Acta Mechanica最新文献

This paper investigates the nonlinear dynamic response of auxetic thin plates subjected to a combination of resonance while resting on a viscoelastic Pasternak foundation. Auxetic materials, known for their unique negative Poisson’s ratio, exhibit superior mechanical properties. It makes them ideal for applications requiring enhanced energy absorption and vibration resistance, such as soft robotic systems. The study derives the governing equation of motion using classical plate theory, nonlocal elasticity, and external influences, including magnetic fields. To solve these nonlinear equations, analytical methods such as the Galerkin method and the multiple time scale perturbation method are employed. While the primary focus is on combination harmonic excitation, the effects of plate thickness, auxetic and small-scale factors on the nonlinear dynamic response are also examined. Furthermore, advanced nonlinear dynamic analysis tools such as Poincaré sections, phase portraits, and Lyapunov exponent evolution are used to evaluate the system’s stability and chaotic behavior. These methods facilitate an understanding of periodic, quasi-periodic, and chaotic responses. Unlike previous studies, this work focuses on the combined effect of harmonic excitations and magnetic fields on auxetic plates. It analyzes how parameters like plate thickness, auxetic ratio, and small-scale effects influence system behavior. Advanced tools, such as phase portraits and Lyapunov exponents, are used to evaluate stability and chaos. The findings offer new insights into designing auxetic structures for vibration control and stability in smart systems and soft robotic applications.

Under plane strain conditions, the leading two terms of the asymptotic stress field near the interface corner of two dissimilar nonlinear elastic–plastic materials with differing hardening behavior were formulated. Assuming that the second material has a higher hardening coefficient (n₂ > n₁), two limiting cases were considered: (1) a rigid case with zero secondary displacement in the second material and (2) a non-rigid case where it equals the first material’s primary displacement. The associated eigenvalues and mixed-mode parameters were then computed for varying angle and hardening levels of the second material. The obtained results exhibited a distinctive characteristic at the angle of 130°, where the mode-mix parameter remains unchanged with varying hardening coefficients. Coefficients for the first two stress terms were determined by minimizing the RMS difference between asymptotic and finite element (FE) stresses under tensile loading. Agreement was assessed across various angles and hardening coefficients. Higher n₁ values improved correlation in the first material by reducing mode-mix contrast in two materials. Larger notch angles and greater hardening in the second material increased deviations, requiring additional asymptotic terms for accuracy.

This paper discusses axisymmetric contact problems of pressing absolutely rigid stamps in the form of bodies of revolution into a homogeneous elastic half-space with static friction. It is assumed that the contact zone is circular with a radius that is not known in advance. Using rotation operators, the problem solution is reduced to a singular integral equation of the second kind with variable coefficients. Based on the theory of the analytic functions, a closed solution in quadratures is constructed. Some important special cases of the problem are considered. Using numerical calculations, the patterns of change in the radius of the contact zone, contact stresses and rigid displacement of the stamp are determined depending on the maximum value of the friction coefficient.

In this work, the isogeometric analysis (IGA) is employed to study the dynamic instability characteristics of functionally graded (FG) multilayer graphene-reinforced composite plate with holes. The laminated nanocomposite plate is subjected to a periodic uniaxial in-plane load. The modified Halpin–Tsai scheme and rule of mixtures are utilized to evaluate the effective material properties of the nanocomposite plate. The third-order shear deformation theory (TSDT) of Reddy is used to describe the displacement field of the plate. Dynamic instability regions of graphene platelets reinforced composite (GPLRC) laminated plates with hole are approximated by applying the IGA and the Bolotin’s method. To demonstrate the capability of the developed formulation in predicting the dynamic instability behavior of GPLRC plates with central holes, several numerical examples are solved and compared with the existing solutions. Then, parametric studies are performed to examine the influences of significant parameters on instability zones of the functionally graded graphene platelet reinforced composite (FG-GPLRC) plates with circular/rectangular holes.

The present study develops an extended analytical framework for investigating Love-type wave propagation in multilayered magneto-electro-elastic (MEE) composites while accounting for nanoscale electrical, magnetic, and mechanical interfacial imperfections. The primary purpose is to establish a generalized dispersion relation that unifies classical Love-wave theory with coupled-field effects and imperfect interface conditions. The methodology employs the complex function approach in conjunction with the Helmholtz equation and wavefield superposition theory. Interfacial imperfection factors are introduced via a spring-type boundary model, leading to an infinite system of equations. A systematic truncation procedure ensures convergence of the analytical solution, and numerical simulations are performed to illustrate the influence of imperfections, thickness ratio, and coupling coefficients on dispersion, attenuation, and coupling efficiency. Findings reveal that imperfections significantly suppress phase velocity, with electrical defects producing stronger effects than magnetic ones, while mechanical bonding imperfections accelerate attenuation. Combined imperfections exhibit a synergistic nonlinear influence, producing dispersion shifts more severe than the sum of individual effects. Comparisons between EMO and EMS boundary conditions highlight that stress-driven EMS interfaces are more sensitive to imperfections than displacement-driven EMO boundaries. Additionally, increasing the guiding layer thickness enhances wave confinement, raising phase velocity and partially mitigating defect influence. Validation is achieved by demonstrating that the model naturally reduces to the classical Love-wave solution in the absence of coupling and imperfections, showing excellent agreement with previously published results. The novelty of the work lies in providing the first comprehensive formulation that integrates piezoelectric, piezomagnetic, and imperfection effects within a unified Love-wave framework. Limitations include restriction to anti-plane shear (SH) motion and idealized isotropic elastic half-space substrates, which may be extended in future studies to anisotropic or viscoelastic media. Practical applications include non-destructive evaluation of layered composites, defect detection, fatigue life prediction, energy harvesting, and the design of piezoelectric/piezomagnetic sensors.

This study develops a unified framework to analyze the random vibration of piezoelectric nanobeams on viscoelastic foundations. Using nonlocal elasticity and Hamilton’s principle, governing equations are derived within a unified shear deformation theory that includes Timoshenko, Reddy, sinusoidal, hyperbolic, and exponential models. A frequency response function is formulated for stationary white noise excitation and validated with literature results. Parametric results show that nonlocal effects increase vibration amplitudes, higher-order theories provide greater accuracy than the Timoshenko model, and voltage and temperature amplify responses due to electromechanical and thermal coupling. The framework offers a versatile tool for designing nanoresonators, sensors, and actuators under random loads requiring precise dynamic modeling.

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.