Acta Mechanica最新文献

In this study, the free vibrations of multiple-cracked nanostructures composed of functionally graded materials (FGMs) are investigated based on the nonlocal elastic theory (NET) and the dynamic stiffness method (DSM). The material properties of the FGMs vary nonlinearly along the height of the beam element. Cracks in the FGM nanostructures are modeled as two elastic springs connecting the intact segments at the cracked section. The differential equations of motion of a multiple-cracked FGM Timoshenko nanobeam element are derived using Hamilton’s principle and the NET with continuity conditions incorporated at the cracked sections. Exact closed-form solutions, which resolve the nonlocal paradox associated with the fundamental frequency of FGM cantilever beams, are proposed to construct the dynamic stiffness matrices for multiple-cracked FGM nanostructures under arbitrary boundary conditions. The proposed DSM model enables efficient and accurate computation of the free vibrations of multiple-cracked FGM nanostructures using a minimal number of elements. The reliability of the proposed DSM-based solutions is validated through comparisons with existing numerical results in the literature. Furthermore, the effects of the nonlocal parameters, material gradation, geometric properties, and elastic foundation on the vibration behavior of multiple-cracked FGM nanostructures are analyzed in detail.

In this study, the effect of width ratio (branch channel width/main channel width) on droplet breakup dynamics in a horizontal microfluidic T-junction using oil–water volume fraction contours, pressure profile, and velocity profile has been investigated using 2D simulation. Simulations have been also conducted to reveal the effect of branch arm length ratio (right arm length/left arm length) on droplet breakup dynamics. The numerical simulation is validated with experimental results taken from the literature. Two types of breakup regimes, along with a non-breakup regime, have been found. The breakup regimes are tunnel breakup, and obstructed breakup, and the non-breakup regime is the alternate movement of droplets. The tunnel breakup and the obstructed breakup are mainly due to the pressure difference in the branch channel and the direction of the velocity vectors which are towards the branch’s exit and the pressure swing phenomenon is the reason behind the alternate movement of the droplets. Breakup with tunnel is found in WR (width ratio) = 0.75, 0.5, breakup with obstruction is found in WR (width ratio) = 0.25 and alternate movement is found in WR (width ratio) = 1 for V_w (velocity of water) = 0.01 m/s, V_o (velocity of oil) = 0.18 m/s. It has been found that breakup tendency increases as we decrease the width ratio (1, 0.75, 0.5, and 0.25) and increase the arm length ratio (0.4, 0.6, and 0.9). Some 3D simulations have been performed regarding these and the 3D simulations confirm the accuracy of the 2D simulations. Droplet breakup conditions have been studied. Various mixed flow regimes have been identified and illustrated. Mixed flow patterns have been displayed with the help of a flow pattern map for the width ratio = 1, 0.75, 0.5, and 0.25. Prediction of simulated pressure gradient have also been done with the help of the Dimensional analysis for width ratio = 1 and 17% of average error is found between predicted and simulated pressure gradient. This quantitative analysis of the pressure drop evidenced that the solver correctly captures viscous dissipation and interfacial forces and the design of bifurcated channel geometry is optimal.

This article presents a study on the dynamical response of FG (functionally graded)-CNTRC (carbon nanotube-reinforced composite) curved pipes subjected to a moving load in thermal field. The effect of Winkler elastic foundation as well as the effect of Pasternak shear foundation is taken into consideration. The distribution pattern of carbon nanotubes is designed through the pipe’s thickness using five various profiles. The kinematic equations are obtained and implemented for the nanocomposite curved pipe based on the higher-order shear deformation theory considering the von Karman type of geometric nonlinearity. The time-dependent governing equations are formulated for the nanocomposite curved pipe via the Hamilton’s principle. The Ritz solution method is implemented to obtain the matrix representation for governing differential equations with three different types of boundary conditions. The obtained time-dependent equations are traced in time by considering the Newmark time marching method. Finally, several numerical examples are discussed to explore the influences of the important parameters on the dynamical response of the FG-CNTRC curved pipes subjected to a moving load.

In this work, we will study, from the analytical point of view, two problems arising in second-gradient thermoelasticity. The first one involves the Lord–Shulman second-gradient theory. An existence and uniqueness result is shown by using the theory of linear semigroups. Then, we prove that the energy decay is of exponential type and that the semigroup associated to the differential operator is not differentiable, which implies that this is not analytic neither. The second problem includes the so-called Moore–Gibson–Thompson second-gradient theory. Two cases will be considered if we assume that the thermal law includes (or not) fourth-order spatial derivatives. In the case of second-order spatial derivatives, we recall that the problem has a unique solution but the energy decay is slow; meanwhile, if fourth-order spatial derivatives are present, the decay is of exponential type. For this last problem, we study the analyticity of the semigroups depending on a constitutive coefficient.

With the development of aerospace industry, the complexity and large size of spacecraft bring huge time cost for simulation. The damping characteristics of materials and the influence of solar heat flux will further lead to a decrease in computational efficiency. In this study, a model order reduction method for viscoelasticity-thermal coupled multibody systems is proposed. The Absolute Nodal Coordinate Formulation (ANCF) and the Kelvin–Voigt viscosity model are used to build the system equation of motion. The Proper Orthogonal Decomposition (POD) method is introduced to reduce the system degrees of freedom. The computational efficiency is further improved by dividing the system motion process into multiple linearized intervals based on the first-order Taylor expansion. To improve the robustness of the reduced-order model, a multi-parameterized reduced-order model is constructed based on Grassmann manifold interpolation theory. Three numerical examples are presented as verification and validation. Results show that the proposed method is able to quickly predict the response of the viscoelasticity-thermal coupled systems with uncertain parameters.

We investigate the expansion or growth of an internally pressurized pre-existing small spherical cavity in soft solid blocks made of compressible isotropic Blatz–Ko materials by accounting for cavity surface effects. We seek to study the influence of the dimensionless elastocapillary parameter called (gamma ^*) and Poisson’s ratio, i.e., (nu _0), on the cavitation phenomenon. In doing so, we revisit the standard approach by transforming the balance equations into a one-dimensional second-order nonlinear ordinary differential equation (ODE). It turns out that the ODE can be solved only numerically when varying the Poisson’s ratio, i.e., (nu _0). Firstly, we focus on the classical case in order to validate our numerical findings, that is, for a specific Poisson’s ratio (nu _0=0.25), the shape factor (eta =) 1.5–100 and zero surface effects. Secondly, we analyze the influence of Poisson’s ratio (nu _0=) 0.25–0.40 on the cavity critical state when (eta =3.5). Thirdly, we study the effects of varying both the Poisson’s ratio and the dimensionless elastocapillary parameter (gamma ^*) on the cavitation phenomenon.

A mechanical model was developed to investigate the effects of micro-morphology and macro-geometry on the bearing capacity of two contacting spheres. First, the influence of the frequency index on the elastoplastic deformation stage was analyzed. Next, by correlating the curvature radii of the two spherical surfaces with the contact area distribution function, an improved asperity contact area distribution function was derived. Finally, a fractal contact model for interacting spherical surfaces was established. The results indicate that internal contact provides a higher load-bearing capacity than external contact. Furthermore, when the radii of the two spheres are equal, internal contact approximates plane contact, and the load-bearing capacity reaches its maximum value. This study provides a theoretical foundation for enhancing the load-carrying capacity of mechanical components such as bearings.

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.