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Search Results (218)

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Keywords = free and forced vibrations

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16 pages, 2224 KiB  
Article
Electromagnetic Noise and Vibration Analyses in PMSMs: Considering Stator Tooth Modulation and Magnetic Force
by Yeon-Su Kim, Hoon-Ki Lee, Jun-Won Yang, Woo-Sung Jung, Yeon-Tae Choi, Jun-Ho Jang, Yong-Joo Kim, Kyung-Hun Shin and Jang-Young Choi
Electronics 2025, 14(14), 2882; https://doi.org/10.3390/electronics14142882 - 18 Jul 2025
Viewed by 288
Abstract
This study presents an analysis of the electromagnetic noise and vibration in a surface-mounted permanent magnet synchronous machine (SPMSM), focusing on their excitation sources. To investigate this, the excitation sources were identified through an analytical approach, and their effects on electromagnetic noise and [...] Read more.
This study presents an analysis of the electromagnetic noise and vibration in a surface-mounted permanent magnet synchronous machine (SPMSM), focusing on their excitation sources. To investigate this, the excitation sources were identified through an analytical approach, and their effects on electromagnetic noise and vibration were evaluated using a finite element method (FEM)-based analysis approach. Additionally, an equivalent curved-beam model based on three-dimensional shell theory was applied to determine the deflection forces on the stator yoke, accounting for the tooth-modulation effect. The stator’s natural frequencies were derived through the characteristic equation in free vibration analysis. Modal analysis was performed to validate the analytically derived natural frequencies and to investigate stator deformation under the tooth-modulation effect across various vibration modes. Furthermore, noise, vibration, and harshness (NVH) analysis via FEM reveals that major harmonic components align closely with the natural frequencies, identifying them as primary sources of elevated vibrations. A comparative study between 8-pole–9-slot and 8-pole–12-slot SPMSMs highlights the impact of force variations on the stator teeth in relation to vibration and noise characteristics, with FEM verification. The proposed method provides a valuable tool for early-stage motor design, enabling the rapid identification of resonance operating points that may induce severe vibrations. This facilitates proactive mitigation strategies to enhance motor performance and reliability. Full article
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33 pages, 4996 KiB  
Article
Rain-Induced Vibration Energy Harvesting Using Nonlinear Plates with Piezoelectric Integration and Power Management
by Yi-Ren Wang, Wei Ting Lin and Bo-Jang Huang
Sensors 2025, 25(14), 4347; https://doi.org/10.3390/s25144347 - 11 Jul 2025
Viewed by 332
Abstract
Vibration energy offers promising potential for renewable energy harvesting, especially in conditions where conventional sources such as solar power may be limited or intermittent. This study proposes a rain energy harvester (REH) that converts the kinetic energy of raindrops into electrical energy using [...] Read more.
Vibration energy offers promising potential for renewable energy harvesting, especially in conditions where conventional sources such as solar power may be limited or intermittent. This study proposes a rain energy harvester (REH) that converts the kinetic energy of raindrops into electrical energy using nonlinear thin plates, integrated with piezoelectric elements. Two plate configurations—fully hinged (H-H-H-H) and clamped–hinged–free–hinged (C-H-F-H)—are investigated. Theoretical modeling and simulation results are compared with experimental data, with special attention paid to the role of slapping forces in improving prediction accuracy. A power management system is also introduced to stabilize and regulate the harvested voltage. Results confirm the feasibility of rain-induced energy harvesting, showing potential for application in rain-prone areas and integration with existing infrastructure such as solar panels, tents, or canopies. Full article
(This article belongs to the Special Issue Advances in Energy Harvesting and Sensor Systems)
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14 pages, 739 KiB  
Article
Variational Principles for Coupled Boron Nitride Nanotubes Undergoing Vibrations, Including Piezoelastic and Surface Effects
by Sarp Adali
Dynamics 2025, 5(2), 21; https://doi.org/10.3390/dynamics5020021 - 8 Jun 2025
Viewed by 735
Abstract
A variational formulation and variationally consistent boundary conditions were derived for a coupled system of two boron nitride nanotubes (BNNTs), with the piezoelectric and surface effects taken into account in the formulation. The coupling between the nanotubes was defined in terms of Winkler [...] Read more.
A variational formulation and variationally consistent boundary conditions were derived for a coupled system of two boron nitride nanotubes (BNNTs), with the piezoelectric and surface effects taken into account in the formulation. The coupling between the nanotubes was defined in terms of Winkler and Pasternak interlayers. The equations governing the vibrations of the coupled system were expressed as a system of four partial differential equations based on nonlocal elastic theory. After deriving the variational principle for the double BNNT system, Hamilton’s principle was expressed in terms of potential and kinetic energies. Next, the differential equations for the free vibration case were presented and the variational form for this case was derived. The Rayleigh quotient was formulated for the vibration frequency, which indicated that piezoelectric and surface effects led to higher vibration frequencies. Next, the variationally consistent boundary conditions were formulated in terms of moment and shear force expressions. It was observed that the presence of the Pasternak interlayer between the nanotubes led to coupled boundary conditions when a shear force and/or a moment was specified at the boundaries. Full article
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18 pages, 4697 KiB  
Article
Wave-Screening Methods for Prestress-Loss Assessment of a Large-Scale Post-Tensioned Concrete Bridge Model Under Outdoor Conditions
by Chun-Man Liao, Felix Bernauer, Ernst Niederleithinger, Heiner Igel and Céline Hadziioannou
Appl. Sci. 2025, 15(11), 6005; https://doi.org/10.3390/app15116005 - 27 May 2025
Viewed by 459
Abstract
This paper presents advancements in structural health monitoring (SHM) techniques, with a particular focus on wave-screening methods for assessing prestress loss in a large-scale prestressed concrete (PC) bridge model under outdoor conditions. The wave-screening process utilizes low-frequency wave propagation obtained from seismic interferometry [...] Read more.
This paper presents advancements in structural health monitoring (SHM) techniques, with a particular focus on wave-screening methods for assessing prestress loss in a large-scale prestressed concrete (PC) bridge model under outdoor conditions. The wave-screening process utilizes low-frequency wave propagation obtained from seismic interferometry of structural free vibrations and high-frequency wave propagation obtained through ultrasonic transducers embedded in the structure. An adjustable post-tensioning system was employed in a series of experiments to simulate prestress loss. By comparing bridge vibrations under varying post-tensioning forces, the study investigated prestress loss and examined temperature-related effects using the coda wave interferometry (CWI) method. Local structural alterations were analyzed through wave velocity variations, demonstrating sensitivity to bridge temperature changes. The findings indicate that wave-based methods are more effective than traditional modal analysis for damage detection, highlighting the dual impacts of prestress loss and temperature, as well as damage localization. This study underscores the need for long-term measurements to account for temperature fluctuations when analyzing vibration measurements to investigate changes in prestressing force in PC structures. Full article
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15 pages, 6253 KiB  
Article
Performance and Mechanism on Sand Mold Ultrasonic Milling
by Bailiang Zhuang, Zhongde Shan, Zhuozhi Zhu, Di Ding and Qi Zhao
Coatings 2025, 15(6), 633; https://doi.org/10.3390/coatings15060633 - 25 May 2025
Viewed by 407
Abstract
Sand mold milling plays a critical role in digital mold-free casting, but it is prone to damage such as corner collapse, collapse, and cracks during the machining process. To address this issue, ultrasonic vibration was used for sand mold milling in this study. [...] Read more.
Sand mold milling plays a critical role in digital mold-free casting, but it is prone to damage such as corner collapse, collapse, and cracks during the machining process. To address this issue, ultrasonic vibration was used for sand mold milling in this study. By incorporating the solid–liquid transition model for sand mold cutting and considering the deformation characteristics of the shear zone, a prediction model for ultrasonic milling forces in sand mold was developed and experimentally validated. The results demonstrate that increasing the spindle speed and decreasing the feed rate lead to a decrease in cutting force. At high speeds, there is a 15% error between the dynamic milling force model and experimental values. Compared with conventional processing methods, ultrasonic processing reduces cutting force by 19.5% at a frequency of 25.8 kHz and amplitude of 2.97 μm, minimizes defects like sand particle detachment pits on the surface of sand mold, significantly improves surface quality, and enables precise, stable, high-precision, and efficient sand mold processing. Full article
(This article belongs to the Special Issue Cutting Performance of Coated Tools)
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33 pages, 2465 KiB  
Article
A Unified Size-Dependent Theory for Analyzing the Free Vibration Behavior of an FG Microplate Under Fully Simply Supported Conditions and Magneto-Electro-Thermo-Mechanical Loads Considering Couple Stress and Thickness Stretching Effects
by Chih-Ping Wu and Cheng-Dao Hsu
J. Compos. Sci. 2025, 9(5), 201; https://doi.org/10.3390/jcs9050201 - 24 Apr 2025
Viewed by 444
Abstract
This work develops a unified size-dependent shear deformation theory (SDSDT) to analyze the free vibration behavior of a functionally graded (FG) magneto-electro-elastic (MEE) microplate under fully simply supported conditions, open- or closed-circuit surface conditions, biaxial compression, magnetic and electric potentials, and uniform temperature [...] Read more.
This work develops a unified size-dependent shear deformation theory (SDSDT) to analyze the free vibration behavior of a functionally graded (FG) magneto-electro-elastic (MEE) microplate under fully simply supported conditions, open- or closed-circuit surface conditions, biaxial compression, magnetic and electric potentials, and uniform temperature changes based on consistent couple stress theory (CCST). The FG-MEE microplate is composed of BaTiO3 (a piezoelectric material) and CoFe2O4 (a magnetostrictive material). Various CCST-based SDSDTs, considering couple stress and thickness stretching effects, can be reproduced by employing a generalized shape function that characterizes shear deformation distributions along the thickness direction within the unified SDSDT. These CCST-based SDSDTs encompass the size-dependent classical plate theory (CPT), first-order shear deformation theory (SDT), Reddy’s refined SDT, exponential SDT, sinusoidal SDT, and hyperbolic SDT. The unified SDSDT is validated by comparing its solutions with relevant three-dimensional solutions available in the literature. After validation and comparison studies, we conduct a parametric study, whose results indicate that the effects of thickness stretching, material length-scale parameter, inhomogeneity index, and length-to-thickness ratio, as well as the magnitude of biaxial compressive forces, electric potential, magnetic potential, and uniform temperature changes significantly impact the microplate’s natural frequency. Full article
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10 pages, 248 KiB  
Article
Vibrations of an Elastic Half-Space
by Bogdan Felix Apostol
Geosciences 2025, 15(4), 144; https://doi.org/10.3390/geosciences15040144 - 9 Apr 2025
Viewed by 453
Abstract
We report on the resolution of the vibration problem for a homogeneous and isotropic elastic half-space (the Lamb problem), with application to the seismic tensorial force. We assume a homogeneous and isotropic half-space with a localized force which produces vibrations. The solution is [...] Read more.
We report on the resolution of the vibration problem for a homogeneous and isotropic elastic half-space (the Lamb problem), with application to the seismic tensorial force. We assume a homogeneous and isotropic half-space with a localized force which produces vibrations. The solution is achieved by introducing vector plane-wave functions. Explicit results are given for an isotropic tensorial force and a half-space with free surface. The contribution of the Rayleigh surface waves to vibrations is analyzed in the special case of a temporal-impulse force, where the solution exhibits unphysical features, as expected: it extends over the entire free surface and time domain, with a (scissor-like) double-wall propagating both in the future and the past. Full article
(This article belongs to the Special Issue Editorial Board Members' Collection Series: Natural Hazards)
21 pages, 7487 KiB  
Article
Free- and Forced-Vibration Characteristic Analysis of a Double-Layered Cylindrical Shell with General Boundary Conditions
by Jianghai Wu, Hongzhen Zhu and Yong Duan
J. Mar. Sci. Eng. 2025, 13(4), 641; https://doi.org/10.3390/jmse13040641 - 24 Mar 2025
Cited by 1 | Viewed by 432
Abstract
The double-layered cylindrical shell represents a key structural configuration for underwater vehicles, where its vibration behavior remains a primary concern in engineering design and analysis. This study develops a spectral element method (SEM) for dynamic modeling of multi-component shell systems by extending the [...] Read more.
The double-layered cylindrical shell represents a key structural configuration for underwater vehicles, where its vibration behavior remains a primary concern in engineering design and analysis. This study develops a spectral element method (SEM) for dynamic modeling of multi-component shell systems by extending the vibrational governing equations of conical shells. The methodology is validated through finite element method (FEM) case studies on both conical shells and double-layered cylindrical configurations. Parametric investigations examine ribbed substructures and solid rib plates within the cylindrical shell assembly, while artificial spring techniques model arbitrary boundary conditions—with validation against classical benchmarks confirming their effectiveness for elastic constraints. Numerical demonstrations reveal the following: rib and plate thickness variations exhibit a negligible impact on low-frequency vibrational responses; the natural frequency sensitivity peaks when the elastic boundary stiffness approaches the inherent dynamic stiffness of the shell’s base configuration, while extreme stiffness values approximate clamped or free boundary conditions with engineering significance. The proposed SEM framework demonstrates a superior computational efficiency and accuracy compared to conventional FEM approaches. These findings deliver practical guidance for marine structural engineering, particularly in the boundary condition specifications and performance optimization of composite shell systems. Full article
(This article belongs to the Section Ocean Engineering)
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25 pages, 17680 KiB  
Article
Evaluating Inertial Parameter Uncertainty in High-Acceleration Movements and Improving Predictions Through Identification Using Free Vibration Measurements
by Takahiro Homma and Hiroshi Yamaura
Biomechanics 2025, 5(1), 18; https://doi.org/10.3390/biomechanics5010018 - 14 Mar 2025
Viewed by 501
Abstract
Background/Objectives: This study aimed to examine how uncertainties in inertial properties and minimal sets of inertial parameters (MSIP) affect inverse-dynamics simulations of high-acceleration sport movements and to demonstrate that applying MSIP identified through the free vibration measurement method improves simulation accuracy. Methods: Monte [...] Read more.
Background/Objectives: This study aimed to examine how uncertainties in inertial properties and minimal sets of inertial parameters (MSIP) affect inverse-dynamics simulations of high-acceleration sport movements and to demonstrate that applying MSIP identified through the free vibration measurement method improves simulation accuracy. Methods: Monte Carlo simulations were performed for running, side-cutting, vertical jumping, arm swings, and leg swings by introducing uncertainties in inertial properties and MSIP. Results: These uncertainties significantly affect the joint torques and ground reaction forces and moments (GRFs&Ms), especially during large angular acceleration. The mass and longitudinal position of the center of gravity had strong effects. Subsequently, MSIP identified by our methods with free vibration measurement were applied to the same tasks, improving the accuracy of the predicted ground reaction forces compared with the standard regression-based estimates. The root mean square error decreased by up to 148 N. Conclusions: These results highlight that uncertainties in inertial properties and MSIP affected the calculated joint torques and GRFs&Ms, and combining experimentally identified MSIP with dynamics simulations enhances precision. These findings demonstrate that utilizing the MSIP from free vibration measurement in inverse dynamics simulations improves the accuracy of dynamic models in sports biomechanics, thereby providing a robust framework for precise biomechanical analyses. Full article
(This article belongs to the Section Sports Biomechanics)
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32 pages, 7060 KiB  
Article
Vibration Analysis of Functionally Graded Material (FGM) Double-Layered Cabin-like Structure by the Spectro-Geometric Method
by Dongze He, Rui Zhong, Qingshan Wang and Bin Qin
Materials 2025, 18(6), 1231; https://doi.org/10.3390/ma18061231 - 10 Mar 2025
Viewed by 706
Abstract
This study presents a spectro-geometric vibration model for analyzing free as well as forced vibration properties for FGM cylindrical double-walled shells with internal structures. The boundary conditions and coupling effects are modeled using an artificial virtual spring approach, which allows for the simulation [...] Read more.
This study presents a spectro-geometric vibration model for analyzing free as well as forced vibration properties for FGM cylindrical double-walled shells with internal structures. The boundary conditions and coupling effects are modeled using an artificial virtual spring approach, which allows for the simulation of arbitrary boundary and coupling conditions by varying the elastic spring stiffness coefficients. The spectral geometry method is employed to represent the displacement variables of the FGM substructure, overcoming the discontinuity phenomenon commonly observed when traditional Fourier series are used. The dynamic equations of the FGM cylindrical double-walled shell with an internal structure are derived using the first-order shear deformation assumption and the Rayleigh–Ritz method, and the corresponding vibration solutions are computed. The model’s reliability and prediction accuracy are confirmed through convergence checks and numerical comparisons. Additionally, parametric studies are conducted to examine the influence of material constants, position parameters, and geometric parameters on the shell’s inherent characteristics and steady-state response. Full article
(This article belongs to the Special Issue Mechanical Behavior of Advanced Composite Materials and Structures)
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21 pages, 6656 KiB  
Article
A Flexible PVDF Sensor for Forcecardiography
by Salvatore Parlato, Jessica Centracchio, Eliana Cinotti, Gaetano D. Gargiulo, Daniele Esposito, Paolo Bifulco and Emilio Andreozzi
Sensors 2025, 25(5), 1608; https://doi.org/10.3390/s25051608 - 6 Mar 2025
Cited by 1 | Viewed by 1634
Abstract
Forcecardiography (FCG) uses force sensors to record the mechanical vibrations induced on the chest wall by cardiac and respiratory activities. FCG is usually performed via piezoelectric lead-zirconate titanate (PZT) sensors, which simultaneously record the very slow respiratory movements of the chest, the slow [...] Read more.
Forcecardiography (FCG) uses force sensors to record the mechanical vibrations induced on the chest wall by cardiac and respiratory activities. FCG is usually performed via piezoelectric lead-zirconate titanate (PZT) sensors, which simultaneously record the very slow respiratory movements of the chest, the slow infrasonic vibrations due to emptying and filling of heart chambers, the faster infrasonic vibrations due to movements of heart valves, which are usually recorded via Seismocardiography (SCG), and the audible vibrations corresponding to heart sounds, commonly recorded via Phonocardiography (PCG). However, PZT sensors are not flexible and do not adapt very well to the deformations of soft tissues on the chest. This study presents a flexible FCG sensor based on a piezoelectric polyvinylidene fluoride (PVDF) transducer. The PVDF FCG sensor was compared with a well-assessed PZT FCG sensor, as well as with an electro-resistive respiratory band (ERB), an accelerometric SCG sensor, and an electronic stethoscope for PCG. Simultaneous recordings were acquired with these sensors and an electrocardiography (ECG) monitor from a cohort of 35 healthy subjects (16 males and 19 females). The PVDF sensor signals were compared in terms of morphology with those acquired simultaneously via the PZT sensor, the SCG sensor and the electronic stethoscope. Moreover, the estimation accuracies of PVDF and PZT sensors for inter-beat intervals (IBIs) and inter-breath intervals (IBrIs) were assessed against reference ECG and ERB measurements. The results of statistical analyses confirmed that the PVDF sensor provides FCG signals with very high similarity to those acquired via PZT sensors (median cross-correlation index of 0.96 across all subjects) as well as with SCG and PCG signals (median cross-correlation indices of 0.85 and 0.80, respectively). Moreover, the PVDF sensor provides very accurate estimates of IBIs, with R2 > 0.99 and Bland–Altman limits of agreement (LoA) of [−5.30; 5.00] ms, and of IBrIs, with R2 > 0.96 and LoA of [−0.510; 0.513] s. The flexibility of the PVDF sensor makes it more comfortable and ideal for wearable applications. Unlike PZT, PVDF is lead-free, which increases safety and biocompatibility for prolonged skin contact. Full article
(This article belongs to the Special Issue Sensors for Heart Rate Monitoring and Cardiovascular Disease)
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18 pages, 5150 KiB  
Article
Effect of Hard-Segment Structure on the Properties of Polyurethane/Poly(Ethyl Methacrylate) Damping Composites
by Jinbao Ma, Chi Ma, Risheng Long, Yan Jiang, Xingjia Wang, Chang Liu, Fan Li and Lee Tin Sin
Polymers 2025, 17(5), 636; https://doi.org/10.3390/polym17050636 - 27 Feb 2025
Viewed by 1172
Abstract
Damping material performance influences the efficacy of vibration and noise reduction. However, traditional damping materials often have low damping peaks or narrow damping temperature ranges. In this study, a series of polyurethane (PU)/poly(ethylene methacrylate) (PEMA) composites were synthesised, in which the PU hard [...] Read more.
Damping material performance influences the efficacy of vibration and noise reduction. However, traditional damping materials often have low damping peaks or narrow damping temperature ranges. In this study, a series of polyurethane (PU)/poly(ethylene methacrylate) (PEMA) composites were synthesised, in which the PU hard segments were varied using toluene diisocyanate (TDI), diphenylmethane diisocyanate (MDI), isophorone diisocyanate (IPDI), and hexamethylene diisocyanate. The soft segments comprised tetrahydrofuran homopolymer glycol. The influence of the hard-segment structure on the properties of the PU/PEMA composites was investigated by infrared spectroscopy, thermogravimetric analysis, dynamic mechanical thermal analysis, and other experimental methods. The performance mechanism was explored from a molecular perspective via integration with molecular dynamics simulations. The PU/PEMA material with IPDI hard segments comprised numerous microphase-separated structures and exhibited greater free volume, fuller molecular-chain movement, and the highest damping performance, with a loss factor of 0.56. The PU/PEMA composites synthesised with TDI and MDI hard segments exhibited better compatibility, with the MDI-PU/PEMA system exhibiting a higher hydrogen-bonding force. This material also exhibited a higher thermal stability, with an initial breakdown temperature of 287.87 °C. This study provides a basis for regulating and optimising the performance of PU-based damping materials. Full article
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19 pages, 3944 KiB  
Article
Study of Reynolds Number Effects on Aerodynamic Forces and Vortex-Induced Vibration Characteristics of a Streamlined Box Girder
by Binxuan Wang, Yifei Sun, Qingkuan Liu, Zhen Li, Yuan Han and Kaiwen Li
Appl. Sci. 2025, 15(4), 2202; https://doi.org/10.3390/app15042202 - 19 Feb 2025
Viewed by 667
Abstract
Due to the limitations of wind tunnel speed and size, achieving a model’s Reynolds number equal to the actual Reynolds number is challenging and may lead to discrepancies between experimental and actual results. To investigate the effects of the Reynolds number on the [...] Read more.
Due to the limitations of wind tunnel speed and size, achieving a model’s Reynolds number equal to the actual Reynolds number is challenging and may lead to discrepancies between experimental and actual results. To investigate the effects of the Reynolds number on the aerodynamic forces and vortex-induced vibration (VIV) characteristics of a streamlined box girder, wind tunnel tests were conducted to study the variations in aerodynamic forces and surface pressures on the static main beam, as well as the VIV response and time–frequency characteristics of the aerodynamic forces on the dynamic main beam, as the Reynolds number varied. The results indicate that in static tests, as the Reynolds number increases, the drag coefficient of the main beam decreases, the lift coefficient slightly increases, and the pitching moment coefficient remains almost unchanged. The root mean square (RMS) values of the wind pressure coefficients show a significant Reynolds number effect, with values generally decreasing as the Reynolds number increases. In free vibration tests, as the Reynolds number increases, the onset wind speed of VIV increases from 14.35 m/s to 16.03 m/s, the maximum amplitude decreases from 0.076 to 0.004, and the VIV lock-in range narrows. The dynamic pressure results indicate that as the Reynolds number increases, the RMS values of the wind pressure coefficients decrease. At some measurement points, the dominant frequencies of the fluctuating pressure amplitude spectra deviate from the corresponding VIV frequency, and the correlation and contribution coefficients between the local aerodynamic forces and the overall vortex-induced force (VIF) decrease. These changes may explain the reduction in the VIV amplitude with an increasing Reynolds number. The motion state of the main beam has a minimal effect on the mean wind pressure coefficients and their Reynolds number effect, whereas it has a more significant effect on the RMS values of the pressure coefficients. Full article
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17 pages, 4722 KiB  
Article
Research on Space Maglev Vibration Isolation Control System Modeling and Simulation
by Mao Ye and Jianyu Wang
Appl. Sci. 2025, 15(3), 1648; https://doi.org/10.3390/app15031648 - 6 Feb 2025
Cited by 1 | Viewed by 880
Abstract
The working accuracy of space optical payloads and sensitive components carried on space aircraft greatly depends on the pointing accuracy and stability of the platform. Based on Disturbance Free Payload (DFP) technology, non-contact maglev technology is proposed in this paper, achieving dynamic and [...] Read more.
The working accuracy of space optical payloads and sensitive components carried on space aircraft greatly depends on the pointing accuracy and stability of the platform. Based on Disturbance Free Payload (DFP) technology, non-contact maglev technology is proposed in this paper, achieving dynamic and static isolation of the platform module and payload module, so that the vibration and interference of the platform module with movable and flexible components will not be transmitted to the payload module, thereby achieving the effect of vibration isolation. High-precision active control of the payload module is adopted at the same time; the platform module follows the master–slave collaborative control strategy of the payload module, meeting the requirements of high-performance payloads. A primary and backup redundant controller is designed, using a one-to-four architecture. The control board achieves high-speed and high-precision driving current control, voltage output, and outputs current feedback signal sampling. Based on uniform magnetic field design, high-precision force control performance is ensured by adjusting current accuracy. Interdisciplinary joint simulation of electric, magnetic, and structural aspects was conducted on the magnetic levitation isolation system. By conducting physical testing and calibration and designing a testing and calibration system, it has been proven that the system meets the design requirements, achieving high-precision current control technology of 0.15 mA and driving force control technology of 0.5 mN. Full article
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26 pages, 8754 KiB  
Article
Weight Effects on Vertical Transverse Vibration of a Beam with a Nonlinear Energy Sink
by Xiang Fu, Sha Wei, Hu Ding and Li-Qun Chen
Appl. Sci. 2025, 15(3), 1380; https://doi.org/10.3390/app15031380 - 29 Jan 2025
Cited by 2 | Viewed by 753
Abstract
Reductions in the vibration of a continuum system via a nonlinear energy sink have been widely investigated. It is usually assumed that weight effects can be ignored if the vibration is measured from the static equilibrium configuration. The present investigation reveals the dynamic [...] Read more.
Reductions in the vibration of a continuum system via a nonlinear energy sink have been widely investigated. It is usually assumed that weight effects can be ignored if the vibration is measured from the static equilibrium configuration. The present investigation reveals the dynamic effects of weight on the vertical transverse vibrations of a Euler–Bernoulli beam coupled with a nonlinear energy sink. The governing equations considering and neglecting weights were derived. The equations were discretized with some numerical support. The discretized equations were analytically solved via the harmonic balance method. The harmonic balance solutions were compared with the numerical solution via the Runge–Kutta method. Finite element simulations were performed via ANSYS software (version number: 2.2.1). Free and forced vibrations, predicted by equations considering or neglecting the weights, were compared with the finite element solutions. For the forced vibrations, the amplitude–frequency responses determined by the harmonic balance method agree well with those calculated by the Runge–Kutta method. The free and forced vibration responses predicted by the equations considering the weights are closer to those computed by the finite element method than the responses predicted by the equation neglecting the weights. The assumption that weights can be balanced by static deflections leads to errors in the analysis of the vertical transverse vibrations of a Euler–Bernoulli beam with a nonlinear energy sink. Full article
(This article belongs to the Special Issue Advances in Architectural Acoustics and Vibration)
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