolerance optimization for initial hole diameter while adopting collaborative design strategies for sleeve thickness and diameter of the extrusion zone of the mandrel. This methodology provides an efficient and economical approach for identifying critical process parameters and optimizing designs, demonstrating significant advantages over traditional physical experimentation and finite element analysis..

In the process of energy storage and power generation in molten salt tanks, the ceramic particle layer at the bottom of the tank plays a critical role in load-bearing and thermal insulation. Under cyclic loading, analyzing the effects of particle compression, flow, and contact stress on the overall settlement of the ceramic particle layer provides an important basis for design. In this study, the Hertz-Mindlin contact model in EDEM software was employed to establish a discrete element particle simulation model for the ceramic particle layer at the bottom of the molten salt tank. Simulations were conducted for the compaction backfill process and full-tank working conditions, and a comparative analysis was performed to investigate the effects of pre-compaction processes and particle size distribution on the compression settlement and maximum equivalent stress of the ceramic particles, as well as the influence of randomness in discrete element analysis results. The results indicate that for a ceramic particle layer height of 1.6 m and a particle size range of 5~20 mm, adopting a segmented compaction backfill process under a 50 000-ton tank load results in a maximum internal particle stress of 18.1~21.8 MPa and an overall settlement of 20.44~29.6 mm. As the particle size increases, the maximum stress decreases, with a maximum stress of 12 MPa observed for particle sizes of 15~20 mm. However, the settlement increases significantly, reaching 184 mm. Therefore, a wide particle size distribution range is beneficial for reducing settlement. Considering these factors comprehensively, the optimal configuration is a particle size range of 5~20 mm with a segmented and repeated pre-compaction process. Accounting for the influence of particle randomness, the maximum stress of the ceramic particle layer is 23.16 MPa, and the maximum settlement is 23.5 mm, meeting the design requirements.

For the dynamic process of harvesting energy from water droplet impact by using piezoelectric beams, a water droplet impact force model was developed. Based on the Euler Bernoulli beam theory, an electromechanical coupling prediction model of piezoelectric cantilever beam was established. Droplet impact tests were conducted, the voltage output characteristics and dynamic response characteristics of the piezoelectric beams were analyzed. By comparing the experimental results and model prediction results under different impact conditions (droplet diameter D_d=2.4~4.4 mm and impact velocity V_d=1.0~3.4 m/s), the accuracy of the force electromechanical coupling model was verified. Results showed that there is a linear relationship between the maximum deformation of cantilever end and the peak voltage under the impact excitation of water droplets. Water droplets exhibit "rebound" and "splashing" characteristics under low and high Weber number conditions, respectively, and the experimental results are highly consistent with the predicted results of the model, verifying the applicability and accuracy of the model. As the cantilever length increases, the natural frequency and the bending stiffness of the system gradually decreases, the output voltage and the total energy harvested gradually increase; however, the electric energy density shows a trend of first increasing and then decreasing, reaching a maximum of d_E=4.27 mJ/m² when the cantilever beam length L=35 mm.

Currently, over 90% of crude steel production is achieved through continuous casting. Increasing the casting speed during continuous casting can significantly enhance production efficiency, but it also impacts the flow field, exacerbating slag entrapment and argon bubble entrainment, which lead to a series of quality defects. These issues have become critical constraints on the development of high-speed continuous casting molds. This paper establishes a multiphase numerical model of the continuous casting mold by coupling Large Eddy Simulation (LES) with the Volume of Fluid (VOF) method and a two-way coupled Discrete Phase Model (DPM). By analyzing flow field variations, steel-slag interface velocity, interface fluctuations, and slag entrapment ration under three different casting speeds, the internal correlation mechanisms are revealed. The study finds that appropriately increasing casting speed can improve production quality, providing a reference for optimizing casting speed in continuous casting processes.

To reveal the instability failure mechanism and energy evolution law of the rock mass with multiple cracks, a numerical model of red sandstone was established by using PFC2D. The mesoscopic parameters of the numerical model were calibrated based on the results of uniaxial compression tests and Brazilian splitting tests of intact red sandstone specimens. On this basis, the particle flow simulation tests of red sandstone with multiple cracks were carried out. The results show that with the increase of λ, the peak strength of the multiple-cracked red sandstone gradually decreases when the inclination angle remains unchanged; with the gradual increase of the inclination angle α, the peak strength of the multiple-cracked red sandstone gradually increases when the short-long axis ratio λ remains unchanged; the failure mode shows a diagonal tensile-shear failure, with tensile as the main and shear as the auxiliary, and the failure and instability mode of the specimens are all along the extension direction of the prefabricated cracks; the failure mode of the multiple-cracked red sandstone is jointly affected by the short-long axis ratio and the inclination angle; before the peak strength, the rock mainly shows the energy accumulation characteristics; at the peak strength, the total energy of the red sandstone is mainly elastic energy and supplemented by dissipated energy; at the instability failure, the total energy of the red sandstone is mainly dissipated energy and supplemented by elastic energy; the energy storage capacity and failure difficulty of the red sandstone change with the variation of the multiple-crack inclination angle α and the working conditions, which can be used as a reference for rock breaking operations; and a high-precision damage constitutive model of red sandstone based on different height-diameter ratios λ and different joint inclination angles α was established.

Due to the low strength of putty, it is impossible to directly measure its fracture toughness using the standard tensile fracture test. In order to accurately measure the tensile fracture toughness of low-strength materials such as putty, this study presents an improved compact tension test method and derives a tensile fracture toughness formula through numerical analysis. The formula is further refined by accounting for boundary effects, and its accuracy is validated through systematic testing with varying initial crack lengths. The results demonstrate that, the modified formula enables direct calculation of material fracture toughness. The stress intensity factor depends on relative boundary conditions rather than absolute boundary effects, with boundary effects becoming more pronounced with increasing initial crack length. The specimens exhibit pure Mode I fracture, with the modified formula yielding a stable fracture toughness of approximately 42 kN/m^3/2. Experimental validation confirms the accuracy of both the improved test method and the modified formula, establishing their applicability for measuring fracture toughness in low-strength materials like putty and contributing to putty material development.