Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (464)

Search Parameters:
Keywords = two degree-of-freedom structure

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
8 pages, 1659 KB  
Proceeding Paper
Coordinate Measuring Machine Touch-Trigger Probe Using Elastic Stylus and Optical Sensors
by Chih-Liang Chu and Chiao-Yu Yeh
Eng. Proc. 2025, 120(1), 2; https://doi.org/10.3390/engproc2025120002 - 23 Dec 2025
Abstract
We developed a three-degree-of-freedom touch trigger probe integrated with two optical sensors. The probe includes an XY-axis cantilever stylus and a Z-axis structure supported by four parallel leaf springs. A laser diode combined with 1D and 2D position-sensing detectors (PSDs) detects [...] Read more.
We developed a three-degree-of-freedom touch trigger probe integrated with two optical sensors. The probe includes an XY-axis cantilever stylus and a Z-axis structure supported by four parallel leaf springs. A laser diode combined with 1D and 2D position-sensing detectors (PSDs) detects angular shifts and displacement when the probe tip touches the measured surface. The optical path change amplifies the PSD response, enhancing sensitivity. Finite-element analysis verifies structural performance, and experimental validation shows the probe achieves a unidirectional repeatability of 0.18 μm. Full article
Show Figures

Figure 1

19 pages, 2210 KB  
Article
Enhancing Seismic Displacement Prediction for Reinforced Concrete Box Girder Bridges Through Nonlinear Time History Analysis
by Bigya Gyawali, Laxman Khanal, Mijia Yang and Peyman Harirchi
Buildings 2025, 15(24), 4458; https://doi.org/10.3390/buildings15244458 - 10 Dec 2025
Viewed by 238
Abstract
Inelastic displacement ratios are critical parameters in the seismic design of reinforced concrete (RC) box girder bridges. Existing approaches of displacement prediction, including the Displacement Coefficient Method and the Capacity Spectrum Method, typically rely on simplified single-degree-of-freedom (SDOF) models, which do not fully [...] Read more.
Inelastic displacement ratios are critical parameters in the seismic design of reinforced concrete (RC) box girder bridges. Existing approaches of displacement prediction, including the Displacement Coefficient Method and the Capacity Spectrum Method, typically rely on simplified single-degree-of-freedom (SDOF) models, which do not fully account for the complex and nonlinear behavior of multi-degree-of-freedom (MDOF) bridge systems. Moreover, the AASHTO Guide Specifications apply the equal displacement rule through the inelastic displacement modification factor Rd, which may underestimate displacement demands for short-period structures. This study evaluates the accuracy of the AASHTO Rd using nonlinear time history analyses of six RC box girder bridge models subjected to 28 recorded ground motions from California. Each ground motion included two orthogonal components applied in the longitudinal and transverse direction. Both elastic and inelastic displacement demands were determined in each direction, and inelastic displacement ratios (Cμ) were computed and compared with AASHTO predictions. A new predictive equation for Cμ was developed to capture response variability. While AASHTO Rd aligns with the average behavior, it fails to provide reliable estimate across the full range of seismic conditions. A comprehensive parametric study was conducted to examine the influence of column boundary condition, column height, superstructure deck width, number of spans, and damping ratio on Cμ. While the elastic and inelastic displacement decreases with an increase in damping ratio, the result shows that Cμ increases with higher damping ratios. Accordingly, a revised amplification factor was proposed to better represent the inelastic displacement demand in MDOF bridge systems. Full article
(This article belongs to the Section Building Structures)
Show Figures

Figure 1

26 pages, 20055 KB  
Article
Design and Development of a Neural Network-Based End-Effector for Disease Detection in Plants with 7-DOF Robot Integration
by Harol Toro, Hector Moncada, Kristhian Dierik Gonzales, Cristian Moreno, Claudia L. Garzón-Castro and Jose Luis Ordoñez-Avila
Processes 2025, 13(12), 3934; https://doi.org/10.3390/pr13123934 - 5 Dec 2025
Viewed by 357
Abstract
This study presents the design and development of an intelligent end-effector integrated into a custom 7-degree-of-freedom (DOF) robotic arm for monitoring the health status of tomato plants during their growth stages. The robotic system combines five rotational and two prismatic joints, enabling both [...] Read more.
This study presents the design and development of an intelligent end-effector integrated into a custom 7-degree-of-freedom (DOF) robotic arm for monitoring the health status of tomato plants during their growth stages. The robotic system combines five rotational and two prismatic joints, enabling both horizontal reach and vertical adaptability to inspect plants of varying heights without repositioning the robot’s base. The integrated vision module employs a YOLOv5 neural network trained with 7864 images of tomato leaves, including both healthy and diseased samples. Image preprocessing included normalization and data augmentation to enhance robustness under natural lighting conditions. The optimized model achieved a detection accuracy of 90.2% and a mean average precision (mAP) of 92.3%, demonstrating high reliability in real-time disease classification. The end-effector, fabricated using additive manufacturing, incorporates a Raspberry Pi 4 for onboard processing, allowing autonomous operation in agricultural environments. The experimental results validate the feasibility of combining a custom 7-DOF robotic structure with a deep learning-based detector for continuous plant monitoring. This research contributes to the field of agricultural robotics by providing a flexible and precise platform capable of early disease detection in dynamic cultivation conditions, promoting sustainable and data-driven crop management. Full article
Show Figures

Figure 1

23 pages, 10451 KB  
Article
Two-Degree-of-Freedom Digital RST Controller Synthesis for Robust String-Stable Vehicle Platoons
by Ali Maarouf, Irfan Ahmad and Yasser Bin Salamah
Symmetry 2025, 17(12), 2067; https://doi.org/10.3390/sym17122067 - 3 Dec 2025
Viewed by 303
Abstract
Cooperative and Autonomous Vehicle (CAV) platoons offer significant potential for improving road safety, traffic efficiency, and energy consumption, but maintaining precise inter-vehicle spacing and synchronized velocity under disturbances while ensuring string stability remains challenging. This paper presents a fully decentralized two-layer architecture for [...] Read more.
Cooperative and Autonomous Vehicle (CAV) platoons offer significant potential for improving road safety, traffic efficiency, and energy consumption, but maintaining precise inter-vehicle spacing and synchronized velocity under disturbances while ensuring string stability remains challenging. This paper presents a fully decentralized two-layer architecture for homogeneous platoons whose identical vehicle dynamics and information flow produce an inherent symmetrical system structure. Operating under a predecessor-following topology with a constant time headway policy, the upper layer generates a smooth velocity reference based on local spacing and relative-velocity errors, while the lower layer employs a two-degree-of-freedom (2-DOF) digital RST controller designed through discrete-time pole placement and sensitivity-function shaping. The 2-DOF structure enables independent tuning of tracking and disturbance-rejection dynamics and provides a computationally lightweight solution suitable for embedded automotive platforms. The paper develops a stability analysis demonstrating internal stability and L2 string stability within this symmetrical closed-loop architecture. Simulations confirm string-stable behavior with attenuated spacing and velocity errors across the platoon during aggressive leader maneuvers and under input disturbances. The proposed method yields smooth control effort, fast transient recovery, and accurate spacing regulation, offering a robust and scalable control strategy for real-time longitudinal motion control in connected and automated vehicle platoons. Full article
(This article belongs to the Section Engineering and Materials)
Show Figures

Figure 1

19 pages, 560 KB  
Article
Modeling PM2.5 Pollution Using a Truncated Positive Student’s-t Distribution: A Case Study in Chile
by Héctor J. Gómez, Karol I. Santoro, Diego I. Gallardo, Paola E. Leal and Tiago M. Magalhães
Mathematics 2025, 13(23), 3838; https://doi.org/10.3390/math13233838 - 30 Nov 2025
Viewed by 186
Abstract
This study revisits a recently proposed member of the truncated positive family of distributions, referred to as the positively truncated Student’s-t distribution. The distribution retains the structure of the classical Student’s-t distribution while explicitly incorporating a kurtosis parameter, yielding a flexible three-parameter formulation [...] Read more.
This study revisits a recently proposed member of the truncated positive family of distributions, referred to as the positively truncated Student’s-t distribution. The distribution retains the structure of the classical Student’s-t distribution while explicitly incorporating a kurtosis parameter, yielding a flexible three-parameter formulation that governs location, scale, and tail behavior. A closed-form quantile function is derived, allowing a novel reparameterization based on the pth quantile and thereby facilitating integration into quantile regression models. The analytical tractability of the quantile function also enables efficient random number generation via the inverse transform method, which supports a comprehensive simulation study demonstrating the strong performance of the proposed estimators, particularly for the degrees-of-freedom parameter. The entire methodology is implemented in the tpn package for the R software. Finally, two real-data applications involving PM2.5 measurements—one without covariates and another with covariates—highlight the model’s robustness and its ability to capture heavy-tailed behavior. Full article
(This article belongs to the Special Issue Mathematical Modelling and Applied Statistics)
Show Figures

Figure 1

19 pages, 3119 KB  
Article
Earthquake-Resilient Structural Control Using PSO-Based Fractional Order Controllers
by Sanoj Kumar, Harendra Pal Singh, Musrrat Ali and Abdul Rahaman Wahab Sait
Fractal Fract. 2025, 9(12), 759; https://doi.org/10.3390/fractalfract9120759 - 23 Nov 2025
Viewed by 442
Abstract
Seismic-induced vibration mitigation in multi-degree-of-freedom (MDOF) building structures calls for efficient and adaptive control strategies. Fractional-order PIλDμ controllers allow increased flexibility in tuning when compared with the conventional proportional integral derivative (PID) controllers. However, considering highly dynamic seismic conditions, selecting [...] Read more.
Seismic-induced vibration mitigation in multi-degree-of-freedom (MDOF) building structures calls for efficient and adaptive control strategies. Fractional-order PIλDμ controllers allow increased flexibility in tuning when compared with the conventional proportional integral derivative (PID) controllers. However, considering highly dynamic seismic conditions, selecting their optimal parameters remains challenging. A Particle Swarm Optimization (PSO)-based fractional order controller approach is presented in this paper for the optimal tuning of five key parameters of the PIλDμ controller using a two-story building model subjected to the 1940 El Centro earthquake. The controller structure is formulated using fractional-order calculus, while PSO is utilized to determine optimal gains and fractional orders without prior knowledge about the model. Simulation results indicate that the proposed fractional order proportional integral derivative (FOPID) controller is effective in suppressing structural vibrations, outperforming both classical PID control and the uncontrolled case. It is demonstrated that incorporating intelligent optimization techniques along with fractional-order control can be a promising approach toward enhancing seismic resilience in civil structures. Full article
Show Figures

Figure 1

15 pages, 4017 KB  
Article
Stiffness Separation Method for Damage Identification in Continuous Rigid Frame Bridges
by Feng Xiao, Linger Xu, Yu Yan and Yujiang Xiang
Sensors 2025, 25(23), 7141; https://doi.org/10.3390/s25237141 - 22 Nov 2025
Viewed by 488
Abstract
Optimization-based damage identification in continuous rigid frame (CRF) bridges faces challenges. As the degrees of freedom of the structure increase, the complexity of the objective functions increases significantly, making convergence more difficult to achieve. This study introduces a stiffness separation method for damage [...] Read more.
Optimization-based damage identification in continuous rigid frame (CRF) bridges faces challenges. As the degrees of freedom of the structure increase, the complexity of the objective functions increases significantly, making convergence more difficult to achieve. This study introduces a stiffness separation method for damage identification in CRF bridges. This method decomposes the overall stiffness matrix of the bridge into the required stiffness submatrices, which greatly simplifies the objective function for identifying structural damage. By dividing the stiffness matrix into smaller stiffness submatrices, the proposed method reduces computational complexity and improves damage detection efficiency. Two CRF bridges are presented to verify the effectiveness of the proposed method. Full article
Show Figures

Figure 1

19 pages, 2318 KB  
Article
Evaluation of the Interactions of Multiple Inverter-Based Resources Using 2DOF Elastic Energy Equivalent System
by Jiangbei Han, Xulin Zheng, Yilan Yu, Lei Shang, Jingjing Bai, Yang Zheng, Yuanyuan Wang, Hao Ding, Zhixiong Su and Xuzhu Dong
Electronics 2025, 14(22), 4479; https://doi.org/10.3390/electronics14224479 - 17 Nov 2025
Viewed by 288
Abstract
Inverter-based resources are widely integrated into power systems, which may interact with each other and induce the risk of oscillation. This paper introduces a two-degree-of-freedom elastic energy equivalent system (2DOF-EEES) to assess interactions in power systems integrated with multiple inverter-based resources. Unlike traditional [...] Read more.
Inverter-based resources are widely integrated into power systems, which may interact with each other and induce the risk of oscillation. This paper introduces a two-degree-of-freedom elastic energy equivalent system (2DOF-EEES) to assess interactions in power systems integrated with multiple inverter-based resources. Unlike traditional impedance-based analysis, the 2DOF-EEES intuitively represents the interactions between multiple inverters and the power network by constructing an equivalent elastic structure with two degrees of freedom. Initially, by equating parallel RLC circuits to a two-degree-of-freedom spring–damper system, the 2DOF-EEES is established. Subsequently, the 2DOF-EEES for the power system, integrated with multiple inverter-based resources, is developed by deriving analytical expressions for common and differential-mode energy. The effectiveness of this method in accurately assessing the oscillatory stability of the system is validated through time-domain simulation. The results further reveal that the differential-mode energy influences the common-mode energy via the equivalent elastic structure in the 2DOF-EEES, thereby affecting the interaction between the wind farm and the network. Full article
Show Figures

Figure 1

21 pages, 5113 KB  
Article
Hysteretic Energy-Based Estimation of Ductility Demand in Single Degree of Freedom Systems
by Baykal Hancıoğlu, Murat Serdar Kirçil and Zekeriya Polat
Buildings 2025, 15(22), 4077; https://doi.org/10.3390/buildings15224077 - 13 Nov 2025
Viewed by 347
Abstract
Ductility, as a fundamental mechanical property, allows structures to undergo inelastic deformations and dissipate seismic energy while maintaining their load-carrying capacity without substantial strength degradation. Thus, the estimation of structural ductility demand has consistently constituted an essential topic of research interest in earthquake [...] Read more.
Ductility, as a fundamental mechanical property, allows structures to undergo inelastic deformations and dissipate seismic energy while maintaining their load-carrying capacity without substantial strength degradation. Thus, the estimation of structural ductility demand has consistently constituted an essential topic of research interest in earthquake engineering. In this study, an iterative procedure for estimating the ductility demand of elastoplastic single-degree-of-freedom (SDOF) systems through dissipated energy is introduced. The proposed procedure helps the determination of ductility demand by use of only elastic response spectra. It initially estimates the hysteretic energy as a proportion of the total input energy. Then, ductility demand is estimated with the help of a developed equation by performing regression analyses based on the nonlinear time history analyses results of elastoplastic single-degree-of-freedom (SDOF) systems with a certain strength. Time history analyses were carried out by using an extensive earthquake ground motion database, which includes a total of 268 far-field records, two horizontal components from 134 recording stations located on firm soil sites. Full article
(This article belongs to the Section Building Structures)
Show Figures

Figure 1

29 pages, 4584 KB  
Article
An Exploratory Study on Vertical Extension with Inter-Story Isolation as a Sustainable Integrated Seismic and Energy Retrofit Strategy
by Michela Basili, Filippo Busato and Rosaria Parente
Sustainability 2025, 17(21), 9713; https://doi.org/10.3390/su17219713 - 31 Oct 2025
Viewed by 422
Abstract
The sustainable rehabilitation of existing buildings is essential to achieve urban resilience, resource efficiency and seismic risk reduction. This study investigates an integrated retrofit strategy that combines vertical extension with inter-story isolation to simultaneously enhance seismic performance and energy efficiency, creating additional usable [...] Read more.
The sustainable rehabilitation of existing buildings is essential to achieve urban resilience, resource efficiency and seismic risk reduction. This study investigates an integrated retrofit strategy that combines vertical extension with inter-story isolation to simultaneously enhance seismic performance and energy efficiency, creating additional usable space without additional land consumption. The inter-story isolation mechanism reduces seismic demand by decoupling a new and existing structure and introducing beneficial damping effects, whereas vertical extension improves a building’s envelope to reduce energy demands for heating and cooling. A tailored design methodology for integrated intervention is presented, according to which, for the structural part, a two-degrees-of-freedom dynamic model is adopted to design the characteristics of the isolation layer. The methodology is applied to a case-study building located in L’Aquila, Italy, where two alternative vertical extensions, one rigid and one lightweight, are analyzed. Time-history analyses and energy simulations for annual primary energy demand are carried out to assess the structural and thermal performance of the integrated retrofit. The results indicate that the proposed solution can reduce top-floor acceleration by up to 35%, inter-story drift by 30–35%, base shear by over 30% and primary energy demand by 11%, demonstrating its effectiveness in improving both seismic safety and energy performance. The main novelty of this study lies in the systematic integration of inter-story isolation with building envelope enhancement through vertical extension, offering a unified design framework that merges structural and energy retrofitting objectives into a single sustainable intervention. Full article
(This article belongs to the Special Issue Sustainable Building: Renewable and Green Energy Efficiency)
Show Figures

Figure 1

21 pages, 4035 KB  
Article
Soft Power Limitation Control for Floating Offshore Wind Turbines
by Kwansoo Kim, Hyun-Gyu Kim, Joong-Hyeok Lee and Jaehoon Son
Energies 2025, 18(21), 5732; https://doi.org/10.3390/en18215732 - 31 Oct 2025
Viewed by 365
Abstract
Floating offshore wind turbines (FOWTs) face significant challenges in maintaining reliable power generation while mitigating structural loads, which are critical for reducing maintenance costs and extending service life. To address these issues, this study evaluates the effectiveness of a Soft Power Limitation Control [...] Read more.
Floating offshore wind turbines (FOWTs) face significant challenges in maintaining reliable power generation while mitigating structural loads, which are critical for reducing maintenance costs and extending service life. To address these issues, this study evaluates the effectiveness of a Soft Power Limitation Control (SPLC) strategy through numerical simulations in DNV Bladed. Two representative design load cases were considered, with design load case (DLC) 1.1 representing normal turbulence and DLC 2.3 representing an extreme operating gust. Under DLC 1.1, SPLC substantially reduced tower fatigue loads, lowering the damage equivalent loads (DELs) of side-to-side and fore–aft bending moments by 21 percent and 15.2 percent, respectively, while blade and mooring loads remained nearly unchanged. Platform motions exhibited modest improvements, including a 6.5 percent reduction in surge peak-to-peak, 2.2 percent in surge RMS, and 2.6 percent in pitch peak-to-peak. Under DLC 2.3, SPLC effectively alleviated extreme responses, decreasing the maximum tower side-to-side bending moment by 30.7 percent and the blade flap-wise bending moment by 15.6 percent, without adverse effects on six-degrees-of-freedom (6-DOFs) platform motions. Overall, the results confirm that SPLC enhances both fatigue and extreme load performance while maintaining stability, highlighting its potential as a practical and cost-effective control strategy to improve the reliability, durability, and commercial viability of FOWTs. Full article
(This article belongs to the Section A3: Wind, Wave and Tidal Energy)
Show Figures

Figure 1

26 pages, 6312 KB  
Article
A Novel Telescopic Aerial Manipulator for Installing and Grasping the Insulator Inspection Robot on Power Lines: Design, Control, and Experiment
by Peng Yang, Hao Wang, Xiuwei Huang, Jiawei Gu, Tao Deng and Zonghui Yuan
Drones 2025, 9(11), 741; https://doi.org/10.3390/drones9110741 - 24 Oct 2025
Viewed by 788
Abstract
Insulators on power lines require regular maintenance by operators in high-altitude hazardous environments, and the emergence of aerial manipulators provides an efficient and safe support for this scenario. In this study, a lightweight telescopic aerial manipulator system is developed, which can realize the [...] Read more.
Insulators on power lines require regular maintenance by operators in high-altitude hazardous environments, and the emergence of aerial manipulators provides an efficient and safe support for this scenario. In this study, a lightweight telescopic aerial manipulator system is developed, which can realize the installation and retrieval of insulator inspection robots on power lines. The aerial manipulator has three degrees of freedom, including two telescopic scissor mechanisms and one pitch rotation mechanism. Multiple types of cameras and sensors are specifically configured in the structure, and the total mass of the structure is 2.2 kg. Next, the kinematic model, dynamic model, and instantaneous contact force model of the designed aerial manipulator are derived. Then, the hybrid position/force control strategy of the aerial manipulator and the visual detection and estimation algorithm are designed to complete the operation or complete the task. Finally, the lifting external load test, grasp and installation operation test, as well as outdoor flight operation test are carried out. The test results not only quantitatively evaluate the effectiveness of the structural design and control design of the system but also verify that the aerial manipulator can complete the accurate automatic grasp and installation operation of the 3.6 kg target device in outdoor flight. Full article
Show Figures

Figure 1

20 pages, 4101 KB  
Article
Research on Aerodynamic Load Simulation Techniques for Floating Vertical-Axis Wind Turbines in Basin Model Test
by Qun Cao, Ying Chen, Kai Zhang, Xinyu Zhang, Zhengshun Cheng, Zhihao Jiang and Xing Chen
J. Mar. Sci. Eng. 2025, 13(10), 1924; https://doi.org/10.3390/jmse13101924 - 8 Oct 2025
Viewed by 563
Abstract
Floating vertical−axis wind turbines present unique advantages for deep−water offshore deployments, but their basin model testing encounters significant challenges in aerodynamic load simulation due to Reynolds scaling effects. While Froude−scaled experiments accurately replicate hydrodynamic behaviors, the drastic reduction in Reynolds numbers at the [...] Read more.
Floating vertical−axis wind turbines present unique advantages for deep−water offshore deployments, but their basin model testing encounters significant challenges in aerodynamic load simulation due to Reynolds scaling effects. While Froude−scaled experiments accurately replicate hydrodynamic behaviors, the drastic reduction in Reynolds numbers at the model scale leads to substantial discrepancies in aerodynamic forces compared to full−scale conditions. This study proposed two methodologies to address these challenges. Fully physical model tests adopt a “physical wind field + rotor model + floating foundation” approach, realistically simulating aerodynamic loads during rotor rotation. Semi−physical model tests employ a “numerical wind field + rotor model + physical floating foundation” configuration, where theoretical aerodynamic loads are obtained through numerical calculations and then reproduced using controllable actuator structures. For fully physical model tests, a blade reconstruction framework integrated airfoil optimization, chord length adjustments, and twist angle modifications through Taylor expansion−based sensitivity analysis. The method achieved thrust coefficient similarity across the operational tip−speed ratio range. For semi−physical tests, a cruciform−arranged rotor system with eight dynamically controlled rotors and constrained thrust allocation algorithms enabled the simultaneous reproduction of periodic streamwise/crosswind thrusts and vertical−axis torque. Numerical case studies demonstrated that the system effectively simulates six−degree−of−freedom aerodynamic loads under turbulent conditions while maintaining thrust variation rates below 9.3% between adjacent time steps. These solutions addressed VAWTs’ distinct aerodynamic complexities, including azimuth−dependent Reynolds number fluctuations and multidirectional force coupling, which conventional methods fail to accommodate. The developed techniques enhanced the fidelity of floating VAWT basin tests, providing critical experimental validation tools for emerging offshore wind technologies. Full article
(This article belongs to the Section Ocean Engineering)
Show Figures

Figure 1

22 pages, 8178 KB  
Article
Vibration Control and Energy Harvesting of a Two-Degree-of-Freedom Nonlinear Energy Sink to Primary Structure Under Transient Excitation
by Xiqi Lin, Xiaochun Nie, Junjie Fu, Yangdong Qin, Lingzhi Wang and Zhitao Yan
Buildings 2025, 15(19), 3561; https://doi.org/10.3390/buildings15193561 - 2 Oct 2025
Viewed by 564
Abstract
Environmental vibrations may affect the functional use of engineering structures and even lead to disastrous consequences. Vibration suppression and energy harvesting based on Nonlinear Energy Sink (NES) and the piezoelectric effect have gained significant attention in recent years. The harvested electrical energy can [...] Read more.
Environmental vibrations may affect the functional use of engineering structures and even lead to disastrous consequences. Vibration suppression and energy harvesting based on Nonlinear Energy Sink (NES) and the piezoelectric effect have gained significant attention in recent years. The harvested electrical energy can supply power to the structural health monitoring sensor device. In this work, the electromechanical-coupled governing equations of the primary structure coupled with the series-connected 2-degree-of-freedom NES (2-DOF NES) integrated by a piezoelectric energy harvester are derived. The absorption and dissipation performances of the system under varying transient excitation intensities are investigated. Additionally, the targeted energy transfer mechanism between the primary structure and the two NESs oscillators is investigated using the wavelet analysis. The reduced slow flow of the dynamical system is explored through the complex-variable averaging method, and the primary factors for triggering the target energy transfer phenomenon are revealed. Furthermore, a comparison is made between the vibration suppression performance of the single-degree-of-freedom NES (S-DOF NES) system and the 2-DOF NES system as a function of external excitation velocity. The results indicate that the vibration suppression performance of the first-level NES (NES1) oscillator is first stimulated. As the external excitation intensity gradually increases, the vibration suppression performance of the second-level NES (NES2) oscillator is also triggered. The 1:1:1, high-frequency, and low-frequency transient resonance captures are observed between the primary structure and NES1 and NES2 oscillators over a wide frequency range. The 2-DOF NES demonstrates superior efficiency in suppressing vibrations of the primary structure and exhibits enhanced robustness to varying external excitation intensities. This provides a new strategy for structural vibration suppression and online power supply for health monitoring devices. Full article
Show Figures

Figure 1

42 pages, 7350 KB  
Review
A Review: Grating Encoder Technologies for Multi-Degree-of-Freedom Spatial Measurement
by Linbin Luo, Maqiang Zhao and Xinghui Li
Sensors 2025, 25(19), 6071; https://doi.org/10.3390/s25196071 - 2 Oct 2025
Cited by 4 | Viewed by 1455
Abstract
In advanced manufacturing, nanotechnology, and aerospace fields, the demand for precision is increasing. Driven by this demand, multi-degree-of-freedom grating encoders have become particularly crucial in high-precision displacement and angle measurement. Over the years, these encoders have evolved from one-dimensional systems to complex multi-degree-of-freedom [...] Read more.
In advanced manufacturing, nanotechnology, and aerospace fields, the demand for precision is increasing. Driven by this demand, multi-degree-of-freedom grating encoders have become particularly crucial in high-precision displacement and angle measurement. Over the years, these encoders have evolved from one-dimensional systems to complex multi-degree-of-freedom measurement solutions that can achieve real-time synchronization. There can also be high-resolution feedback. Its structure is relatively compact, the signal output is also very stable, and the integration degree is high. This gives it a significant advantage in complex measurement tasks. Recently, there have been new developments. The functions of grating encoders in terms of principle, system architecture, error modeling, and signal processing strategies have all been expanded. For instance, accuracy can be improved by integrating multiple reading-heads, while innovative strategies such as error decoupling and robustness enhancement have further advanced system performance. This article will focus on the development of two-dimensional, three-dimensional and multi-degree-of-freedom grating encoders, exploring how the measurement degrees of freedom have evolved, and emphasizing key developments in spatial decoupling, error compensation and system integration. At the same time, it will also discuss some challenges, such as error coupling, system stability and intelligent algorithms for integrating real-time error correction. The future of grating encoders holds great potential. Their applications in precision control, semiconductor calibration, calibration systems, and next-generation intelligent manufacturing technologies can bring promising progress to both industrial and scientific fields. Full article
(This article belongs to the Section Optical Sensors)
Show Figures

Figure 1

Back to TopTop