Meccanica最新文献

This paper presents a one-dimensional theory for moderately thick piezoelectric beam-type structures with imperfect resistive electrodes. For practical applications, a special goal is also the finite element discretization of the electromechanically coupled partial differential equations, which combine the Telegrapher’s equations with the elastic properties of a Timoshenko beam. Unlike ideal electrodes, which satisfy the equipotential area condition, the voltage distribution in resistive electrodes is governed by the diffusion equation. For the electrical domain, Kirchhoff’s voltage and current rules are applied to derive the parabolic differential equation, which is driven by the time derivative of the axial strain. It is demonstrated that the current flow through the electrodes of the piezoelectric layer depends on the electrode resistance and the capacitance. For the mechanical domain, d’Alembert’s principle is combined with the piezoelectric constitutive equations to derive an extended version of the Timoshenko beam equations, incorporating the x-dependent voltage drop across the electrodes. A one-dimensional finite element is then formulated using Timoshenko shape functions for the deflection and the rotation angle, along with linear shape functions for the voltage drop along the beam segment. For the validation of the model a clamped-hinged piezoelectric beam is used as a benchmark example to compare the results of the one-dimensional discretization with two-dimensional finite element (FE) simulations. Various types of resistive electrodes are considered, including static deflections, dynamic vibrations, and eigenfrequency analyses. The results demonstrate that the derived piezoelectric beam model also includes the case of ideal electrodes (short- and open-circuited), when the sheet resistance is very low, and the case of a non-electroded piezoelectric beam, when the sheet resistance is very high.

To improve the aerodynamic performance and optimize the flow field structure of H-type vertical axis wind turbines (VAWTs), a split trailing-edge double-flap structure inspired by bionic fish tail fins was proposed, while maintaining the original airfoil parameters. Using 2D and 3D computational fluid dynamics (CFD), the effects of varying flap relative lengths (x/c), upper and lower flap deflection angles, and active control strategies on aerodynamic performance (C_p) were systematically investigated. First, the power coefficient and instantaneous torque of individual blades through comparative analysis to determine the optimal x/c. Second, the influence of different upper and lower flap deflection angles on the overall torque was investigated. Finally, active control strategies were applied to explore their effects on the power coefficient and tangential force. Results showed that x/c = 0.2 provided the most significant improvement. At an upper flap deflection angle of 30°, notable performance enhancements were observed across the studied tip speed ratio (TSR) range. When both deflection angles were 30°, the improvement extended to a wider TSR range. Active control increased blade surface velocity gradients, optimized velocity distributions, and enhanced blade torque.

This study examines the resonance frequency shift due to adsorption in a biomolecule-resonator sandwich nanobeam system under a temperature-induced load. The analysis incorporates shear deformation, distributed adatoms, and small-scale effects within the framework of nonlocal elasticity theory (NET). The sandwich nanobeam consists of three sections: a perforated core with a uniform square-hole pattern and two bonded functionally graded porous (FGP) layers. Adsorption-induced energy is modeled using a distribution-based approach for spike proteins and bio-receptors. The dynamic model of the nanobeam resonator integrates surface stress effects. The functional nanobeam and localized biomolecule models are used in conjunction with van der Waals (vdW) forces, employing the Lennard–Jones (6–12) and Morse potentials to assess all influencing factors. Shear force and inertia moment are explicitly derived from the nonlocal Timoshenko beam equations, with residual stress considered as an additional axial load. The Navier technique and differential quadrature method (DQM) are employed to solve the motion equations, enabling a comprehensive interpretation of the results. Numerical findings reveal that surface properties, adsorbed adatoms, perforation dimensions, hole number, thermal loads, variation in power law index, porosity parameters, and the positioning of receptors and spikes all influence the frequency shift. Results further indicate that interatomic interactions reduce system stiffness, emphasizing their significance in computational analysis. The proposed model effectively evaluates the dynamic response of biomolecule-resonators and can determine the mass and density of viruses and spikes while accounting for adatom bonding effects.

The automation of transportation systems inevitably faces the challenge of enhancing both the safety and intelligence of passenger vehicles. In this transitional stage toward full automation, advanced driver assistance systems (ADAS) play a critical role in bridging the gap. A key component of ADAS is vehicle stability control (VSC), which ensures motion stability during highly nonlinear handling maneuvers. This paper addresses the system nonlinearity under critical driving conditions and the loop delays within feedback processes by proposing a delay-tolerant feedback structure for VSC. The approach utilizes only the linearized dynamics along the trajectory of the maneuver, where the target-tracking performance is optimized. A nonlinear vehicle model is first constructed, followed by an investigation of its open-loop characteristics through equilibrium analysis and local linearization. Time delays arising from control sampling and actuation are incorporated into the feedback torque, yielding a delayed nonlinear system. A semi-discretized method is developed to construct stability charts of the tunable control gains, whose aggregation yields a conservative delay-tolerant domain. Two gain scheduling strategies are proposed to achieve maximum target-tracking performance, tailored for either real-time (RT) or offline implementation. The proposed method is designed for stable tracking of dynamic motion references under nonlinear conditions and is validated using experimental data-based simulations. The results demonstrate that a linearized control law, when properly designed, can deliver high-performance VSC with strong adaptability across different control loops subject to varying delays.

In this work, a computationally efficient multiscale strategy is proposed for accurately predicting failure in composite materials under general loading conditions. The main ingredient of this strategy is a data-driven surrogate model for damaging anisotropic microstructures, to be obtained through several nonlinear hierarchical homogenization processes performed on the same repeating unit cell subjected to different macrostrain paths. The adopted macroscale constitutive model considers the overall secant elastic moduli as internal variables, and introduces a general fourth-order damage surface tensor, representing the macroscale anisotropic damage evolution, which depends on both the overall secant moduli and applied macrostrains. A deep neural network (DNN) approach is used to derive an approximate functional form for this damage surface tensor, based on the best fitting of nonlinear micromechanical results. Then, the numerical accuracy of the proposed data-driven multiscale model is assessed by comparing the relevant results with those coming from a nonlinear periodic homogenization approach, with reference to a regularly perforated microstructure subjected to arbitrary macrostrain histories, involving both proportional and nonproportional paths.

This paper introduces a systematic method for analyzing the free and forced vibrations of hybrid double-beam systems under axial force, utilizing the linear multibody system transfer matrix method. The hybrid double-beam system consists of two types of elements, the double-beam segments and the spring-supported rigid bodies. This configuration is commonly found in research and engineering applications. The frequency equation of the system can be directly obtained through successive multiplication of the element transfer matrices, accommodating arbitrary boundary conditions. The transfer equation for the axially loaded Timoshenko beam are derived analytically, thereby avoiding the accuracy loss due to spatial discretization. And there is no need to discuss the derivation for different cases. The orthogonality of the augmented eigenvectors of the hybrid double-beam system is mathematically proven. The forced vibration of the system is solved using the modal superposition method. Three numerical examples verify the systematicity, simplicity and high accuracy of the proposed method. Furthermore, the effects of axial force, spring support stiffness, and rigid body mass on the vibration characteristics of the hybrid double-beam system are analyzed, providing valuable insights for optimizing designs and avoiding undesirable vibrations.

Ultra-High Performance Fiber-Reinforced Concrete (UHP-FRC), a construction material that has been introduced and refined over the past two decades, offers exceptional advantages that set it apart from traditional concrete. The mechanical response of UHP-FRC is often evaluated in the laboratory using tests that include compression, tensile, and three-point bending, in which non-homogeneous deformation fields develop, resulting in the localization of failure processes. Here, we utilize a second gradient continuum theory, applicable to UHP-FRC, developed within the granular micromechanic framework to model the deformation and failure behavior. The granular micromechanic framework accounts for the variability in grain-pair orientations within a continuum material point, integrating interactions across the orientational space to capture the evolving macroscale behavior of UHP-FRC. A key outcome of the model is the prediction of directional evolution in damage and plasticity, leading to emergent anisotropy in the material’s response. As a result, a comprehensive micromechanic framework is developed that can characterize the deformation behavior of UHP-FRC, providing a robust connection between microscale processes and macroscale performance. This method incorporates Piola’s ansatz to link granular micromechanics with the continuum scale and introduces objective kinematic descriptors to represent grain-to-grain relative displacements under finite deformations. Evolution equations for damage and plastic variables, derived using Karush–Kuhn–Tucker (KKT)-type conditions, govern the interactions at the grain level. The model’s applicability is demonstrated through numerical simulations and comparisons with experimental tests in terms of the force–displacement curves. A parametric analysis is also conducted to assess the influence of input parameters on the simulation results. The model replicates the superior tensile and residual strength, excellent crack control, and remarkable resistance to crack propagation that enhance durability and structural integrity of UHP-FRC. The theoretical insights and analysis capability offered by the described model can form a basis for exploiting the immense potential of UHP-FRC for innovative and resilient applications in structural engineering.

Multiple bifurcations due to symmetry often occur when analyzing nonlinear structural motifs with axial symmetry. The identification of multiple bifurcation points and the tracing of bifurcation paths become significant challenges in numerical analysis. In this paper, we address a numerical problem of nonlinear bifurcation in a symmetric structure exhibiting double bifurcation points. By focusing on the initial imperfection vector corresponding to the partial irreducible representation of its symmetry, we propose a modified stiffness method. This method utilizes the orthogonalization transformation differences to separate the multiple bifurcation points of the second-order irreducible representation of the stiffness matrix into a single bifurcation point. As a numerical example, bifurcation analysis of an axially symmetric fullerene truss structure is conducted to demonstrate the effectiveness of the proposed method. This study successfully addresses the issue of multiple bifurcations in axially symmetric structures by incorporating group-theoretic bifurcation theory and modifying the stiffness method, as validated by the numerical analysis of a fullerene truss structure.

Monolayered pantographic waveguides are mechanical apparatus consisting of flexible elements hinge-connected in a diamond shape, that store elastic deformation energy on stretch gradients and exhibit an extensible-to-inextensible transition in tension. This yields exotic dispersion properties and leaves room to the hypothesis that elastic solitary waves may propagate through these waveguides. The present communication delves into this issue by exploiting a homogenized continuum description based on Hookean interaction potentials at the micro-scale—where flexible elements are considered to be inextensible—to derive admissibility conditions for solitary wave propagation. It is found that monolayered pantographic waveguides admit elastic rarefaction solitary waves. Solitary waveforms and their spectral stability are analyzed numerically.