Variational Mode Decomposition (VMD) is a powerful formalism for the time-scale analysis of vibration signals from rotating machinery. However, its performance is often compromised by complex parameter configuration, where subjective manual tuning leads to mode mixing or information loss. In this study, we present a physics-guided framework that generalizes VMD optimization across diverse operating conditions. We utilized a meta-dataset combining three distinct sources (CWRU, HUST, UO) to validate the approach. Through a shaft-normalized segmentation strategy and K-Means++ clustering, we identified six distinct signal archetypes based on spectral morphology. Central to this framework is the Energy-Dispersion Index (EDI), a novel physically interpretable metric designed to differentiate between structured fault transients and stochastic noise. Extensive validation via a full-factorial Design of Experiments (8640 trials) confirmed the statistical superiority of EDI over benchmarks like kurtosis and envelope entropy, yielding an 8.3% improvement in modal fidelity. Furthermore, a rigorous ablation study demonstrated that the proposed archetype-based parameterization is highly efficient. This strategy achieved a 392× speedup over online optimization while maintaining statistically equivalent diagnostic accuracy. Additionally, by generalizing parameters from high-quality archetype representatives, the framework reduced spectral leakage (Orthogonality Index) by 51.4% compared to instance-wise optimization. The resulting framework provides a mathematically rigorous, real-time solution for automated vibration signal decomposition.
The free vibration of stiffened plates analyzed using classical plate–beam theoretical theory (PBM) simplified the vibrations of stiffeners parallel to the plane of the stiffened plate as the first-order torsional vibration of the stiffener cross-section. This simplification introduces errors in both the natural frequencies and mode shapes of the structure for stiffened plates with relatively tall stiffeners. To mitigate the issue previously described, this paper proposes an enhanced plate–beam theoretical model (EPBM). The EBPM decouples stiffener deformation into two components: (1) bending deformation along the transverse direction of the stiffened plate, governed by Euler–Bernoulli beam theory, and (2) transverse deformation of the stiffeners, modeled using thin plate theory. Virtual torsional springs are introduced at the stiffener–plate and stiffener–stiffener interfaces via penalty function method to enforce rotational continuity. These constraints are transformed into energy functionals and integrated into the system’s total energy. Displacement trial functions constructed from Chebyshev polynomials of the first kind are solved using the Ritz method. Numerical validation demonstrates that the EBPM significantly improves accuracy over the BPM: errors in free-vibration frequency decrease from 2.42% to 0.63% for the first mode and from 9.79% to 1.34% for the second mode. For constrained vibration, the second-mode error is reduced from 4.22% to 0.03%. This approach provides an effective theoretical framework for the vibration analysis of structures with high stiffeners.
Honeycomb structures are widely utilized in engineering due to their light weight, high strength, high stiffness, excellent energy absorption, and outstanding vibration isolation performance. In this study, we propose a novel tuning fork–honeycomb megastructure, which demonstrates excellent tunable vibration isolation capabilities. The geometric configuration of the structure before and after shape memory–induced deformation is described, and a theoretical model for the natural frequency of the initial configuration is established. The vibration isolation performance of the structure is validated through simulations and experiments, and three strategies for tuning its vibrational behavior are proposed. First, by exploiting variable stiffness, shape memory materials are used to achieve a linear shift in the bandgap position. At 75 °C, the starting frequency of the bandgap decreases to 95% of its value at room temperature. Second, based on shape memory programming, the deformed structure exhibits a 20% reduction in the center frequency of the first bandgap and a 47% reduction in the center frequency of the second bandgap compared to the undeformed configuration. Then, by altering the geometry of the tuning fork structure, in–plane deformation is shown to provide superior low–frequency vibration isolation performance compared to out–of–plane deformation. Finally, the design method of programmable mechanical pixel metamaterials is introduced. This method achieves tunable full–band vibration isolation through shape–memory–induced deformation and temperature–induced stiffness variation. It enhances the structural diversity, modularity, and reconfigurability. Moreover, a shape memory tuning fork structure could be combined with any type of cellular structure with excellent vibration isolation performance. It offers a new paradigm for designing structures with adjustable wide–frequency vibration isolation performance.
Measurement results of train-induced vibrations are evaluated for characteristic frequencies, amplitudes and spectra, leading to a prediction which is based on transfer functions of the vehicle–track–soil system, the soil, and the building–soil system. The characteristic frequencies of train-induced vibrations are discussed following the propagation of vibrations from the source to the receiver: out-of-roundness frequencies of the wheels, the sleeper passage frequency, the vehicle–track eigenfrequency, the car-length frequency and multiples, axle-distance frequencies, bridge eigenfrequencies, the building–soil eigenfrequency, and floor eigenfrequencies. Amplitudes and spectra are compared for different train and track types, for different train speeds, and for different soft and stiff soils, where high frequencies are typically found for stiff soil and low frequencies for soft soil. The ground vibration is between the cut-on frequency due to the layering and the cut-off frequency due to the material damping of the soil, but the dominant frequency range also changes with distance from the track. The frequency band of the axle impulses due to the passing static loads obtains a signature from the axle sequence. The high amplitudes between the zeros of the axle-sequence spectrum are measured at the track, the bridge, and also in the ground vibrations, which are even dominant in the far field. A prediction software is presented, which includes all three parts: the excitation by the vehicle–track interaction, the wave transmission through the soil, and the transfer into a building.
Ball balancers are nonlinear, electromechanical, multivariable, open-loop unstable systems widely used in research laboratories, aerospace, military, and automotive industries to evaluate control mechanism effectiveness. The inherent difficulty in precisely managing ball position, combined with actuator saturation and system sensitivity to disturbances, makes trajectory tracking a persistent challenge. Conventional controllers often exhibit oscillatory responses with steady-state errors exceeding acceptable limits. Sliding mode control (SMC) offers robustness against model uncertainties; however, chattering finite-frequency, finite-amplitude oscillations near the sliding surface caused by switching imperfections, time delays, and actuator dynamics remain a significant limitation. This study addresses chattering through explicit vibration model compensation integrated into the SMC design for a 2-DOF ball balancer system using a visual servoing approach. A double-loop control architecture is implemented, where the inner loop handles servo angular position control and the outer loop manages ball position tracking through visual servoing feedback. The sliding mode controller is designed with a power rate reaching law, synthesizing two control laws: one with explicit vibration model compensation incorporating damping and stiffness terms, and one without. Experimental validation confirmed that SMC with compensation achieved significantly reduced steady-state error (0.034 mm vs. 0.386 mm) and lower overshoot (3.95% vs. 13.81%) compared to the uncompensated variant, with chattering amplitude reduced by approximately 72%.
The Ritz method is applied to an in-plane vibration analysis to obtain accurate frequencies of isotropic annular plates. The method is formulated in a manner that allows all combinations of free boundary conditions, two types of supported (constraining only either radial or circumferential displacement) boundary conditions, and clamped boundary conditions. Admissible functions for the two displacement components are chosen as products of trigonometric functions in the circumferential coordinate and special algebraic polynomials in the radial coordinate, enabling all possible boundary-condition combinations to be satisfied. In the numerical study, after the solution’s accuracy is verified through convergence and comparison tests, extensive and accurate frequency parameters are presented to cover all combinations of the four in-plane boundary conditions along the outer and inner edges of the annular plates.
This work investigates trapped modes induced by localized inhomogeneities in semi-infinite elastic waveguides in the form of a point mass or a meta-spring attached to the edge. Explicit relations linking the parameters of the meta-spring and the mass are presented with a string or beam resting on a Winkler foundation. Asymptotic expansions are derived to describe the limiting behavior of the obtained solutions, including small- and large-mass regimes. Special emphasis is placed on the less-studied trapped modes in an elastically supported beam, providing new insights into the peculiarities of wave localization phenomena, e.g., the analysis of the associated frequency equation.
Helicopter vibration is an inherent characteristic of rotorcraft operations, arising from transmission dynamics and unsteady aerodynamic loading, posing challenges to flight control and longevity of structural components. Excessive vibration elevates pilot workload and accelerates fatigue damage in critical components. Leveraging advances in optimal control and microelectronics, the active vibration control methods offer superior adaptability compared to the passive techniques, which are limited by added weight and narrow bandwidth. In this study, a comprehensive vibration analysis and optimal control framework are developed for the Bo 105 helicopter rotor blade exhibiting flapping, lead-lag, and torsional (triply coupled) motions, where a Linear Quadratic Regulator (LQR) is employed to suppress vibratory responses. An analytical formulation is constructed to estimate the blade’s sectional properties, used to compute the coupled natural frequencies of vibration by the modified Galerkin method. An orthogonality condition for the coupled flap–lag–torsion dynamics is established to derive the corresponding state-space equations for both hovering and forward-flight conditions. The LQR controller is tuned through systematic variation of the weighting parameter Q, revealing an optimal range of 102–104 that balances vibration attenuation and control responsiveness. The predicted frequencies of the vibrating rotor blade are compared with the finite element modeling results and published experimental data. The proposed framework captures the triply coupled rotor blade dynamics with optimal control, achieves modal vibration reductions of approximately 60–90%, and provides a clear theoretical benchmark for future actuator-integrated computational and experimental studies.
A new lumped-parameter matrix method is proposed to model the decoupled, in-plane longitudinal and transverse free undamped vibrations of a collinear system with fixed ends and formed of two end flexible and prismatic members linked by a middle rigid connector. The method calculates the natural frequencies associated with the system’s three degrees of freedom by solving a linear algebraic characteristic equation related to the dynamic matrix, which is obtained from the system compliance and mass matrices. The linear, small-displacement model characterizes either long or short beams by adequately formulating the compliance and mass matrices. The lumped-parameter model is comprehensively validated by two separate distributed-parameter models, which determine the system’s longitudinal-vibration and long-beam, bending-vibration natural frequencies. Numerical simulations are performed with the lumped-parameter model to identify the sensitivity of the natural frequencies to system parameters variations and model variants. The system’s matrices are also utilized to perform frequency-domain analysis of the three-member system in a displacement/acceleration sensing application. The method can be adapted and expanded to describe more complex configurations with multiple, non-collinear, and non-prismatic members.
Construction of precast reinforced concrete (PRC) industrial halls in seismically active areas has been increasing in recent decades. As connections are one of the most sensitive and vulnerable zones of PRC structures, there is a need to pay special attention to their investigation and modeling in seismic analysis. Knowing that each PRC system is specific and unique, this study aims to evaluate the actual seismic performances of PRC industrial halls built in the AMONT system, which represent a significant portion of the existing industrial building stock in Italy, the Balkans, and Turkey. As there is a lack of published research data on its specific joints, the results of the quasi-static full-scale experiments carried out up to failure on the models of four characteristic connections are presented. Since the implementation of nonlinear dynamic analysis in everyday engineering practice can be demanding, a simplified model of the structure considering the effects of the connections’ stiffness is proposed in this paper. The differences in the roof top displacements between the proposed model and the model with the rigid joints of the analyzed frames are in the range from 16.53% to 66.93%. The values of inter-story drift ratios are larger by 10–100% when the real stiffness of connections is considered, which is above the limit value provided by standard EN 1998-1. These results confirm the necessity of considering the nonlinear behavior and stiffness of connections in precast frame structures when determining displacements, which is particularly important for the verification of the serviceability limit state of structures in seismic regions.
Off-road vehicle control designs often neglect the complex tire–soil interactions inherent to soft terrain. This paper proposes a Variable Impedance Control (VIC) strategy integrated with a high-fidelity terramechanics model. First, a real-time sinkage estimation algorithm is derived using experimentally identified Bekker parameters and the quasi-rigid wheel assumption to capture the nonlinear feedback between soil deformation and vehicle dynamics. Building on this, the VIC strategy adaptively regulates virtual stiffness, damping, and inertia parameters based on real-time suspension states. Comparative simulations on an ISO Class-C soft soil profile demonstrate that this framework effectively balances ride comfort and safety constraints. Specifically, the VIC strategy reduces the root-mean-square of vertical body acceleration by 46.9% compared to the passive baseline, significantly outperforming the Linear Quadratic Regulator (LQR). Furthermore, it achieves a 48.6% reduction in average power relative to LQR while maintaining suspension deflection strictly within the safe range. Moreover, unlike LQR, the VIC strategy improves tire deflection performance, ensuring superior ground adhesion. These results validate the method’s robustness and energy efficiency for off-road applications.
Rolling bearings are critical components in rotating machinery, and their failures may lead to significant economic losses and safety hazards. However, early fault signals are often weak and masked by strong background noise, making accurate fault diagnosis extremely challenging. To address this issue, this paper proposes a fault diagnosis method for rolling bearings based on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), an autoregressive (AR) model, and observer-based eigenvalue extraction, combined with a particle swarm optimization-based kernel extreme learning machine (PSO-KELM). Targeting rotating machinery with rolling bearings, the approach begins by applying ICEEMDAN as a preprocessing step to decompose non-stationary vibration signals into multiple intrinsic mode functions (IMFs), from which all essential fault-related information is extracted. The preprocessed vibration signal is then reconstructed. Subsequently, an AR model is used to establish a state-space representation for the observer, which processes the reconstructed signal and generates a residual output by comparing it with the actual mechanical signal. Features are then extracted from the residual signal, including its mean, variance, maximum and minimum values, kurtosis, waveform factor, pulse factor, and clearance factor. These features serve as inputs to the PSO-KELM classifier for fault diagnosis. To validate the method, real vibration data from electric motor bearings were employed in a case study, covering normal conditions and three typical fault types: outer race fault, inner race fault, and rolling element fault. The results demonstrate that the proposed method effectively enables fault feature extraction and accurate identification of bearing conditions.
In a sentinel health event investigation of a back disorder claim, the vibration exposure and ergonomic function of a modified suspension seat were assessed. Background: In a forensic occupational injury investigation, an aftermarket-altered operator seat in a railroad rail-track tamper machine was evaluated. Methods: Detailed whole-body vibration (WBV) exposure measurements were conducted according to current applicable technical standards and guidelines (i.e., ISO 2631-1:1997) on a 09-16 DYNACAT Continuous Action Tamper with Stabilizer during routine track repair services. The modified Grammer Mfg. suspension operator seat was evaluated for performance and ergonomic features (i.e., adjustability, posture, and suspension quality). Results: The tested seat appeared to underperform and was overloaded with the aftermarket control devices, attachments and modifications. The suspension system’s end-stopper was damaged. The seat system had excessive play and wobbles; it was not firmly braced and attached. The vector sum (av) results ranged from 0.26 m/s2 (no tamping) to a maximal 0.55 m/s2 (tamping). The seat transfer (SEAT) analysis showed magnification of vibration input and variable performance of the suspension depending on operational tasks. Conclusions: The modified suspension seat underperformed and seemed to magnify and worsen the vibration, jolts and shock exposures of the seated operator. The heavy and bulky seat modifications likely limited the suspension function. The malfunctioning seat was more likely than not a contributing factor in the pathogenesis of the spinal disorders of the injured machine operator.
Helical gear transmissions in wind turbine gearboxes operate under high torque, variable speed, and complex rolling-sliding contact conditions, where friction-induced wear evolves in a spatially non-uniform manner. However, most existing dynamic models assume uniform or mild wear and therefore fail to capture the nonlinear coupling between localised tooth surface degradation, gear mesh dynamics, and vibration response. In this work, a nonlinear dynamic model of a helical gear pair is formulated by incorporating time-varying mesh stiffness, elasto-hydrodynamic lubrication (EHL)-based friction forces, and wear-dependent contact geometry. The governing equations of motion are derived to explicitly account for the influence of inhomogeneous tooth wear on the contact load distribution and frictional excitation during meshing. Wear evolution is represented as a spatially varying modification of tooth surface topology, enabling the progressive coupling between wear depth, mesh stiffness perturbations, and dynamic transmission error. The model is employed to analyse the effects of non-uniform wear on system stability, vibration spectra, and dynamic response under wind turbine operating conditions. Numerical results reveal that uneven wear introduces nonlinear modulation of gear mesh forces and generates characteristic sidebands and amplitude variations in the vibration signal that are absent in conventional mild-wear formulations. These wear-induced dynamic features provide mathematically traceable indicators for the onset and progression of uneven tooth degradation. The proposed framework establishes a physics-based link between wear evolution and measurable vibration responses, providing a rigorous foundation for advanced vibration-based diagnostics and model-driven condition monitoring of wind turbine gearboxes.
This study develops a semi-analytical method for free vibration analysis of joined conical–cylindrical shell with axially stepped thickness. The computational framework is built through the domain decomposition method, artificial spring technology and shear deformation shell theory. Kinematic admissible functions are constructed via superposition of Chebyshev orthogonal polynomials and trigonometric series. Subsequently, the Rayleigh–Ritz method is employed to solve for the system’s characteristic frequencies. The accuracy of the method is further verified by the excellent agreement between the current results and those from published studies and finite element simulations. Ultimately, the influence of boundary conditions, structural parameters and stepped thickness distribution on the free vibration characteristics of conical–cylindrical shells are systematically discussed. These findings reveal the critical methodological constraints in free vibration modeling of stepped thickness shell systems, thereby advancing vibration design optimization for the stepped thickness structures.
This study presents a specific analytical solution procedure to the local-buckling problem in angle steels using a two-dimensional improved Fourier-series method (2D-IFSM). The effect of coupling between the sub-plates of an angle steel on its local-buckling behaviour is studied by incorporating rotational spring constraints between them. The proposed solution procedure enables one to convert the local-buckling problem of angle steels into solving sets of linear algebraic equations, thereby effectively simplifying its solution process. The critical load and related buckling-mode results obtained in this study are in good agreement with the existing analytical solutions and finite-element-method numerical data, verifying the effectiveness of the proposed method. Based on the derived solutions, a quantitative analysis is conducted to investigate the influences of aspect ratio, width–thickness ratio, and rotational constraint degree on the local-buckling behaviour of angle steels.
Impact-echo/impact response testing is widely used to detect cracks, voids, and delamination, but transient signals and crowded spectra can complicate diagnosis. This study presents a nonlinear, harmonic-based framework that characterizes delamination using higher-order harmonics in the impact-free response, instead of the amplitude-dependent resonance–frequency shift. The delaminated region is formulated as a locally vibrating nonlinear plate/oscillator with polynomial material and geometric nonlinearities, predicting harmonic components whose levels depend on impact intensity and nonlinearity parameters. The approach is validated on a concrete slab containing an artificial delamination, excited by repeatable impacts, and measured with an accelerometer. Frequency-domain analysis shows that intact regions exhibit a distinct spectral pattern, whereas the delaminated region produces a clear fundamental component and, with modestly increased impacts, a strong second harmonic that serves as a defect signature; time series metrics corroborate nonlinearity. The results demonstrate a nondestructive technique that can localize and characterize delamination without driving the specimen into damaging strain. Looking ahead, the same harmonic signature principle can be extended to vibroacoustic/impact monitoring of lithium-ion batteries to flag mechanically induced internal defects (e.g., separator/electrode delamination) that can precipitate internal short circuits and elevate thermal runaway risk, improving quality control and in-service safety.
Enterprises in industries such as coking and metallurgy possess extensive industrial equipment requiring real-time monitoring and timely fault detection. Transmitting all monitoring data to servers or cloud platforms for processing presents challenges, including substantial data volumes, high latency, and significant bandwidth consumption, thereby compromising the monitoring system’s real-time performance and stability. This paper proposes a cloud–edge collaborative approach for edge feature extraction in equipment monitoring. A three-tier collaborative architecture is established: “edge pre-processing-cloud optimization-edge iteration”. At the edge, lightweight time-domain and frequency-domain feature extraction modules are employed based on equipment structure and failure mechanisms to rapidly pre-process and extract features from monitoring data (e.g., equipment vibration), substantially reducing uploaded data volume. The cloud node constructs a diagnostic feature library through threshold self-learning and data-driven model training, then disseminates optimized feature extraction parameters to the edge node via this threshold learning mechanism. The edge node dynamically iterates its feature extraction capabilities based on updated parameters, enhancing the capture accuracy of critical fault features under complex operating conditions. Verification and demonstration applications were conducted using an enterprise’s online equipment monitoring system as the experimental scenario. The results indicate that the proposed method reduces data transmission volume by 98.21% and required bandwidth by 98.25% compared to pure cloud-based solutions, while effectively enhancing the monitoring system’s real-time performance. This approach significantly improves equipment monitoring responsiveness, reduces demands on network bandwidth and data transmission, and provides an effective technical solution for equipment health management within industrial IoT environments.
This article explores whether jerk, the derivative of acceleration, should be limited in trajectory planning for position-controlled mechanical systems or in the controller. The excess jerk excites structural resonances and increases actuator wear, motivating the use of a limited jerk. However, we question the necessity of incorporating the jerk directly in trajectory planning by comparing third-order jerk-limited trajectories with second-order trajectories with reduced controller bandwidth that regulate torque gradients. We demonstrate by a typical practical application that reducing controller bandwidth can achieve comparable or superior jerk reduction without extending overall motion time for point-to-point trajectories. As a result, second-order parabolic trajectory profiles simplify on-line implementation. This investigation relies on a detailed sensitivity analysis of a one-dimensional model, incorporating crucial elements such as signal and sensor quantisation, sampling, and modes of structural resonances. The study shows that smooth trajectories reduce resonant vibrations and wear, but the jerk limitation may be addressed more effectively within the controller rather than within the trajectory generator. We conclude that although the limitation of the jerk in the trajectories is valuable, feedback controllers can reduce the jerk more effectively by bandwidth reduction, allowing simpler point-to-point trajectory designs without compromising performance.
Safety is the most important requirement in flight operations. This also affects the application for an extreme lightweight glider in this paper. Essential properties are the target weight below 120 kg and the electric propulsion. The unsymmetric inertia from the two-blade propeller at the rear in combination with the light and flexible aluminium tube support makes it necessary to investigate the risk of mechanical instability. Starting from the equations of motion, the time-variant system matrices are set up. The simulation of Floquet multiplier and Hill’s hyper-eigenvalue problem provide the necessary information about the system stability. The conclusion is that the potential instability due to structural damping in the observed system can be avoided in the range of operation. The damping, experimentally determined by approximately 2%, is sufficient.
