Archive of Applied Mechanics最新文献

This study investigates sandwich FGM diaphragms for high-temperature capacitive pressure sensors. A three-dimensional high-order shear deformation theory with novel polynomial–trigonometric shape function is developed, with solutions obtained using Galerkin’s method. Results reveal boundary conditions significantly impact performance, with clamped boundary conditions reducing deflection by 50.75% versus simply supported boundary conditions. Material composition in sandwich FGM diaphragms substantially affects sensitivity, as metal-rich configurations (1-3-1) demonstrate 6.01% higher capacitive response than ceramic-rich configurations (2-1-2). Geometric parameters create competing effects: Increased width enhances sensitivity up to 37.36%, while thicker plates show reduced responsiveness despite higher initial capacitance. The inclusion of elastic foundation modeling reveals how foundation stiffness modulates both sensitivity and linearity, providing an additional design parameter for application-specific optimization. Temperature gradients and microscale effects further enable fine-tuning of sensor performance. The analytical model shows excellent agreement with finite element simulations (discrepancies < 5%), offering valuable design guidelines for high-temperature pressure-sensing applications.

In this manuscript, we investigate both the direct and converse flexoelectric effects in an elastic, isotropic dielectric nanotube. To examine these phenomena, we consider two loading scenarios applied at the lateral surface of the nanotube: a mechanical moment (torsional loading) and distributed electric charges. The ends of the nanotube are assumed to be subject to fixed mechanical or electrical boundary conditions, depending on the case. The governing field equations are derived using a variational approach based on the strain energy functional and the virtual work of external forces. All boundary conditions, both mechanical and electrical, are assumed to be satisfied a priori. The formulation is developed in a general form and later specialized according to the geometry of the nanotube. We compare the mechanical responses induced by the applied moment to the electrical responses induced by surface charges, with a particular focus on the influence of the ratio between the material length scale and the micro-inertia length scale. The results are presented graphically and analyzed in detail. In summary, the study highlights that the internal length scale of the material plays a significant role in the flexoelectric response, especially when it is comparable to or smaller than the macroscopic dimensions of the structure. Furthermore, Saint-Venant's principle is found to be applicable to both the mechanical and electrical responses in this context.

This paper presents a vibrational analysis of a thin plate, simply supported on all four edges, to identify the impact force. The plate is made of a composite material—concrete reinforced with steel fibers. Anisotropy is considered to compare two approaches: The Huber approach and our own, focusing on the element representing shear stiffness. The effectiveness of the Tikhonov and TGSVD methods is examined in reconstructing multiple and successive impacts. Successive impact identification is analyzed with respect to fiber orientation, sensor positioning, and the influence of measurement noise. The study develops a successful method for analyzing the orientation of steel fibers in the three selected directions, particularly with respect to the primary shear direction. Quantitative results demonstrate that our method significantly improves reconstruction accuracy compared to the Huber approach, achieving relative errors as low as 2.96 × 10^⁻2% using TGSVD and 4.05 × 10^⁻2% using Tikhonov regularization, whereas Huber’s method yields errors of 6.66 × 10^⁻2% with TGSVD and 4.73 × 10^⁻2% with Tikhonov under similar conditions, particularly regarding the effect of shear stiffness in the primary direction. The study confirms that Tikhonov and TGSVD methods effectively stabilize inverse reconstructions, enabling reliable impact force identification even in the presence of noise and anisotropic material behavior.

This study employs an improved kinematic beam model to investigate the free vibration response of functionally graded sandwich (FGS) curved beams. The model takes into account the thickness stretching effect and utilizes a new parabolic shear and normal deformations curved beam theory. The boundary conditions at the upper and bottom ends of the beam are satisfied without the use of any shear correction coefficient. The vertical displacement is expressed through a parabolic function, dividing it into bending, shear, and thickness stretching components. The dynamic evolution of material properties within the skins is intricately linked to the structural integrity of the system. This evolution is assumed to change continuously along the thickness coordinates and is contingent upon the volume fraction of constituents. Two distinct functions, the power-law (P-FGM) and the sigmoid-law (S-FGM) distributions, are meticulously characterized to represent this transformation. In contrast, the core of the structure remains composed of a uniform material, contributing to its overall stability. The theoretical framework, shaped by Hamilton’s principle, is utilized to establish governing equilibrium equations, specifically tailored to elucidate the free vibration response of curved beams. By considering the interplay of material variations and structural geometry, this approach allows for a comprehensive understanding of the system’s dynamic behavior, offering insights into its vibrational characteristics and overall performance. The Navier’s solution method and the eigenvalue technique are employed to solve these equations and obtain the non-dimensional fundamental frequencies of simply supported FGS curved beams. The credibility of the proposed mathematical model is authenticated through a comparative analysis with the available literature review based on higher-order shear deformation theories (HSDTs). The impacts of variables such as geometry, power-law coefficient, and radius of curvature on the dynamic response of FGS curved beams are investigated. The results presented in this study can serve as reference points for comparison with numerical methods such as the finite element (FE), differential quadrature (DQ), Ritz, and others approaches.

This study investigates the propagation characteristics of Rayleigh-type surface waves in layered viscoelastic media, with a particular focus on the role of impedance boundary conditions. The effects of material gradation, viscoelastic damping, and geometric configuration on wave speed and dispersion behavior are comprehensively analyzed, providing insights into the complexities of wave dynamics in heterogeneous media. A combination of analytical formulations and robust numerical techniques is employed to investigate the dispersive and damping characteristics of Rayleigh-type waves. The analysis systematically examines the effects of affecting parameters, including layer thickness, material gradation profiles, and viscoelastic properties, under impedance boundary conditions, thereby assessing their individual and combined influence on wave propagation behavior. The study demonstrates a pronounced sensitivity of Rayleigh-type wave characteristics to both impedance contrasts and material gradation parameters, highlighting the complex interplay between structural inhomogeneity and viscoelastic dissipation. These results provide valuable insights into the behavior of surface waves in engineered layered systems as well as in heterogeneous natural media. This work presents a novel framework for analyzing Rayleigh-type wave behavior under realistic boundary conditions and heterogeneous media. The findings have significant implications for geophysical exploration, structural health monitoring, and the design of advanced materials. Moreover, the results provide a solid foundation for future investigations in applied mechanics and wave-based diagnostics in layered viscoelastic systems.

The hydrodynamic behavior of water waves interacting with a surface-piecing π-shaped breakwater over uneven seabed configurations is analyzed using the eigenfunction matching method (EMM). The continuous seabed is modeled by shelves separated by steps. By employing eigenfunctions with unknown coefficients, the conservations of mass and momentum for each step are formulated into a system of linear equations. The hydrodynamic forces and moment on a variable floating breakwater with and without barriers over variable bottom are formulated. In the absence of thin vertical barriers, the system simplifies to the case involving a floating breakwater over variable bottoms. To assess the accuracy of the proposed model, the computed results are compared with the existing data from the literature, demonstrating excellent agreement. The model is further applied to investigate wave diffraction characteristics. Reflection and transmission coefficients, as well as wave forces, are analyzed in relation to various geometric parameters. Numerical results indicated that the π-shaped floating breakwater significantly alters wave diffraction patterns and energy distribution. Additionally, the structure is shown to reduce excitation wave forces when subjected to incoming waves.

The element-free Galerkin method (EFGM), a meshless approach, was applied to the stress analysis of adhesively bonded single-lap joints and compared with finite element method (FEM) and analytical solutions. EFGM successfully reproduced the general stress distributions, including three-dimensional effects such as anticlastic bending, free-corner stresses, and out-of-plane components that are not captured by classical analytical models. Error analysis revealed that FEM consistently provided closer agreement with analytical solutions, while EFGM exhibited larger quantitative discrepancies, particularly in σ_y and τ_yz. The novelty of this work lies in applying EFGM to the three-dimensional stress analysis of adhesively bonded joints, with a systematic comparison against FEM and analytical solutions, including explicit error analysis and evaluation of out-of-plane stress components. These results demonstrate that, although less accurate quantitatively, EFGM provides valuable qualitative insight and remains attractive for problems involving complex geometries or large deformations where mesh generation for FEM is difficult.

Graphical abstract

Shear deformable beams modelled in accordance with the first-order Timoshenko theory in presence of multiple cracks are the object of this study. Contrarily to the Euler–Bernoulli theory, forced vibrations of the latter multi-cracked beam model have not been satisfactorily studied in the literature. The contribution to the above issue provided by this work consists, first, in the derivation of the “extended” mode shapes explicitly formulated, by means of a distributional approach, to include the effect of multiple cracks on bending and shear stiffness in presence of external proportional damping. Then, it is proved that the orthogonality property of the proposed mode shapes embedding the effect of multiple cracks is preserved and the relevant conditions are explicitly formulated. On this ground, forced vibrations of the multi-cracked beam are analysed by making use of modal superposition exploiting explicit expressions of the Impulse Response Function.

In this short review, the multiscale modeling of dissipative composites undergoing fully coupled thermomechanical processes is outlined through the models presented in a collection of recent works. The aim is to demonstrate the challenges and limitations of: (1) the multiscale approaches (full-field or mean-field techniques), (2) the computational approaches dealing with complex material systems, (3) the alternative methodologies dedicated to the analysis of composite structures, such as those founded on the data-driven modeling and the model order reduction techniques.

This paper focuses on explaining the presence of ice cover in the linear surface wave scattering and radiation by a circular cylinder submerged in a finite-depth ocean. The ice cover has the property that it behaves like a thin elastic plate. Under small-breadth structural oscillations, analytical expressions of the three-dimensional problem are derived in each flow region for the wave motion by an eigenfunction expansion method. However, the velocity potentials of the incident and scattered waves involve the Bessel and Hankel functions for each region. To get complete analytical solutions, we solve the obtained integral equations by the multi-term Galerkin method, where the ultra-spherical Gegenbauer polynomial is chosen as a basis function. This logical approach gives rapid convergence and provides six-figure delicacy in the results of hydrodynamic quantities. The hydrodynamic quantities acting on the rigid cylinder are shown graphically against the frequency. The study also highlights the significance of crucial parameters such as depth, radius of the cylinder, and flexural rigidity of the ice cover to design the breakwater. Based on the numerical results, it can be concluded that the present cylindrical breakwater design is quite capable of attenuating the wave forces and roll moment amplitudes.