Search Results (29)

Under cyclic moving load action, tensile-dominant structures are prone to crack initiation due to cumulative damage effects. The presence of cracks leads to structural stiffness degradation and nonlinear redistribution of dynamic characteristics, thereby compromising str18uctural integrity and service performance. The current research on the dynamic behavior of cracked structures predominantly focuses on transient analysis through high-fidelity finite element models. However, the existing methodologies encounter two critical limitations: computational inefficiency and a trade-off between model fidelity and practicality. Thus, this study presents an innovative analytical framework to investigate the dynamic response of cracked simply supported beams subjected to moving loads. The proposed methodology conceptualizes the cracked beam as a system composed of multiple interconnected sub-beams, each governed by the Euler–Bernoulli beam theory. At crack locations, massless rotational springs are employed to accurately capture the local flexibility induced by these defects. The transfer matrix method is utilized to derive explicit eigenfunctions for the cracked beam system, thereby facilitating the formulation of coupled vehicle–bridge vibration equations through modal superposition. Subsequently, dynamic response analysis is conducted using the Runge–Kutta numerical integration scheme. Extensive numerical simulations reveal the influence of critical parameters—particularly crack depth and location—on the coupled dynamic behavior of the structure subjected to moving loads. The results indicate that at a constant speed, neither crack depth nor position alters the shape of the beam’s vibration curve. The maximum deflection of beams with a 30% crack in the middle span increases by 14.96% compared to those without cracks. Furthermore, crack migration toward the mid-span results in increased mid-span displacement without changing vibration curve topology. For a constant crack depth ratio (γ_i = 0.3), the progressive migration of the crack position from 0.05 L to 0.5 L leads to a 26.4% increase in the mid-span displacement (from 5.3 mm to 6.7 mm). These findings highlight the efficacy of the proposed method in capturing the complex interactions between moving loads and cracked concrete structures, offering valuable insights for structural health monitoring and assessment. Full article

The mode superposition method has been widely used for the seismic response analysis of two-dimensional (2D) sites to enhance computational efficiency. However, this method lacks a guideline of modal truncation to control errors of acceleration responses. In this paper, the mode contribution coefficient of acceleration is proposed to be used as a criterion for modal truncation in the seismic acceleration response analysis of soil layers. Comparative analysis with the modal participation mass and modal contribution factor demonstrates the effectiveness of the proposed factor for the modal truncation of acceleration responses. The computational accuracy of the method for calculating acceleration from displacement using the central difference scheme is verified, which would further improve the computational efficiency in calculating site acceleration responses. A homogeneous soil site and a scarp topography site show that the proposed factor for modal truncation effectively controls the computational error of soil acceleration responses. Additionally, computing acceleration time histories from displacement time histories via the central difference method yields errors comparable to those from directly computing generalized coordinate accelerations. However, modal truncation based on modal participation mass or modal contribution factor results in fewer modes retained and larger computational errors. Full article

Torsional vibration dampers effectively mitigate torsional oscillations and additional stresses in diesel engine crankshaft systems, ensuring operational safety and reliability. Traditional damper selection principles, grounded in dual-pendulum dynamic models, focus on minimizing maximum torsional angles but fail to accurately characterize vibration behaviors in multi-cylinder engines. This study addresses this limitation by investigating dynamic modeling and numerical methods for an eight-cylinder diesel crankshaft system. A torsional vibration model was developed using Cholesky decomposition and the Jacobi sweep method for free vibration analysis, followed by dynamic response calculations through model decoupling and modal superposition. Parameter optimization of the damper was achieved via the NSGA-II multi-objective algorithm combined with a Bayesian-hyperparameter-optimized BP neural network. The results show that high-inertia-ratio dampers effectively suppress vibration and stress, while low-inertia-ratio configurations require approximately 20% elevated tuning ratios beyond theoretical parameters to achieve an additional 5% stress reduction, albeit with amplified torsional oscillations. Additionally, the study critically evaluates the numerical reliability of conventional dual-pendulum-based tuning ratio selection methods. This integrated approach enhances the precision of damper parameter matching for multi-cylinder engine applications. Full article

In transducer arrays, symmetric grouping of identical elements is often employed to achieve uniform array performance. Such arrays can possess high coupling, preventing localized operation of individual transducers. This paper provides insight into how forced vibration localizes in a symmetric system of coupled oscillators. We use a simple lumped-parameter model of highly coupled oscillators derived from ultrasound transducer arrays. Forced vibration localization can be shown to be inversely related to the coupling strength between the oscillators. The results demonstrate how forced vibration in a coupled symmetric system may localize through modal superposition and how it may be tuned via the spacing of natural frequencies. Breaking the system’s symmetry leads to normal mode localization, which can be shown to affect the forced vibration response. The results reveal a variation in the system’s resonance frequency, attributed to curve veering effects. Full article

This study investigates the dynamic amplification effect of the main girder of cable-stayed bridges after cable rupture. The expression for the dynamic amplification effect is derived using the modal superposition method, and the influence of the duration of cable rupture on the dynamic amplification effect is investigated. The results indicate that, for a single-degree-of-freedom (SDOF) system without damping, the displacement dynamic amplification factor (DAF) can reach a maximum of 2.0. For the main girder of cable-stayed bridges, the dynamic amplification factor can exceed 2.0 and is related to the weight of the projection components of the response on the mode shapes. Using the modal superposition method of calculation, the higher-order modes have the greatest influence on shear force, followed by the bending moment, while they have the least influence on displacement. The theoretical derivation is validated using a simplified model, and it is shown that the commonly used equivalent static load calculation method with a factor of 2.0 for the static cable force poses potential safety risks. Furthermore, this study shows that the shorter the duration of cable rupture, the more pronounced the dynamic amplification effect. It is recommended that the duration of the cable rupture should not exceed 0.01 times the fundamental period of the structure when the maximum impact effect is calculated to ensure the rationality of the calculation results. Full article

The stability and behavior of jet flows are critical in various engineering applications, yet many aspects remain insufficiently understood. Previous studies predominantly relied on modal methods to describe small perturbations on jet flow surfaces through the linear superposition of modal waves. However, these approaches largely neglected the interaction between different modes, which can lead to transient energy growth and significantly impact jet stability. This work addresses this gap by focusing on the transient growth of disturbances in jet flows through a comprehensive non-modal analysis, which captures the short-term energy evolution. Unlike modal analysis, which provides insights into the overall trend of energy changes over longer periods, non-modal analysis reveals the instantaneous dynamics of the disturbance energy. This approach enables the identification of transient growth mechanisms that are otherwise undetectable using modal methods, which treat disturbance waves as independent and fail to account for their coupling effects. The results demonstrate that non-modal analysis effectively quantifies the interplay between disturbance waves, capturing the nonlinearity inherent in transient energy growth. This method highlights the short-term amplification of disturbances, providing a more accurate understanding of jet flow stability. Furthermore, the impact of dimensionless parameters such as the Reynolds number, Weber number, and initial wave number on transient energy growth is systematically analyzed. Key findings reveal the optimal conditions for maximizing energy growth and elucidate the mechanisms driving these phenomena. By integrating non-modal analysis, this study advances the theoretical framework of transient energy growth, offering new insights into jet flow stability and paving the way for practical improvements in fluid dynamic systems. Full article

This paper presents a decoupled modal reduction method for the steady-state vibration analysis of vibro-acoustic systems characterized by non-classical damping. The proposed approach initially reduces the order of the coupled governing equations of the vibro-acoustic system through the utilization of non-coupled modes, subsequently employing the complex mode superposition technique to address non-classical damping effects. By leveraging non-coupled modes, this method circumvents the need to solve for coupled modes as required in traditional modal reduction techniques, thereby diminishing both computational complexity and cost. Furthermore, the complex mode superposition method facilitates the decoupling of coupled governing equations with non-classical damping, enhancing computational efficiency. Numerical examples validate both the accuracy and effectiveness of this methodology. Given that modal decomposition is independent of frequency, an analysis of computational efficiency across various stages further substantiates that this method offers significant advantages in terms of efficiency for computational challenges encountered over a broad frequency range. Full article

The effective vibration area includes most of the catenary vibration caused by pantograph–catenary interactions and is the basis of the real-time catenary model for hardware-in-the-loop simulation. However, while the length of the effective vibration area is one of the most important parameters of the real-time catenary model, it has not been fully studied at present. In this paper, the length of the effective vibration area is first investigated. A pantograph–catenary interaction model is developed based on the modal superposition method. After the validation of the model, the vibration energy distribution of the catenary is used to determine the length of the effective vibration area based on the converged total energy. The influence of vehicle velocity and contact wire tension on the vibration energy distribution and length of the effective vibration area is investigated. The obtained appropriate length of effective vibration area is validated by a real-time catenary model and online measurement data of the contact force. The investigation results show that the energy distribution of the catenary can accurately determine the length of effective vibration area, and it increases with increasing vehicle velocity but decreases with increasing contact wire tension. The appropriate length of effective vibration area should be at least 160 m (approximately three spans) in the pantograph–catenary system. Full article

In the field of wind power prediction, traditional methods typically rely on one-dimensional time-series data for feature extraction and prediction. In this study, we propose an innovative short-term wind power forecasting approach using a “visual” 2D image prediction method that effectively utilizes spatial pattern information in time-series data by combining wind power series and related environmental features into a 2D GASF image. Firstly, the wind power data are decomposed using the ICEEMDAN algorithm optimized by the BWO (Beluga Whale Optimization) algorithm, extracting the submodal IMF (Intrinsic Mode Function) components with different frequencies. Then, modal reconstruction is performed on the basis of the permutation entropy value of the IMF components, selecting meteorological features highly correlated with reconstructed components through Spearman correlation analysis for data splicing and superposition before converting them into GASF images. Finally, the GASF images are input into the UniFormer model for wind power sequence prediction. By leveraging wind power data predictions from a coastal wind farm in East China and Sotavento in Spain, this study demonstrates the significant benefits and potential applications of this methodology for precise wind power forecasting. This research combines the advantages of image feature extraction and time-series prediction to offer novel perspectives and tools for predicting renewable energy sources such as wind power. Full article

There are many excitation sources and complex vibration environments in combine harvesters. The coupling and superposition of different vibration signals on the plate and shell seriously affect the working parts of the body. This also reduces the reliability of the whole machine. At present, domestic and foreign research on existing harvesters mainly focuses on harvesting performance, with less research on vibration characteristics. Therefore, in this paper, the vibration response of the metal plate–shell under the two connection modes of bolt connection and welding is studied, in order to optimize the design and structure of the plate–shell structure of the combine harvester and improve the overall performance. First, the welded and bolted plates are numerically modeled using Hypermesh pre-processing functions. Then, the boundary conditions are simulated by continuous variable stiffness elastic constraint experiments. Finally, the intrinsic vibration dynamic model of the four-sided simply supported plate and four-sided solidly supported plate is established using the modal superposition method. By analyzing the modal frequencies and vibration patterns, the following results are obtained. The connection method between the plate and the frame has a significant impact on the inherent vibration characteristics of the plate. The bolt connection will make the plate’s intrinsic vibration frequency higher than that of the welding method, but the effect on the plate’s intrinsic vibration pattern is more minor. At the same time, in order to verify the accuracy of the model, the actual modal vibration patterns and frequencies of the same proportion of plates in the modal test are compared with the results of modal vibration patterns and frequencies obtained by Ansys. The errors of the two dynamic model analytical methods are within 1% and 3%, respectively. This result verifies the accuracy of the dynamic model of the metal plate and shell structure under different connection methods. Full article

The low-frequency vibro-acoustic characteristics of a mechanical equipment—floating raft—cylindrical shell—underwater acoustic field coupled system with nonlinear supports are studied in this paper. Firstly, the state space equations were established by a modal superposition theory for the coupled system, and a modal parameter identification method was deduced and verified for the cylindrical shell—underwater acoustic field coupled subsystem. On this basis, the formulas were derived for transmitted power flow in the coupled system, and the nonlinear stiffness constitutive relation of the vibration isolation supports was expressed by softening and hardening characteristics. Finally, dynamic simulations were carried out by the Runge—Kutta method to analyze the effect of nonlinear stiffness characteristic parameters on the low-frequency vibration modes and vibro-acoustic transfer characteristics in the coupled system. The research shows that a superharmonic phenomenon is common in the steady vibration mode of the coupled system with a nonlinear softening (or hardening) stiffness characteristic under harmonic excitation. The stronger the softening (or hardening) stiffness characteristic is, the more complex the vibration form is, and the smaller (or larger) the low-frequency vibro-acoustic transfer level in resonance regions is. Full article

Curved structures are used in many engineering applications. Temperature affects the performance of structural vibration and acoustics and can damage the equipment when its effects are severe. A theoretical model of the sound transmission loss (STL) of a simply supported curved plate considering the effect of temperature was established. Moreover, a numerical solution was obtained using the modal superposition method. The finite element results were compared to validate the theoretical model. The effects of temperature and acoustic loading on the modal frequency and STL were considered, and the variation laws of the radius of curvature, opening angle, and loss factor on the STL were analyzed. The results showed that the modal frequency increased with decreasing temperature, the frequency ratio of the same-order modal frequency varied approximately linearly with temperature, and the trough of the STL shifted toward high frequencies. The pitch angle substantially influenced the STL, whereas the azimuth angle was negligible. A larger radius increased the effect of temperature. In addition, an increase in the opening angle formed an aggregation of STL at (1, 1)-order modal frequencies. The loss factor affects only the amplitude of the trough position of the STL. Therefore, the proposed theoretical model can aid in the vibroacoustic design of curved plates in a thermal environment. Full article

The high-order mechanical resonances of the sensing element in a high-vacuum environment can significantly degrade the noise and distortion performance of seismic-grade sigma–delta MEMS capacitive accelerometers. However, the current modeling approach is unable to evaluate the effects of high-order mechanical resonances. This study proposes a novel multiple-degree-of-freedom (MDOF) model to evaluate the noise and distortion induced by high-order mechanical resonances. Firstly, the MDOF dynamic equations of the sensing element are derived using the principle of modal superposition and Lagrange’s equations. Secondly, a fifth-order electromechanical sigma–delta system of the MEMS accelerometer is established in Simulink based on the dynamic equations of the sensing element. Then, the mechanism through which the high-order mechanical resonances degrade the noise and distortion performances is discovered by analyzing the simulated result. Finally, a noise and distortion suppression method is proposed based on the appropriate improvement in high-order natural frequency. The results show that the low-frequency noise drastically decreases from about −120.5 dB to −175.3 dB after the high-order natural frequency increases from about 130 kHz to 455 kHz. The harmonic distortion also reduces significantly. Full article

MEMS suspended inductors are susceptible to deformation under external forces, which can lead to the degradation of their electrical properties. The mechanical response of the inductor to a shock load is usually solved by a numerical method, such as the finite element method (FEM). In this paper, the transfer matrix method of linear multibody system (MSTMM) is used to solve the problem. The natural frequencies and mode shapes of the system are obtained first, then the dynamic response by modal superposition. The time and position of the maximum displacement response and the maximum Von Mises stress are determined theoretically and independently of the shock. Furthermore, the effects of shock amplitude and frequency on the response are discussed. These MSTMM results agree well with those determined using the FEM. We achieved an accurate analysis of the mechanical behaviors of the MEMS inductor under shock load. Full article

The flow-induced vibration characteristic of the U-section rubber outer windshield structure of high-speed train is the key factor to limit its high-speed movement. Accurate and effective flow-induced vibration analysis of windshield structures is an important topic. In this paper, a hybrid modeling method for the analysis of flow-induced vibration of windshield structure is innovatively proposed for the U-section rubber windshield system of high-speed train. The method uses the external aerodynamic load obtained by aerodynamic simulation as the input condition of the flow-induced vibration model, and maps the aerodynamic load to the structural dynamics model characterized by the modal test data of the windshield structure. The flow-induced vibration model is established by means of modal superposition method and the time-domain response is effectively integrated by Runge Kutta method with variable step size. The results show that this method can effectively simulate the flow induced vibration of the wind baffle structure, and the real-time relationship between the aerodynamic load and the modal characteristics of the structure and the response of displacement and velocity can be obtained. On this basis, the comprehensive dynamic performance of the windshield system of high-speed trains at 400 km/h under external aerodynamic load is studied, that is, the force, displacement and velocity variation rules of the flexible structure are examined. It is determined that the displacement and velocity response curve of the measuring point near the lower side of the U-section rubber outer windshield is significantly higher than that of other parts. Moreover, the contribution of the first mode to the dynamic response of the structure is very obvious. This method provides an efficient calculation method for analyzing the flow-induced vibration characteristics of complex flexible structures. Full article