Geometrically nonlinear static analysis of materially imperfect composite doubly curved shells is investigated via the generalised differential quadrature method. The effects of both shear and thickness deformation are considered through a thickness- and shear-deformable third-order theory formulated in curvilinear coordinates, while the influence of large deformations is accounted for using the von Kármán-type strain–displacement relationships. On the basis of Hamilton's principle, eight nonlinear deformation equations and associated boundary conditions, assumed to be simply supported with movable edges, are derived and discretised. A direct iterative method of the Newton–Raphson type is used to solve the resulting nonlinear algebraic system of equations. In this study, two different types of doubly curved shells are analysed, namely, spherical and elliptical. To describe the continuous variation in material properties, the Voigt bound method is employed, which is further modified to account for material imperfections, such as porosities (voids). Convergence and comparison studies are conducted to validate the accuracy of the proposed numerical model. Numerical results for displacements and stresses are obtained for the two shell geometries, material gradation profiles, porosity distributions, and radii of curvature.
The derivation of linearized equations and subsequent eigenvalue analysis is the basis for tasks such as frequency-domain response analysis, control design, and stability assessment for mechanical systems. However, for general multibody systems with redundant or nonholonomic constraints, practical challenges persist in achieving numerically stable linearization and reliable eigenvalue analysis. This study provides numerically reliable linearization and eigenvalue analysis algorithms of Lagrange's equations of the first kind for general multibody systems, and forms a systematic computational framework. First, a robust linearization methodology is developed to automatically generate linearized state-space equations. Coordinate partitioning is employed not only to eliminate redundant constraints and dependent coordinates, but also to significantly simplify the calculations. Second, a direct eigenvalue analysis on Redundant Coordinate Set Jacobians is performed instead of decomposing the state matrix, for its better numerical conditioning and sparsity. The equivalence of the eigenvalue problems is strictly proven theoretically. The methodology is validated by various benchmark problems and practical cases. The proposed approach has been implemented and released with a general-purpose rigid-flexible coupled multibody dynamics software INTESIM-FMBD (v7.0), and provides a reliable numerical tool for linearizing general mechanical systems.
In the present era, powering sensors using green energy is a significant challenge. One promising solution for the power supply of small sensors relies on piezoelectric energy harvesters excited by vortex-induced vibrations (VIVs) generated by wind. In these devices, the harvester typically features a cylindrical bluff body that generates the vortex shedding and also tunes the natural frequency of the cantilever according to the frequency of the excitation. However, in many practical applications, the harvester is not mounted on a perfectly rigid base. The compliance of the base can significantly influence the behavior of the system. Furthermore, harvesters are often installed on moving structures or machines, where base vibrations introduce additional complexities. Therefore, understanding the impact of both harmonic and random base excitations on VIV is essential for harvester design. This paper investigates these phenomena in a comprehensive way. It presents a multiphysics mathematical model of a piezoelectric energy harvester mounted on a moving base, numerical results, and a wide series of experimental tests. The model reliably predicts the harvester behavior under various conditions and enables to extend the experimental investigation. Experimental and numerical results show that base vibrations and VIV can generate voltage in a synergistic way. Nevertheless, for large base vibrations, nonlinear effects take place that affect the maximum amplitude of the generated voltage in the lock-in region. The study shows that these phenomena happen with both harmonic and random base excitation.
This work addresses the challenge of bidirectional trajectory tracking in solar-powered wheeled mobile robots (WMRs), considering the mechanical structure, actuator-driver, and power stage subsystems. Notably, this is the first study to explicitly model and control the actuator-driver subsystem within this context. The proposed solution relies on a comprehensive three-stage average controller scheme: the top-stage applies an input–output linearization strategy to ensure accurate bidirectional tracking; the mid-stage employs a control based on differential flatness theory to manage the dynamic behavior of the actuators and their driver, represented by an H-bridge; and the low-stage, also based on flatness theory, regulates the power stage, modeled as a Buck converter. The proposed multistage control strategy is experimentally validated using a differential-drive WMR prototype, where a B&K Precision PVS60085MR source is used to replicate the operational characteristics of a commercial photovoltaic panel. System integration is achieved through a DS1104 control board, with real-time implementation carried out in MATLAB/Simulink. Experimental results demonstrate that the controller successfully fulfills the bidirectional trajectory tracking task, even in the presence of system parameter variations and disturbances in the variable-voltage source.
This study investigates the hydrodynamic influence of forward transom tapering on a displacement catamaran hull using computational fluid dynamics (CFD) simulations. Five taper configurations ranging from a vertical transom base design to a fully tapered stern (1.00B) were evaluated over a wide Froude number range (Fr = .3 to 1.0). The simulations were performed using a RANS-based solver coupled with the volume of fluid (VOF) method to accurately capture free-surface effects. Turbulence was modeled using the SST k–ω approach to account for boundary layer evolution and wake separation. The analysis focused on resistance components, free-surface wave elevation mapping, transom pressure distribution, and wake streamline to assess hydrodynamic performance. Results indicate that forward tapering significantly affects pressure resistance while frictional resistance is slightly altered. The 0.75B taper configuration consistently demonstrated optimal performance, reducing the total resistance coefficient (CT) by up to 6.39% and enhancing stern pressure recovery without introducing flow instabilities at higher speeds. Wave elevation analysis revealed a marked reduction in stern hollows and improved surface coherence with longer tapers. Transom pressure mapping showed attenuation of suction zones, while streamline visualizations illustrated wake narrowing and recirculation suppression in tapered configurations. The novelty of this study lies in its focus on geometric forward transom tapering. These findings not only advance the understanding of transom hydrodynamics but also establish the 0.75B forward taper configuration as a practical and efficient design recommendation for resistance reduction in high-speed displacement catamarans.
In-wheel motor drive is the developing direction of automobile electrification and intelligence. However, the increased unsprung mass in in-wheel motor-driven electric vehicles (IWMEVs) leads to higher dynamic tire loads, thereby intensifying vehicle–road coupling interactions. To address this problem, an 11-degree-of-freedom nonlinear dynamic model of a vehicle–motor–road coupled system is developed, incorporating nonlinear suspension, tire stiffness, and road foundation. Using the Galerkin method and trigonometric product formulas, an analytical expression for the sandwich plate road model on a nonlinear viscoelastic foundation is obtained. The vehicle–motor–road coupled model is solved with a validated fixed-step Runge–Kuta method to investigate the coupled effects of electromagnetic excitation, road irregularity, and road vibration. Results reveal that the amplitude–frequency characteristics of electromagnetic excitation are closely related to vehicle–road coupled vibrations. Multiple excitations adversely affect the IWMEV ride comfort. Furthermore, comparative analysis of linear and nonlinear models demonstrates the importance of the developed nonlinear vehicle–motor–road coupling model.
Hydraulic manipulators exhibit strong coupling, pronounced nonlinearities, and significant modeling uncertainties, which hinder high-precision motion control. This paper proposes a finite-time disturbance observer–based nonlinear robust adaptive control (RAC-FTDO) framework enhanced by a physically consistent dynamic parameter identification scheme. The entire system dynamics, including the hydraulic dynamics, is first derived. A weighted least squares approach is employed to obtain inertial and friction parameters under physical constraints, enabling reliable feedforward compensation. Building on back-stepping principles, an adaptive controller systematically integrates an FTDO and a nonlinear robust strategy, enabling rapid and accurate estimation and compensation of both parametric uncertainties and unmodeled disturbances, while suppressing residual estimation errors and avoiding high-gain feedback. Through Lyapunov stability analysis, the proposed controller achieves improved transient behavior and asymptotic tracking performance. The proposed approach can be extended to multi-degree-of-freedom serial systems and has been experimentally validated on a hydraulic manipulator against several benchmark controllers, demonstrating its effectiveness.
Modern industrial demand for efficient material handling in confined spaces has driven the need for overhead cranes capable of short-distance point-to-point maneuvers without compromising payload stability. Conventional three-stage shaper profiles, experiencing acceleration, cruising, and deceleration, become inefficient or infeasible for short distances where cruising speed cannot be reached before deceleration begins. This paper proposes a single smooth waveform command-shaping controller specifically designed for two-stage acceleration–deceleration maneuvers when the cruising stage is eliminated due to distance constraints, offering closed-form coefficients for easy implementation without the need for complex optimization processes. To define where a two-stage shaper is required, feasibility maps defining operational limits across cable lengths, distances, and time constraints are presented. Experimental validation on a laboratory crane confirms strong agreement with numerical simulations, achieving minimal residual oscillations for short-distance and rapid-cycle operations. Sensitivity analysis shows robustness improves with cable length, and the two-stage shaper outperforms the three-stage approach under natural frequency variations. The proposed novel two-stage shaper provides a practical, vibration-free solution for short-distance crane operations where total cycle time must be minimized.
An accurate launch-dynamics computational method is critical for barrel weapon service life assessment and multiphase physics field refinement. Given the lack of studies on the solid-phase buildup behavior at the projectile base, this paper provides an improved method for calculating the launching dynamics under high pressure and high speed. The method realizes the compensation of projectile base pressure and velocity under the impact of numerous propellant particulates by modifying computational boundaries and appending propulsive forces. Unlike previous studies, it is found that the solid-phase propulsion for the projectile is significantly larger than the gas-phase propulsion for the projectile at the early stage of launch. Moreover, an artillery launch experiment with a large charge zone is conducted to verify the reliability of the computational method. The results show that the dynamic time wrapping deviations of the pressure and velocity based on the proposed method from the launch experiment are only 0.82% and 0.93%, respectively, and the root mean square error values are 2.1 MPa and 3.2 m/s, respectively, which are smaller than the deviation before compensation.
Understanding the dynamic behavior of structural components is crucial for optimizing performance and ensuring structural integrity. This study presents a new method that combines a systematic experimental investigation of four distinct hole geometries (circular, square, compact rectangular, and long rectangular) with varying hole counts, all designed to maintain equal material removal, and the application of Gaussian Process Regression to model and predict natural frequencies from experimental modal analysis. Experimental modal testing was conducted on 36 beam specimens to evaluate changes in vibrational properties. The results demonstrate a clear relationship between hole geometry and the attenuation of natural frequencies: circular holes resulted in minimal reductions due to uniform stress distribution, whereas square and rectangular holes caused greater stiffness loss, with the most substantial attenuation observed in beams with long rectangular holes where the first natural frequency decreased by up to 44%. The proposed Gaussian Process Regression model achieved high predictive accuracy on the test set, with coefficients of determination (R2) of approximately 0.98 for the first natural frequency, 0.93 for the second, and 0.92 for the third. Sensitivity analysis identified the number of holes as the most influential parameter, contributing 67.8% to variations in the first natural frequency. These findings provide practical guidelines for structural design by identifying optimal hole geometries and counts to achieve weight reduction while maintaining stiffness, and demonstrate the utility of Gaussian Process Regression for reliable modeling of vibrational behavior in perforated beams.
Despite the great potential of diamagnetic levitation accelerometers in detecting low-frequency and weak motion, there is still a demand to further enhance their sensitivity for geophysical and microgravity applications. In this study, a straightforward structural modulating approach is presented to enhance the sensitivity of diamagnetic levitation accelerometer from both theoretical and experimental aspects. It is demonstrated that by regulating the structural parameters of sensing element and permanent magnets, one can refine the magnetic field, diamagnetic forces, and eddy current effect, making it feasible to improve the sensitivity. With the optimized structural parameters, a remarkable sensitivity of 7.32 mm/g, accompanied by ultra-low frequency detection capability (0–1.8 Hz), fine resolution (32 μg), and low noise (6.256 μg/Hz1/2), can be achieved, highlighting the viability of structural design in developing a high-sensitivity accelerometer.
This study explores the nonlinear dynamics associated with a passive dynamic walker (PDW), focusing on the bifurcation and stability insights derived from spring and damper mechanics. PDWs, which rely on gravity for stable locomotion without active control, exhibit a rich spectrum of behaviors, from periodic to chaotic motion. The study examines the effects of key system parameters, such as the hip mass ratio, the leg center of mass (CoM) location, spring stiffness, and damper coefficient, on the stability and gait performance of the walker. Through a combination of theoretical analysis and numerical simulations, the paper identifies bifurcation points where periodic orbits transition into chaotic dynamics, shedding light on the critical conditions for stable walking. The results reveal that increased hip mass, spring stiffness, and leg CoM location ratio contribute to faster walking speeds. All of these physical parameters show a non-monotonic effect on stability. Stability first improves and then deteriorates as the parameter values increase. In contrast, the influence of damping on passive walking is relatively minor, and increasing damping does not significantly improve stability, even sometimes leading to the inability to find a stable solution. Moreover, the results also suggest that the addition of the spring can mitigate the bifurcations of the system. This research provides a deeper understanding of the stability transitions in PDWs, with implications for the design of more efficient and robust legged robots.