Acta Mechanica最新文献

The free vibration characteristics of a shallow-spherical shell mounted on the viscoelastic foundation which is characterized by the fractional-order Maxwell model is studied. Firstly, the fractional-order Maxwell viscoelastic model of foundation is introduced, this model is applicable to engineering scenarios where the foundation exhibits significant viscoelastic behavior, such as the clay stratum and liquid saturated porous stratum, and the frequency-dependent complex modulus and the reaction force resulted from foundation are given. Then, with the help of the stress function, the governing differential equations of the shallow-spherical shell mounted on the viscoelastic foundation are derived in term of only the stress function and the transversal displacement. The complete analytic solution of the stress function and the transversal displacement are finally obtained in term of the classical Bessel functions and the modified Bessel functions. The complex natural frequency is introduced to reflect the attenuation feature of the free vibration. Finally, the numerical example is provided for shallow-spherical shell with the fixed-edge boundary conditions. The first three orders of natural frequencies and the vibration pattern and the corresponding attenuation index are estimated and shown in tables and 3D cloud figure. The influences of the viscoelastic foundation and the two typical vibration patterns with the axisymmetric and the non-axisymmetric properties are discussed in detail.

This study investigates the propagation of Rayleigh-type surface waves in a homogeneous, transversely isotropic piezoelectric half-space under various boundary conditions—specifically, stress-free, electrically open- or short-circuited, and thermally insulated or isothermal surfaces. We analyze the problem within the framework of the Green–Naghdi type III (GN-III) and three-phase-lag thermoelastic models named as model I. Also, studies carry the comparative study with Rayleigh surface wave propagation in piezoelectric media influenced by thermal effects and the presence of voids where this has analytical solutions for Rayleigh wave propagation in a nonlocal piezo-thermoelastic medium with voids, employing the Moore–Gibson–Thompson thermoelasticity theory that incorporates memory-dependent effects named as model II. Plane harmonic wave solutions are employed to determine mechanical displacements, electric potential and temperature variations. Using these results, expressions for stress, electric displacement and temperature gradient are derived. Four secular equations corresponding to different boundary conditions are formulated for the considered half-space. The trajectories of surface particles are shown to follow elliptical paths in a vertical plane parallel to the direction of wave propagation, with the eccentricity of these ellipses explicitly calculated. When there is no phase difference between the vertical and horizontal displacement components, the particle motion degenerates into a straight-line path. A previously established analysis is recovered as a special case of the present model. The effects of various wave characteristics—including phase velocity, attenuation coefficient and specific loss—are illustrated graphically for both the GN-III and three-phase-lag models, using cadmium selenide (a 6-mm class, hexagonally symmetric material) as the representative medium. The findings of this study highlight several distinct scenarios that enhance the understanding of Rayleigh wave propagation in complex material systems, especially those containing voids. This research offers important insights into the interplay between piezoelectric components and surface wave behavior, paving the way for advancements in sensor design, improved energy harvesting techniques and innovative seismic monitoring applications. This mathematical framework can serve as a foundation for the design and development of temperature sensors and other piezoelectric surface acoustic wave devices.

Functionally graded (FG) piezoelectric materials are widely used in designing intelligent components for micro-/nanoelectromechanical systems (MEMS/NEMS). However, as the scale decreases, the size dependence of electromechanical coupling properties becomes an important problem in component design. This paper investigates the electromechanical coupling response of plate-type piezoelectric components commonly employed in MEMS/NEMS. Based on extended dielectric theory, Kirchhoff’s plate theory and von Karman’s geometric nonlinearity, a dynamic model of FG piezoelectric microplate with flexoelectric effect is constructed. The governing equations, boundary conditions and initial conditions are obtained by applying the Hamilton’s variational principle and subsequently discretized via differential quadrature method. The electromechanical coupling response of FG piezoelectric microplate is examined under periodic loading leading to large deflection deformation. The coupling response between piezoelectric effect and flexoelectric effect is analyzed. The influence of functionally gradient index on dimensionless deflection and induced potential is also discussed. This study provides insights beneficial for the design of common plate-type micro-actuators in MEMS/NEMS.

To address the issues of fixed bandgaps and limited regulation capability in traditional phononic crystals, this paper proposes a new type of piezoelectric phononic crystal structure. By integrating active control mechanisms, intelligent optimization algorithms, and real-time feedback systems, this structure achieves precise dynamic regulation of bandgap characteristics. While maintaining structural compactness and lightweight properties, it breaks through the limitations of traditional designs and realizes adaptive adjustment of bandgaps. Based on the electromechanical-thermal multi-physical field coupling mechanism, a complete closed-loop control framework from static parameter optimization to dynamic adaptive adjustment is constructed. The main contents include: a propeller-inspired configuration that enhances low-frequency vibration suppression capability, a PWE/FE hybrid calculation method that solves the problem of multi-field coupling, the MOCOA-CPO-SVR algorithm that improves optimization efficiency, and a sensor–controller–actuator closed-loop system that achieves high-precision frequency matching. This research provides a breakthrough solution for vibration and noise control in fields such as shipbuilding and aerospace.

The growing development of innovative sandwich structures utilizing auxetic metamaterials with improved mechanical properties has enabled a more effective balance between strength and lightweight design in demanding applications, such as aerospace and aeronautical shells, which often feature complex curved geometries subjected to extreme loading conditions and destabilizing forces. With the primary objective of improving the thermomechanical stability of lightweight shells under complex loadings, this work investigates the nonlinear stability of sandwich toroidal shell segments (TSSs) with an auxetic core and carbon nanotube (CNT)-reinforced face sheets. The TSSs, supported by the Kerr foundation, are subjected to combined thermomechanical loading, including axial compression, radial pressure, and thermal effects. The thermal conditions considered include uniform temperature rise and linear or nonlinear gradients across the shell thickness. CNTs are embedded within the temperature-dependent polymer matrix in the face sheets. A novel star-shaped auxetic metamaterial is proposed as the core in the sandwich structure, which provides significant advantages over conventional re-entrant auxetic cellular structures. The governing equations are derived within the framework of Reddy's third-order shear deformation theory (TSDT) and von Kármán-type geometric nonlinearity, and the Galerkin method is used to solve the nonlinear equations. Model validation through comparison with existing studies confirms its high accuracy. Numerical analyses demonstrate the greater effectiveness of the star-shaped auxetic core compared to conventional re-entrant auxetic structures, with critical buckling loads reaching up to 16.07% improvement in thicker shells under elevated thermal loading, highlighting its advantages in a lightweight metamaterial TSS design. Through a comprehensive parametric study, the effects of key geometric parameters of the star-shaped auxetic core on the effective properties of the lattice metamaterial structure are investigated. The study also examines the influence of various combined thermomechanical loading conditions, shell geometric parameters, and Kerr foundation properties on critical buckling loads and postbuckling paths. The results demonstrate that by properly selecting the auxetic core's geometric parameters, auxeticity can be tailored while achieving higher stiffness in the lattice structure to meet diverse application requirements.

This study investigates the free vibration behavior of rotating circular sandwich plates featuring a variable-thickness porous core and composite facesheets reinforced with randomly distributed and agglomerated carbon nanotubes (CNTs). Three porosity distribution patterns—monotonous, symmetric, and non-symmetric—are considered for the core. The stochastic dispersion and agglomeration of CNTs within the facesheets are also taken into account. The analysis is based on the first-order shear deformation theory (FSDT), and the equations of motion are derived using Hamilton’s principle and solved via the generalized differential quadrature method (GDQM). The influence of several parameters—including porosity patterns, CNT mass fraction and agglomeration, thickness variation, and geometric factors—on the natural frequencies of the plate is comprehensively examined. The results reveal that while increased porosity tends to slightly raise the natural frequencies, a higher CNT mass fraction significantly enhances them. These findings are valuable for the design and optimization of advanced structural components in aerospace, defense, and marine applications.

The present study offers a groundbreaking analysis of photo-thermal transport phenomena in semiconductor materials subjected to a mobile heat source. Addressing key limitations of traditional heat transfer theories, this research adopts the Atangana–Baleanu fractional derivative model, which is characterized by a non-singular kernel function. This modern mathematical framework enables a more realistic and accurate depiction of thermal behaviors by capturing the memory-dependent and non-local effects often neglected in classical models.

Using the Laplace transform technique combined with the eigenvalue approach, the study derives closed-form analytical solutions in the frequency domain. These solutions provide deep insights into the dynamic behavior of several field variables—namely temperature distribution, mechanical displacement, carrier density, and induced thermal stresses. Graphical simulations explore how these quantities evolve under varying parameters such as semiconductor depth, fractional-order values, photo-generated carrier lifetime, and the velocity and intensity of the heat source. One of the most significant outcomes of this investigation is the clear demonstration of the finite speed propagation of thermal waves, a feature that conventional hyperbolic thermoelastic models fail to accurately capture. By incorporating fractional calculus, the study reveals the nuanced and time-dependent nature of thermal interactions in semiconductor media. This distinction underlines the effectiveness of the Atangana–Baleanu model in portraying complex thermophysical phenomena.

Guided wave tomography (GWT) methods for precise multi-defect reconstruction are crucial for structural health monitoring. In this work, an improved physics-informed wave tomography framework (PIWT) is proposed for the quantitative reconstruction of multiple defects in plates. A trunk-branch network is employed to reconstruct the wave travel time and velocity field by synergizing the waveguide governing equations and the real travel time data from sensors. This approach speeds up the network convergence of loss function which includes the travel time data, its first-order derivatives, and the physical principle of wave equations to constrain the space of parameters for accurate defect reconstruction. Based on simulation data, the results demonstrate that PIWT achieves the highly accurate defect with the errors of 4.25% in position and 5.5% in depth. Also, experimental validations are conducted to demonstrate the feasibility of PIWT with a defect position error of less than 1.7% and depth location error under 15%. Furthermore, uniform manifold approximation and projection is applied to enable a clear visualization of trajectories representing the defect reconstruction convergence, thereby revealing how incremental sensor data enhance the model’s capability to approximate the true solution. This interpretation provides useful insights into the latent dynamics to bridge the gap between the black-box nature of deep neural networks and the need for transparent and explainable AI, ultimately reinforcing confidence in the model's applicability for broader engineering applications.

This paper investigates the well-posedness and asymptotic behavior of a suspension bridge system, modeling the deck using Timoshenko–Ehrenfest beam theory with fractional damping. Using semigroup theory, we establish existence and uniqueness via the Lumer–Phillips Theorem, showing that the system’s operator generates a contraction (C_0)-semigroup. Spectral analysis proves strong stability, while the Gearhart Theorem rules out uniform stability. Finally, polynomial decay is obtained via the Borichev–Tomilov and Batty–Chill–Tomilov Theorems.