Acta Mechanica最新文献

This paper presents an analytical approach for the nonlinear buckling and postbuckling responses of functionally graded graphene platelets-reinforced composite (FG-GPLRC) complexly curved caps with porous core under uniformly distributed thermal and external pressure resting on the nonlinear elastic foundation using the first-order shear deformation theory (FSDT) with the geometrical nonlinear sense of von Kármán. Four cap types are considered including spherical caps, ellipsoid caps, sinusoid caps, and paraboloid caps in this paper, and the results of circular plates can be obtained by the radius of the shell’s curvature approaches infinity. The graphene platelet (GPL) nanofillers are distributed into the polymer matrix of two coatings according to the uniformly and functionally graded laws in the thickness direction. The Galerkin method is applied and the expressions of thermal critical buckling loads and thermal and mechanical postbuckling curves of the caps are determined. The effects of cap types, geometrical properties, imperfect deflection, and nonlinear elastic foundations on the critical buckling loads and postbuckling curves of the caps and plates are discussed in numerical results.

In this paper, we consider the linear theory for a model of a thermopiezoelectric nonsimple body as presented in Passarella (Entropy 24:1229, 2022) in which the second displacement gradient and the second gradient of electric potential are included in the set of independent constitutive variables and in which an entropy production inequality model proposed by Green and Laws is considered. After recalling the constitutive equations of the theory, the focus is on isotropic materials, for which the constitutive coefficients were first derived and used to determine the constitutive and field equations. An exponential stability result will be established and a qualitative analysis of plane harmonic wave propagation in the isothermal case will be discussed. Exponential stability will be proved, through the Hurwitz criterion, for a one-dimensional system of a thermopiezoelectric material whose equations involve as unknown fields the displacement, the relative temperature and the electric potential. The qualitative properties of wave propagation for some specific piezoelectric materials (quartz, tourmaline, PZT and LGS), of which values of constitutive constants are known, will be shown.

Significant restrictions have been found in the selection of piezoelectric materials and the direction of wave propagation in earlier studies on surface acoustic wave sensors. The primary goal of the current work is to investigate how wave propagation direction influences the performance of SAW macro- and nano-sensors in an effort to remove such barriers in the technological revolution of SAW sensors. A proposed model is established to study Shear Horizontal (SH) and anti-plane SH wave propagation in piezoelectric materials with surface effects. The theoretical forms are constructed and used to present the wavenumber of surface waves in any direction of the piezoelectric medium, based on the Extended Stroh formalism. In addition, we take into account surface elasticity theory in order to obtain the phase velocity equation based on the wavenumber expression. The model incorporates surface elasticity, piezoelectricity, and permittivity to account for nanoscale surface phenomena. Two configurations are examined: an orthotropic piezoelectric material layer over an elastic framework and a piezoelectric material half-space with a nano substrate. Analytical expressions for frequency equations are derived for both symmetric and anti-symmetric waves. Numerical results highlight the critical thickness of the piezoelectric layer, where surface energy significantly influences dispersion properties. The effects of surface elasticity and density on wave velocity are analyzed, revealing a spring force-like influence on boundaries. The research investigates SH wave transmission in anisotropic, transversely isotropic piezoelectric nanostructures. The findings could aid in designing SAW devices and piezoelectric sensors, as well as producing more effective surface acoustic wave sensors, based on recent theoretical work summaries.

This investigation employs a three-dimensional coupled thermomechanical finite element analysis to ascertain the characteristics of the initiation of cracks in railway curves. The proposed numerical simulation of wheel–rail contact aims to examine the influence of different curvature radii and slip ratios on the temperature rise, fatigue parameters, and fatigue life of crack initiation. The load history is obtained via Universal Mechanism software and utilized in the FE model. This is the inaugural investigation wherein the cyclic plastic material response, as delineated by the hardening model proposed by Chaboche and Lemaitre, and the thermomechanical coupling have been considered in the context of a curved track. Abaqus software uses numerical modeling to determine the stress fields, temperature distributions, and contact pressure during the wheel–rail interaction. To ascertain the fatigue parameter (FP) and the direction of fatigue crack initiation in the rail, the Jiang and Sehitoglu damage model is employed. The critical plane concept is used to establish the initiated crack’s direction. As the FP grows in critical conditions, the crack creation orientation moves toward the depth of the rail rather than the surface. This phenomenon may cause dangerous rail failure and should be prevented by accurately controlling the wheel–rail contact conditions. Incorporating nonlinear thermal effects into the mechanical model resulted in a maximum increase in fatigue parameters and life of 32% and 80%, respectively.

In this paper, the development and application of a perturbation technique is carried out to analyze the behavior of unshearable and inextensible planar beams, with specific attention to the buckling phenomenon and to the application of prescribed shortening, under different boundary conditions. The mechanical model is driven from the literature and revisited in order to specifically address the case of large longitudinal force, which naturally arises in the considered applications. The problem is tackled by deriving an analytical solution, accounting for a proper scaling and expansion of the variables, depending on the considered case (namely, free or prescribed shortening). The mechanical response is then systematically compared to a numerical solution derived via a finite difference approach, showing an excellent agreement within the considered ranges.

Compression-twist metamaterials exhibit unique properties of compression-induced twisting, presenting new possibilities for the development of smart materials. However, achieving multifunctionality solely through conventional configuration design and parametric studies of individual cells is relatively constrained. Gradient metamaterials, which are characterized by continuous spatial variation in physical and mechanical properties through the gradient design of geometric parameters, offer a promising approach for development multifunctional and smart materials. In this study, a novel 3D gradient compression-twist metamaterial (GCTMM) is proposed, with its mechanical properties and deformation mechanisms under in-plane compression investigated by theoretical analysis, experiment, and numerical simulations. The experimental and simulation results demonstrate a nonlinear relationship between the twist angle and compressive displacement. The height and number of cell layers influence the overall stiffness of the GCTMM and affect the deformation coordination between layers. The structure’s compression-twist coupling properties are significantly reduced due to the plastic yield of the inclined rods. Analytical models were developed to describe the twist angle and initial yield displacement, accurately predicting the nonlinear variation in compression-twist coupling behavior and the degradation of the mechanical performance. To enhance structural reliability, an improved GCTMM with protective support columns was designed and analyzed through numerical simulations. The results indicate that the maximum stress within the structure remains below the material’s yield strength, ensuring its reliability and durability. These findings offer valuable insights for the design of gradient buffer materials, the development of mechanical signal enhancement or conversion devices, and the creation of multistage signal transmission sensors.

To overcome certain limitations like shape control and high acoustic impedance of monolithic piezoelectric materials, piezoelectric fiber-reinforced composites (PFRCs) and piezoelectric-viscoelastic (PV) composites have emerged as obvious and amazing replacements. Particularly in PFRCs, piezoelectric fibers are surrounded by non-piezoelectric materials, and the effective material properties of PFRCs are dependent on both the constituent materials and the amount of piezoelectric fibers (fiber volume fraction) present in the elementary units of the composite. The present research article focuses on the transference of Love-type surface acoustic waves in a PFRC layer sandwiched between a viscoelastic polymer layer and a functionally graded piezoelectric-viscoelastic (FGPV) substrate. The effective material properties of the PFRC layer obtained by the rule of mixtures along with the strength of materials approach are used for mathematical computation. The interface between PFRC and FGPV substrate is mechanically and dielectrically imperfect. The material properties of the FGPV substrate vary along the structure’s depth. Dispersion relations have been obtained for both electroded and non-electroded states. Parametric responses of fiber volume fraction, mechanical and electrical imperfections, viscosity, and functional grading on dispersion traits of Love-type wave are demonstrated through graphical plotting. The outcomes of the study can be utilized to theoretically understand the dispersion in PFRCs.

In contacts of rough surfaces, the real contact area is much smaller and thus the contact pressure can be far beyond the yield strength of solids. Therefore, the influence of plastic deformation should be quite considerable in practice. In this paper, an improved incremental contact model is proposed to examine the elastic–plastic contact between a self-affine fractal rough surface and a rigid flat under the plane strain condition. For different rough surfaces with various material properties, the load-contact area relations predicted by the present model are in accordance with direct finite element simulations, and show a linear dependence within 15% contact fraction. Compared with the solution of purely elastic contact, the existence of plastic deformation results in a lower mean contact pressure over the real contact area. For rough surface with a small yield strain, the mean contact pressure rises with the yield stress in a power law: P/(E^*A_c) ∝ (σ_y/E^*)^0.89. This study provides an efficient method for contact evaluation of elastic–plastic solids with highly anisotropic rough surfaces.

This paper proposed a novel combined vibration control method, designed to rapidly stabilize the flexible cantilever beam driven by MFC actuators and rotary motor. Firstly, the dynamic model of the flexible cantilever beam system, incorporating MFC actuators and a rotary motor, was established based on the Euler–Bernoulli beam theory and Hamilton’s principle, using orthogonal polynomials as mode shapes. Then, the voltage applied to the MFC actuators and the rotation angle of the rotary motor, both serving as inputs, have a phase delay relative to the elastic deformation deflection of the flexible cantilever beam to achieve combined control. Moreover, convergence analysis and model effectiveness verification were conducted. Finally, the effects of the phase delay coefficient, voltage control gain, and rotation angle control gain on vibration control effectiveness and system energy were studied. The results show that compared to the individual action of either the MFC actuators or the rotary motor alone, the combined action of the MFC actuators and the rotary motor can achieve superior vibration control effectiveness. These results confirm the feasibility of applying the combined vibration control to suppress the vibration of the flexible cantilever beam and provide a new approach to vibration control for flexible cantilever structures.

The present research contribution investigates a molecular resonant system’s adsorption-induced relative resonant frequency shift, considering the quality of distributed adatoms, the effect of shear distortion, and small-scale effects using non-local elasticity theory. We considered the structure’s several properties of perforation, sandwich, FGM, and porosity. The nanobeam structure can be considered a one-dimensional multi-property system. Using Eringen’s theory of elasticity, small-scale behaviour is modelled. To find the total energy transformation, the substrate-adatom energy and the adatom-adatom energy were calculated based on the van der Waals (vdW) interactions in the framework of the Morse potential and the Lennard–Jones (6–12) potential. The shear beam model (SBM) and the Euler beam model (EBM) were deduced by relying on the mechanical equations and modifying the coupled system equations. Computation was analysed analytically via the Navier-Type solution and numerically using the differential quadrature method. The SBM and EBM yield distinct relative frequency shifts, highlighting the importance of considering shear effects. The results indicate a significant dependency of the resonant frequency shift on the nanobeam’s structural properties and external conditions. This study provides a comprehensive understanding of the dynamic behaviour of multi-property nanobeams under various conditions. The findings can be applied to the design of advanced detection microdevices and microsensors.