Search Results (238)

To overcome the limitations of existing three-degree-of-freedom milling stability models in representing axial cutting conditions, this study develops a stability prediction framework that accounts for both axial segmentation and the axial contact angle. A three-degree-of-freedom dynamic model of the milling system is first formulated by introducing the axial contact angle. The tool axis is then discretized, so that the cutting force coefficients can be evaluated in different axial sections and the non-uniform distribution of cutting forces along the tool can be captured more accurately. After incorporating the regenerative mechanism, the milling dynamics are expressed in the form of a linear time-delay differential equation. To enhance the numerical accuracy of the time-delay system solution, a full-discretization scheme using third-order Lagrange–Hermite interpolation is developed for constructing the state transition matrix. The stability boundary is subsequently determined based on Floquet theory, from which the stability lobe diagram is generated. The proposed model and solution procedure are validated by comparison with existing methods and by time-domain simulation. The results show that, when the spindle speed ranges from 5000 to 10,000 rpm and the axial depth of cut ranges from 0 to 8 mm, the overall variation rate of the predicted stability region is 11.19% after incorporating axial discretization and 59.88% after considering the axial contact angle. The stable and unstable cutting responses obtained from time-domain simulations are consistent with the regions predicted by the stability lobe diagram, which supports the validity of the proposed approach. Further investigation shows that, for the established three-degree-of-freedom milling model and the specified cutting parameters, the axial contact angle exerts a pronounced nonlinear effect on the stability boundary. Specifically, as the axial contact angle $\epsilon$ increases within the range $0^{°}<\epsilon \le {45}^{°}$, the stable region gradually shrinks; when $\epsilon$ increases from 45° to 90°, the stable region expands instead. These observations can provide useful guidance for selecting milling parameters and identifying stable machining conditions. Full article

To address the structural deformation and mechanism jamming frequently observed in critical linkages during retraction and extension of door-coupled landing gear systems, this study proposes a rigid–flexible coupled dynamic modeling approach. A representative landing gear system was studied, and a high-fidelity rigid–flexible multibody dynamics model was developed based on a conventional rigid-body framework. The left linkage, which was prone to failure, was modeled as a flexible finite element component, while the remaining parts were treated as rigid bodies. A multibody dynamics method based on nonlinear finite element was adopted, incorporating elastoplastic constitutive relations and Lagrange constraint equations. Two materials, ultra-high-strength 300M steel and high-strength 7075-T6 aluminum alloy, were evaluated to investigate the influence of structural stiffness on critical linkage stress and door kinematics during deployment. Results showed that maximum stress occurred at the hinge joint, identified as the critical region for strength assessment. The peak stress for 300M reached approximately 168 MPa, about 8.4% higher than that of 7075-T6. However, 7075-T6 exhibited lower stress oscillation frequency and superior damping performance, which helped suppress high-frequency vibration. Material selection had negligible influence on door centroid displacement, velocity, and opening angle, and the motion trajectories remained highly consistent. Full article

In this study, we develop a novel variable-order fractional extension of an eight-dimensional (8D) hyperchaotic differential equation system modeled via the Liouville–Caputo operator. Moving beyond constant fractional-order models, our system implements time-variable orders, which enable its historical memory structure to evolve dynamically over time. To numerically approximate the trajectories of this complex 8D system, a second-order Lagrange numerical integration approach is formulated. An extensive dynamic analysis explores the behavior of this variable-order framework under two distinct configurations: a slowly periodic memory function and a smooth, monotonic hyperbolic tangent function. Topological complexity and multidimensional chaos are characterized using parameter-dependent bifurcation diagrams, phase portraits, Kaplan–Yorke fractal dimensions, and Kolmogorov–Sinai metric entropy. Numerical results show that both variable-order configurations display robust hyperchaotic dynamics characterized by four positive Lyapunov exponents. Crucially, the proposed variable-order extension enhances the phase space footprint of the baseline system, achieving a maximum Kaplan–Yorke dimension of 7.100, thereby offering excellent topological density for secure cryptographic applications. Full article

Lunar in situ resource utilization requires solar concentrating systems that can be launched in a compact configuration and deployed reliably on the lunar surface. This paper presents a multi-link coupled deployable support mechanism for a reflector-Fresnel concentrating system. The mechanism adopts a shape-memory-alloy rigid release for the stowed state and passive spring hinges for autonomous deployment, aiming to reduce drive complexity while maintaining a high deployment ratio. To avoid interference caused by coupled link motion, a motion-envelope model is established for joint trajectory planning. The deployment process is then analyzed through vector-based kinematic modeling, D’Alembert force analysis, and Lagrange dynamic equations. The analytical predictions are corroborated through high-fidelity multibody dynamic simulations: the predicted driving torque of Link 3 is 0–0.68 N⋅m, close to the simulated range of 0–0.70 N⋅m, with a relative peak-value error of 2.8%; the maximum angular acceleration is 0.08 rad/s². Finite-element modal analysis gives a first locked-state natural frequency of 54.969 Hz. NSGA-II optimization further reduces the maximum driving torque by 10.9%, reduces torque fluctuation by 9.7%, and increases the maximum deployment ratio from 5.6 to 7.2. The results provide a quantified design and simulation basis for passive deployable concentrating mechanisms intended for lunar surface concentrating systems. Full article

The ground mobile platform pointing system (GMPPS) suffers from poor stability and low pointing accuracy under uncertain disturbances due to nonlinear rigid–flexible coupling and structural uncertainties. A UDO-LQR control strategy is proposed, achieving superior control performance compared with the conventional PID control. In this work, a rigid–flexible coupled nonlinear dynamic model of the GMPPS with disturbances is established using Lagrange’s equations of the second kind. Based on the torque compensation equivalence principle, the electromechanical coupling equations are derived. An uncertainty disturbance observer (UDO) is designed to estimate the state variables corresponding to unmodeled disturbances, and a linear quadratic regulator (LQR) is employed to effectively suppress uncertain disturbances, achieving attitude stabilization of the pointing system (PS). The proposed UDO-LQR (UDO-augmented-LQR) strategy delivers an 83.79% performance improvement in azimuth and a 70.45% improvement in elevation in terms of RMSE compared with PID under standard road profile excitations, making it suitable for stable control of the PS under field road conditions compared to the PID control scheme. Full article

This paper investigates the dynamic characteristics of rotating functionally graded material (FGM) micro-beams based on Euler–Bernoulli beam theory, Euler–Bernoulli beam theory incorporating shear deformation, and Timoshenko theory. The deformation field of the micro-beam is described within a floating coordinate system using the meshless point interpolation method (PIM/RPIM). The couple stress tensor and curvature tensor, which capture the size effect, are incorporated into the potential energy formulation. Employing Lagrange’s equations of the second kind, a higher-order rigid-flexible coupled dynamic model for rotating FGM micro-beams is established under various beam theories. Simulation results obtained from the Euler–Bernoulli theory with shear correction and the Timoshenko model are compared with those from the classical beam model and previous literature. The influences of material gradient index, material characteristic length parameter, and rotational speed profiles on the transient dynamic response and steady-state free vibration of rotating micro-beams are systematically examined. The results show that increasing the material gradient index reduces the structural stiffness, resulting in lower natural frequencies and larger vibration amplitudes, whereas increasing the characteristic length parameter enhances the size effect and improves system stiffness. Full article

For the trajectory tracking control problem of a 7-DOF redundant hydraulic manipulator, an adaptive fuzzy sliding mode control method based on a novel fast reaching law is proposed. Based on the kinematic analysis of the manipulator, its dynamic equation is constructed using the Lagrange dynamic equation. A trajectory planning method for the manipulator, integrating seventh-order polynomial interpolation and genetic algorithm optimization, is proposed. Taking the planned trajectory as the expected trajectory, a sliding mode controller is designed to achieve trajectory tracking control of the manipulator. A sliding mode disturbance observer is used to observe the system uncertainties, and an adaptive fuzzy logic system is designed to estimate the observation error of the disturbance observer. The sliding mode control law is deduced based on the fast reaching law, which can achieve global fast convergence of the sliding mode function while reducing the chattering of the controller. The simulation results show that the proposed control method has good tracking performance and strong robustness. Full article

Different approaches to describing the kinematics and dynamics of a mobile robot equipped with four Mecanum wheels are compared. Due to the no-slip rolling condition, the kinematic constraints imposed on the system are nonholonomic; therefore, the equations of nonholonomic mechanics must be used to model such a system. The necessary and sufficient conditions under which the dynamics of this system can be described using Lagrange equations of the second kind are derived. The solvability of the kinematic constraint equations using the pseudoinverse matrix is also analyzed. Full article

Housner’s classical rocking model assumes a rigid base, which often leads to inaccurate seismic assessments under real–world soil conditions. This study quantitatively establishes the applicability limits of the rigid–base assumption and defines a reference range for its validity. To address these limitations, a novel soil–structure interaction (SSI) rocking model was developed using Lagrange’s formulation, incorporating an event–driven spring–dashpot mechanism to characterize contact forces. Validation against LS–DYNA simulations and existing compliant base models confirms high predictive accuracy across diverse geometries and ground motions. Crucially, an empirical formulation for the interface stiffness of rocking structures was derived to ensure the alignment of the proposed analytical model with numerical observations, thereby enhancing its practical utility in industrial design. Our findings reveal that rocking behavior depends not only on soil stiffness but also on the inherent stiffness of the structure. Specifically, soft soils significantly alter rocking initiation thresholds and amplify peak angles. The proposed SSI–rocking model provides a computationally efficient and FE–compatible tool for optimizing the seismic stability of unanchored structures on flexible foundations. Full article

We propose an exploratory framework for a Bohmian model of quantum matter propagating on a classical curved spacetime background. The gravitational sector is governed by classical Einstein field equations throughout; no quantisation of spacetime is attempted. The wave function emerges as the scalar contraction $\mathrm{\Psi }={\psi }_{\nu }{\psi }^{\nu }\in \mathbb{C}$ of a complex-valued tensorial field ${\psi }^{\mu }$, encoding quantum dynamics in a geometric object. The wave tensor interacts with spacetime via the stress–energy tensor $T_{\mu \nu }$, mediated by a real scalar field a of dimension volume, so that $a{T}_{\mu \nu }{\psi }^{\mu }{\psi }^{\nu }$ yields the correct potential energy. We derive a covariant Adapted Schrödinger Equation as the unique minimal covariant lift of the standard equation, justify it from four guiding principles, and verify three internal consistency checks. Under seven explicit approximations the framework reproduces the Schrödinger equation with Coulomb potential for the hydrogen atom. We also derive a dynamical equation for ${\psi }^{\mu }$ that entails the Adapted Schrödinger Equation by contraction. Two open problems are then resolved. First, a complete Lagrangian formulation is provided: a real-valued action for $\mathrm{\Psi }$ yields the Adapted Schrödinger Equation via the Euler–Lagrange equations; a separate action for ${\psi }^{\mu }$, extended by a non-polynomial term, yields the full dynamical equation variationally. Second, two experimental predictions are derived. Expanding to first post-Newtonian order, the perturbation Hamiltonian has coefficients $(3, 1)$ on the kinetic and potential operators; via the virial theorem these produce a coordinate-time blueshift, which after photon propagation yields the universal Einstein gravitational redshift $\delta \nu /\nu =\mathrm{\Phi }/c^2$, confirming consistency with the equivalence principle. The same kinetic coefficient independently predicts that free quantum wave packets spread more slowly by the fractional amount $3\left|\mathrm{\Phi }\right|/c^2$, a correction absent in standard non-relativistic quantum mechanics. Full article

Roof instability in the heading area of fully mechanized excavation roadways, together with insufficient coordinated operation between excavation and support, severely restricts tunneling safety and construction efficiency. A novel track-mounted advanced support equipment structure with an articulated curved roof beam is proposed in this study. Considering actual underground working conditions, including uneven roof contact, eccentric loading and local support failure, a three-degree-of-freedom dynamic model covering vertical, pitch and roll motions is established based on Lagrange’s equations. Dynamic characteristics under varying load amplitudes, excitation frequencies, static load offsets and typical support failure modes are systematically analyzed. The results reveal that only vertical vibration emerges under the full support condition, and the resonance frequency of the system is approximately 10 Hz. The maximum steady-state vertical displacement reaches 0.6406 mm with an RMS of 0.5472 mm under an intact support state. The pitch vibration amplitude caused by the failure of the first support group is three times that of the second group, proving front supports dominate anti-overturning capacity. Side beam failure triggers remarkable roll-coupled vibration, while middle beam failure mainly enlarges vertical displacement. This paper clarifies the vertical–pitch–roll coupling vibration mechanism induced by local support failure. Parameter sensitivity analysis reveals that static load offset has the highest sensitivity, while excitation frequency (within 4–6 Hz) and damping ratio exhibit negligible influence on the steady-state response. The obtained quantitative results can provide a reliable theoretical reference for structural optimization, stability regulation and safety monitoring of track-mounted advanced support facilities. Full article

Monopile offshore wind turbines are vulnerable to excessive vibration under coupled wind, wave, and seismic loading because of their slender and flexible structural characteristics. This study investigates a single-sided vibro-impact nonlinear energy sink (SSVI NES) installed inside the nacelle of a 5 MW monopile offshore wind turbine. A reduced-order ten-degree-of-freedom dynamic model is established using the Euler-Lagrange formulation, and turbulent wind, irregular wave, and seismic inputs are generated using TurbSim, the Kaimal and JONSWAP spectra, the Morison equation, and 15 PEER ground-motion records. The proposed SSVI NES is compared with an optimized tuned mass damper (TMD) under nominal and frequency-detuned conditions. Under the nominal design condition, the optimized TMD and the representative SSVI NES reduce the RMS nacelle fore-aft displacement by approximately 55% and 50%, respectively, indicating that the SSVI NES provides near-benchmark vibration mitigation. Meanwhile, the maximum absorber stroke of the SSVI NES is reduced by approximately 40% compared with that of the optimized TMD, which is beneficial for nacelle-integrated implementation. Under frequency detuning, the response-reduction effectiveness of the TMD decreases from approximately 55% to 20%, whereas the SSVI NES retains approximately 80% of its nominal RMS-based control effectiveness. These quantified results show that the SSVI NES offers a balanced combination of competitive nominal response reduction, reduced absorber motion demand, and improved robustness against structural-frequency variations. The proposed device therefore provides a promising passive-control strategy for enhancing the serviceability and multi-hazard resilience of monopile offshore wind turbines. Full article

We consider the translational–rotational motion of a small axisymmetric body in the gravitational field of two stars of variable masses moving under the influence of their mutual gravitational attraction. The two stars are assumed to lose their masses isotropically with different rates and their total mass decreases according to the joint Meshcherskii law. The relative motion of the stars is described by the corresponding exact solution to Gyldén’s equation and is considered to be given. The small axisymmetric body may change its mass, size and shape while its initial dynamic structure is retained. The problem is analyzed in the framework of Lagrange’s formalism, and equations of translational–rotational motion are derived in terms of the osculating elements of aperiodic motion on quasi-conic sections and the Andoyer variables. As equations of motion of the small body are not integrable, the perturbation theory is applied with the perturbing function expanded into power series in terms of eccentricity and inclination, which are assumed to be small. Averaging these equations over the mean longitudes of the two bodies and two Andoyer angles in the absence of commensurability of frequencies, we obtain the differential equations describing the long-term evolution of the orbital elements and Andoyer variables which may be investigated numerically for different laws of the system parameters’ variation. All the relevant symbolic calculations are performed with the computer algebra system Wolfram Mathematica. Full article

To address the vibration reduction problem of the six-degrees of freedom(6-DOF) half-vehicle model and to improve ride comfort and handling stability, a piezoelectric stack actuator based on the inverse piezoelectric effect was introduced. A 6-DOF half-vehicle dynamic model coupling the cab, body, and wheels was established based on the Lagrange equation. Based on this model, a vertical-pitch dual sliding surface RBF neural network sliding mode control strategy was proposed, with two independent RBF neural networks designed to separately approximate, online, the comprehensive uncertainties in the vertical and pitch channels associated with unmodeled dynamics, external disturbances, and modeling simplifications. The variable-speed reaching law (dsat) function was used to design the sliding mode reaching law, balancing sliding surface convergence speed and vibration suppression. Six indicators, including vertical acceleration of the cab and vertical acceleration of the vehicle body, were selected as performance evaluation metrics to establish the fitness function. Combined with a genetic algorithm, the dual sliding surface coefficients, RBF network parameters, adaptive update rates, and variable-speed reaching law parameters were globally optimized. The vibration reduction effects of four schemes—passive control, traditional sliding mode control, RBF sliding mode control, and genetic algorithm optimized RBF dual-sliding-mode control—were compared and analyzed. Simulation results show that the genetic algorithm optimized RBF dual-sliding-mode control achieves improved vibration suppression in several key ride-comfort-related indices and provides better overall coordination among ride comfort, suspension working space, and tire dynamic deflection. The research results validate the effectiveness of this method and provide a new solution for addressing vehicle vibration reduction problems. Full article

Micro- and nanoscale mass sensing is crucial for applications such as molecular detection and wearable monitoring. However, the observation of mass perturbations in flexible composite structures requires systematic theoretical evaluation. This study develops a dual-mode vibration-based mass-sensing model based on a film–substrate composite strip. By releasing and re-stretching pre-strain in the soft substrate, the ribbon can reversibly switch between a two-dimensional flat configuration (Mode 1) and a three-dimensional buckled configuration (Mode 2), leading to distinct dynamic responses. Under a finite-deformation Euler–Bernoulli beam assumption, displacement fields and kinematic relations are formulated for both configurations. An energy-based approach is employed to decompose the total energy into stretching and bending contributions, while an added-mass block is incorporated into the kinetic energy as a lumped mass. The governing equations of motion are derived using the Lagrange equations and the Hamiltonian function. Based on these results, the influence of the added mass on displacement signatures is examined, and the mode-dependent observability in the flat versus buckled states is compared, providing an analytical basis for mass sensor evaluation. Full article