Meccanica最新文献

This study introduces a geometrically nonlinear electromagnetic energy harvester employing symmetrical inclined springs. Precise adjustment of vertical spring spacing enables controlled configuration of either bistable or tristable potential wells and their depths. Global dynamic analysis of this energy harvesting system (combining extended averaging, Runge–Kutta, and cell-mapping methods) reveals resonant characteristics, potential-well transitions, and the evolution of basins of attraction (BAs) under harmonic base vibration. It is found that the tristable system enables voltage generation under ultra-weak vibrations near trivial equilibrium. By comparison, the bistable system achieves high-energy orbits with lower activation thresholds for high-energy intra-/inter-well states and sustains high-voltage output across a wider effective bandwidth. High-energy attractors demonstrate extreme sensitivity to initial states due to fractal basin boundaries, leading to unpredictable collapses to low-energy states that critically compromise reliability. The bistable configuration exhibits superior robustness across medium-to-high vibration amplitudes, attributed to its larger and contiguous BAs supporting high-output responses, which counters claims of tristable peak-voltage superiority under extreme base vibrations. These results provide theoretical support for guiding reliable optimization of geometrically nonlinear energy harvesters in low-frequency vibration environments.

This study investigates the size-dependent eigen-buckling behavior of Kirchhoff microplates within the framework of a modified strain gradient theory (MSGT), which introduces three intrinsic material length scale parameters and leads to a sixth-order governing differential equation. Using the variational principle, both classical and non-classical boundary conditions are systematically derived in a concise form. The direct separation of variables method is extended to solve the eigenvalue problem arising from the MSGT model. In particular, for configurations where two adjacent edges are clamped and the remaining edges are either clamped or simply supported, closed-form analytical solutions which have previously been considered unattainable are achieved for the first time. A comprehensive parametric study is performed to examine the influence of various boundary conditions and material length scale parameters on the critical buckling loads, thereby elucidating the inherent size-dependent stability behavior at micro- and nano-scales. These results provide critical insights into the eigen-buckling characteristics of Kirchhoff microplates and further contribute to the theoretical foundation for the design and analysis of micro-/nano-scale systems.

The introduction of the Delta parallel robot and the SCARA serial manipulator marked a significant milestone in the evolution of industrial robotics. Since then, there has been a growing wave of innovative proposals for robots capable of executing Schönflies motion. Parallel manipulators with identical limbs have played a crucial role in shaping these robotic topologies. However, maintaining symmetry presents crucial challenges, particularly due to the complexity of mechanical assembly and the high precision required in manufacturing. This work explores the kinematics of an innovative Schönflies-motion parallel manipulator through the application of screw theory, an algebraic framework with profound geometric significance. The manipulator is composed of serial kinematic chains with two distinct degrees of freedom. While this design compromises symmetry, it significantly streamlines both kinematic analysis and overall construction. By eliminating passive kinematic chains, it offers a practical alternative to traditional parallel manipulators constructed from closed kinematic chains incorporating parallelogram-type linkages. To ensure the reliability of the proposed kinematic analysis method, numerical validation is performed using an alternative approach: an algorithm based on numerical data fitting.

This study presents a novel and efficient modal analysis framework for thick cylindrical structures with complex geometry and material variability, subject to arbitrary boundary conditions. The methodology is applied to an electric motor (e-motor) stator assembly modelled as a thick cylindrical shell incorporating stator teeth, windings, and housing or cooling jacket effects. The model accommodates both continuous and piecewise variations in material properties and thickness. Based on First-Order Shear Deformation Shell Theory (FSDST), it accounts for shear deformation, rotary inertia, and trapezoidal stress distributions, enabling accurate prediction of axial, circumferential, torsional, and bending vibration modes. A segmentation approach is used along the axial direction, with artificial massless springs enforcing continuity and permitting general boundary conditions. Displacement fields are constructed using orthogonal Jacobi polynomials, and the eigenvalue problem is solved via the Rayleigh–Ritz method. Notably, the methodology allows accurate and efficient prediction of axisymmetric (breathing) modes in thick, non-uniform cylindrical shells – a capability rarely addressed in existing literature, despite its importance in Noise, Vibration, and Harshness (NVH) analysis. Validation against Finite Element Analysis (FEA) and Experimental Modal Analysis (EMA) on both generic cylindrical shells and a real Permanent Magnet Synchronous Machine (PMSM) stator shows excellent agreement, with natural frequency deviations typically below 5% and highly consistent mode shapes. The framework also achieves over 95% reduction in computational time compared to FEA, establishing it as a highly adaptable and practical tool for vibration analysis in electric motor design and NVH engineering applications.

Quasi-static upward pull-off of a horizontal pressure-sensitive tape pulled at an internal location (double peeling) is analyzed. The finite-length tape is modeled as an inextensible elastica (beam), so that bending resistance predominates and stretching of the tape is neglected. (If bending were neglected, the tape would look like an inverted V and the process has been called V-peel.) The beam is either pulled at its center or off-center. The adhesive is modeled as a Winkler foundation, and the criterion at a peel front, based on the common fracture mechanics approach, can be written as a given critical stretching of the foundation. Displacement control is considered, and the deflections and rotations may be large. Equilibrium curves of the associated force versus vertical deflection of the pulling location are determined (typically involving at least one jump of the force), along with shapes of the beam during pulling. As the beam is pulled, the configuration changes from double peeling to single peeling. Detachment of the beam from the foundation is examined. Relevant parameters are nondimensional versions of the beam length, the pulling location, and the work of adhesion (or, equivalently, the critical stretched length of the foundation).

Piecewise linear elasticity represents the multiple states of a structure, where each state can be handled as a linear state as long as the switching does not occur. As long as each linear state is linear, the modal analysis can be used for the dynamic analysis, with the implementation of the switching between the states. Truncated modal analysis and the inelastic or plastic switching cause energy loss during the switching in discrete PL-elastic systems. This work introduces formulae for the quantitative analysis of this energy loss, allowing its substitution by a viscous damping ratio. It is shown that the energy dissipation during the switching can reach a significant ratio under specific conditions. The type of impact and the degree of modal truncation affect the magnitude of energy loss. Through simple examples, the evaluation of the possible outcomes is presented.

This paper considers the swing-up control of a three link manipulator with two joint forcing. A dynamics test of the manipulator is proposed using a controller based on inertial quasi-velocities (IQV). The benefits of describing both the control scheme known from the literature and the one designed based on the IQV are demonstrated. The presented algorithm applies dynamics equations derived from the decomposition of the manipulator’s inertia matrix. As a result, the IQV is introduced, which can be used for various purposes, namely for studying dynamics and control. This description provides some insight into the manipulator dynamics when the proposed controller is incorporated into the system. Furthermore, the use of the IQV changes the behavior of the closed-loop system due to the inclusion of couplings between the links. The proposed control scheme is not intended to improve performance but primarily to analyze the dynamics of a closed system and estimate couplings in the manipulator. Theoretical considerations are supported by simulation results on an underactuated 3 degree of freedom (DOF) manipulator.

Energy Gradient Theory has been developed in recent years for a better understanding of the flow instability and transition from laminar to turbulence in the fluid flow. In this work, we reconstruct the energy gradient theory to establish a relation between the point of inflection and Taylor-Görtler-Like (TGL) vortices in the three-dimensional (3D) rectangular lid-driven cavity flow and find out the exact location from where the TGL vortices start to be formed. Point of inflection declares whether a flow is stable or not, whereas TGL vortices are formed due to the instability or disturbances of the flow. To build the relation among them, we utilize the notion of inflectional instability for the formation of TGL vortices in the lid-driven cavity. Further, we investigate the reason for the formation of Tollmien-Schlichting or T-S waves in the cavity and how this wave plays an important role in the development of the TGL vortices. In the process, we also find the region of maximum kinetic energy, which is the birthplace of TGL vortices in the cavity. The formation of TGL vortices and their consistent relation with mushroom-shaped vortices are also discussed.

This study investigates the buckling behavior of high-density polyethylene (HDPE) pressure vessel domes—including torispherical, hemispherical, and ellipsoidal heads (aspect ratios k = 1.25, 1.5, 1.75, 2.0)—under internal pressure. Thin-walled shells are highly prone to buckling, and even small geometric imperfections can greatly reduce the critical buckling pressure (often by up to ~ 50%). Using nonlinear finite element analysis (static Riks method), we evaluate several imperfection types (eigenmode-affine shape deviations, circular cutouts, single-point load dents, and flat patches) across a range of imperfection amplitudes (e.g., dent depths from 0.01 to 10 mm). A comprehensive parametric study reveals that buckling is predominantly elastic (occurring prior to significant plastic yielding in HDPE) and that imperfection sensitivity varies strongly with dome geometry: more curved shapes (hemispherical) have higher initial buckling strength but suffer larger strength reductions due to imperfections, whereas flatter shapes are less imperfection-sensitive. Notably, adopting a variable wall thickness profile (thicker at the apex and thinner toward the equator, 11.6 mm to 8.4 mm) substantially enhances buckling resistance—by roughly 20%—in the optimal elliptical domes (k = 1.25 and 1.5) compared to constant-thickness shells. These findings underscore the importance of managing geometric imperfections and demonstrate the potential of optimized thickness designs to improve the structural stability and performance of HDPE pressure vessels.

To address the gear interference problem in harmonic drive (HD) flexsplines (FS) during meshing transmission caused by tooth profile axial inclination after wave generator (WG) assembly under actual working conditions, this study focuses on composite cycloidal tooth profiles. Two methods, namely the linear modification(LM) method and the finite-element-method-based tooth profile modification (FEMM, defined as the construction of nonlinear axial modification along the tooth-width direction from the assembled finite-element displacement field), are employed, and MATLAB is used to simulate and analyze the pre- and post-modification motion trajectories. Finite element analyses were then conducted on HD models with linear method modification, finite element method modification, and unmodified profiles, comparing deformation and stress conditions during assembly and loaded operation. Due to the assembly-induced axial displacement being nonlinear along the tooth width and coupled with angular position (θ), linear approximation causes end-region mismatch, leading to secondary deformation and contact concentration. Accordingly, we adopt a FEMM that directly constructs nonlinear axial modification t(z) along the tooth width from the assembled 3D FE displacement field, thus eliminating the root causes of mismatch and contact concentration. Consequently, FEMM achieves lower peak stress and more uniform contact distribution under both assembly and loaded conditions. We also establish general criteria for operational stability and negligible secondary deformation, and propose a process-oriented FEMM workflow to provide transferable design guidelines across tooth profiles, tooth widths, and material parameters. For manufacturability, t(z) is parameterized as a three-station, low-degree spline with end weighting to ease machining and inspection. Compared with the linear method, FEMM only adds one assembled field extraction and one curve-fitting/verification step, resulting in limited additional computational cost.