Vibration

31 pages, 751 KB

Open AccessReview

Modeling and Control of Rigid–Elastic Coupled Hypersonic Flight Vehicles: A Review

by Ru Li, Bowen Xu and Weiqi Yang

Vibration 2026, 9(1), 8; https://doi.org/10.3390/vibration9010008 - 27 Jan 2026

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With the development of aerospace technology, hypersonic flight vehicles are evolving towards larger size, lighter weight, and higher performance. Their cross-domain maneuverability and extreme flight environment led to the rigid–flexible coupling effect and became the core bottleneck restricting performance improvement, seriously affecting flight [...] Read more.

With the development of aerospace technology, hypersonic flight vehicles are evolving towards larger size, lighter weight, and higher performance. Their cross-domain maneuverability and extreme flight environment led to the rigid–flexible coupling effect and became the core bottleneck restricting performance improvement, seriously affecting flight stability and control accuracy. This paper systematically reviews the research status in the field of control for high-speed rigid–flexible coupling aircraft and conducts a review focusing on two core aspects: dynamic modeling and control strategies. In terms of modeling, the modeling framework based on the average shafting, the nondeformed aircraft fixed-coordinate system, and the transient coordinate system is summarized. In addition, the dedicated modeling methods for key issues, such as elastic mode coupling and liquid sloshing in the fuel tank, are also presented. The research progress and challenges of multi-physical field (thermal–structure–control, fluid–structure–control) coupling modeling are analyzed. In terms of control strategies, the development and application of linear control, nonlinear control (robust control, sliding mode variable structure control), and intelligent control (model predictive control, neural network control, prescribed performance control) are elaborated. Meanwhile, it is pointed out that the current research has limitations, such as insufficient characterization of multi-physical field coupling, neglect of the closed-loop coupling characteristics of elastic vibration, and lack of adaptability to special working conditions. Finally, the relevant research directions are prospected according to the priority of “near-term engineering requirements–long-term frontier exploration”, providing Refs. for the breakthrough of the rigid–flexible coupling control technology of the new-generation high-speed aircraft. Full article

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25 pages, 11645 KB

Open AccessArticle

Seismic Assessment of an Existing Precast Reinforced Concrete Industrial Hall Based on the Full-Scale Tests of Joints—A Case Study

by Biljana Mladenović, Andrija Zorić, Dragan Zlatkov, Danilo Ristic, Jelena Ristic, Katarina Slavković and Bojan Milošević

Vibration 2026, 9(1), 7; https://doi.org/10.3390/vibration9010007 - 23 Jan 2026

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Abstract

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 [...] Read more.

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. Full article

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21 pages, 4867 KB

Open AccessArticle

Variable Impedance Control for Active Suspension of Off-Road Vehicles on Deformable Terrain Considering Soil Sinkage

by Jiaqi Zhao, Mingxin Liu, Xulong Jin, Youlong Du and Ye Zhuang

Vibration 2026, 9(1), 6; https://doi.org/10.3390/vibration9010006 - 14 Jan 2026

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Abstract

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 [...] Read more.

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. Full article

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21 pages, 3392 KB

Open AccessArticle

Free Vibration Analysis of Wind-Tunnel Stiffened Plates Considering Stiffeners’ Transverse Deformation

by Yueyin Ma, Zhenhua Chen, Wanhua Chen, Bin Ma, Xinyu Gao, Xutao Nie and Daokui Li

Vibration 2026, 9(1), 5; https://doi.org/10.3390/vibration9010005 - 14 Jan 2026

Viewed by 159

Abstract

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 [...] Read more.

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. Full article

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35 pages, 4724 KB

Open AccessArticle

Vibration and Optimal Control of a Composite Helicopter Rotor Blade

by Pratik Sarker, M. Shafiqur Rahman and Uttam K. Chakravarty

Vibration 2026, 9(1), 4; https://doi.org/10.3390/vibration9010004 - 1 Jan 2026

Viewed by 339

Abstract

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 [...] Read more.

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. Full article

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16 pages, 3351 KB

Open AccessArticle

Stability Analysis for an Ultra-Lightweight Glider Airplane with Electric Driven Two-Blade Propeller

by Joerg Bienert and Simon Regnet

Vibration 2026, 9(1), 3; https://doi.org/10.3390/vibration9010003 - 29 Dec 2025

Viewed by 257

Abstract

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

k g

and the electric propulsion. The unsymmetric inertia from the two-blade propeller [...] Read more.

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

k g

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. Full article

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16 pages, 6189 KB

Open AccessArticle

Research on Edge Feature Extraction Methods for Device Monitoring Based on Cloud–Edge Collaboration

by Lei Chen, Longxin Cui, Dongliang Zou, Yakun Wang, Peiquan Wang and Wenxuan Shi

Vibration 2026, 9(1), 2; https://doi.org/10.3390/vibration9010002 - 21 Dec 2025

Viewed by 337

Abstract

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 [...] Read more.

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. Full article

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15 pages, 2920 KB

Open AccessArticle

Should We Forget the Jerk in Trajectory Generation?

by Robbert van der Kruk

Vibration 2026, 9(1), 1; https://doi.org/10.3390/vibration9010001 - 20 Dec 2025

Viewed by 717

Abstract

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 [...] Read more.

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. Full article

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Vibration, Volume 9, Issue 1 (March 2026) – 8 articles

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