Archive of Applied Mechanics最新文献

The model of ice surface softening is represented by a system of three one-dimensional partial differential parabolic equations, taking into account the spatial inhomogeneity. Using one-mode and adiabatic approximations, an analytical soliton solution of a one-dimensional Ginzburg–Landau differential equation for the spatial normal distribution of shear strain to the ice surface is obtained. The analytical form of the numerical procedure for solving the equations, including initial and boundary conditions, is written on the basis of an explicit two-layer difference scheme. The distributions of time and stationary values of static friction force, kinetic friction force and temperature are constructed. Two cases were considered: 1) the upper and lower surfaces move with equal velocities in opposite directions; 2) the upper surface moves along the stationary lower surface. The dependencies of stress, strain and temperature on the coordinate in the normal direction to the surface are determined for different time series. It is shown that a stationary distribution of friction forces and temperature along the thickness of the near-surface ice layer is established with time. The values of the kinetic and static friction forces in the near-surface ice layer increase monotonically with distance from the friction surfaces, while the coordinate dependence of the temperature has a nonmonotonic appearance. The stationary values of the static friction force in the near-surface ice layer decrease with increasing temperature of the friction surfaces, indicating that the surface transforms to a more liquid-like state, while the coordinate dependence has a monotonically increasing form.

The objective of this study is to investigate the reflection phenomena of plane waves from the free surface of an initially stressed rotating nonlocal micropolar transversely isotropic generalized thermoelastic half-space considering Lord–Shulman (LS) and Green–Lindsay (GL) theory. Closed-form expressions for the phase velocities of reflected quasi-longitudinal displacement (qLD), quasi-transverse displacement (qTD), quasi-transverse microrotation (qTM) and quasi-thermal (qT) waves are derived, and boundary conditions yield a system of algebraic equations to determine reflection coefficients. Energy ratios of the reflected waves are also calculated, and it is observed that the law of conservation of energy holds good in the entire reflection phenomena. Numerical results for phase velocity and reflection coefficients are computed using MATLAB examining the effects of initial stress, rotation and nonlocal parameters. Comparisons between micropolar transversely isotropic thermoelastic (MTIT) and nonlocal micropolar transversely isotropic thermoelastic (NMTIT) media highlight the significant influence of these parameters on wave behavior. The model is validated by reducing the problem to a specific case and matching it with established results. The findings are graphically demonstrated providing new insights into wave propagation in anisotropic micropolar thermoelastic materials and significant influences of initial stress, rotation and nonlocal parameters on phase velocity and reflection coefficients offering insights for geophysical exploration.

The aerothermoelastic characteristics of curved fiber composite laminated panels subjected to supersonic airflow are proposed. Based on the refined zig-zag theory, the refined zig-zag theory is adopted to describe the panel and the quasi-steady first-order piston theory is utilized for calculating the aerodynamic force. With considering uniformly distributed temperatures as thermal loads throughout the panel thickness, a finite element method is employed to solve the discretization equation of aerothermoelastic motion using the complex mode method. The validity of this aerothermoelastic model is substantiated through a meticulous comparison of computed results with existing solutions documented in the literature. The maximum error of the present critical flutter dynamic pressure of the curvilinear fiber composite laminates is 0.16% comparing with the literature. Furthermore, different plate theories are investigated to explore aerothermoelastic stability, including flat, critical buckling, and limit cycle oscillation for curvilinear fiber composite laminated panels. Detailed discussions are provided on how curvilinear fiber angle and temperature rise influence natural frequencies and flutter characteristics of composite laminates.

This study is the first in the literature to investigate the beating characteristics of functionally graded graphene platelet reinforced composite (FG-GPLRC) spatially curved (helical) beams using a warping-included mixed finite element (W-MFE) formulation. Integrating GPLs into the matrix material significantly increases the strength and load-carrying capacity of GPLRC structures. This addition also allows the tailoring of properties such as stiffness and tensile strength within the composite structure through the FG dispersion of GPLs. In this study, the GPLRC helical beams are modeled with uniform and nonuniform FG gradation patterns through the thickness. The beam is subjected to a uniformly distributed dynamic load characterized by a half-wave rectified sine function. The forced vibration analysis is carried out using the Newmark time integration scheme. A two-noded curved element is utilized with twelve field variables at each node, three displacements, three cross-sectional rotations, three forces, and three moments expressed in the Frenet coordinate frame. Satisfactory results are obtained for the warping-included natural frequency, normal/shear stresses, displacements, and reactional forces of an FG-GPLRC helical beam with lesser degrees of freedom compared to the three-dimensional behavior of brick finite elements. Through the examples, the effect of the distribution patterns and weight fractions of GPL nanofillers, and the pitch angle of the helical beam on the dynamic behavior of the FG-GPLRC semi-circular helical beam under half-rectified sinusoidal dynamic load are studied in detail. By increasing the pitch angle, the oscillation magnitude of displacements and normal stress distributions of the helical beam decreases for non-uniform distribution patterns. The distribution pattern with the GPL-rich mid-part of the cross-section is more affected by the variation of the pitch angle compared to the case where the top and bottom of the cross-section are GPL-rich.

Materials with a negative Poisson’s ratio are known as auxetic materials, which are highly desirable for improved resistance to indentation and impact. Angle-ply composite laminates with high anisotropy exhibit auxetic behavior within a specific range of layup angles. In this research, the influence of negative Poisson’s ratio on the mechanical response and the enhancement of the damage behavior of carbon/epoxy composite laminates under low-velocity impact has been numerically investigated. For this purpose, a MATLAB code based on classical lamination theory relationships was developed to determine the range of layup angles to achieve both negative Poisson’s ratio in-plane and through-thickness (out-of-plane). Then, the layups with the most negative through-thickness and in-plane Poisson’s ratio values were selected. Also, two new stacking sequences were investigated so that both of them partially exhibited the characteristic of negative through-thickness and in-plane Poisson’s ratio. The progressive damage model is written and implemented using a computer code in the Abaqus user-material subroutine. The progressive damage model consists of Hashin and Puck failure criteria and the damage evolution model based on the equivalent strain method to predict the initiation and evolution of damage for matrix and fiber. The results indicate that the new laminate configurations have 66% higher effective longitudinal modulus and 173% higher effective transverse modulus compared to the in-plane and through-thickness auxetic ones, respectively. In addition, the proposed configurations showed less overall damage under low-velocity impact loading compared to the auxetic laminates. Based on the investigations, the new configurations with features such as high impact force, low impact time, and low maximum displacement could be suitable for use in structures with a hardwall design approach.

This research aims to establish the semi-analytical approach for nonlinear dynamic buckling and vibration responses of functionally graded graphene platelet reinforced composite (FG-GPLRC) circular plates and spherical shells subjected to time-dependent radial pressure and thermal loads. The higher-order shear deformation theory with von Karman’s nonlinearities and the nonlinear viscoelastic foundation model is used to establish the expression of the fundamental equations of considered structures. The shells and plates are considered with clamped and immovable edge, and shallow curvature of the shells is applied. The Lagrange function is applied to establish the total energy of structures, and the potential function of viscous damping of the viscoelastic foundation is expressed using the Rayleigh dissipation function. The motion equation of the structures can be formulated using the Euler–Lagrange function. The dynamic responses are obtained using the numerical method, and the critical dynamic buckling loads are obtained using the dynamic buckling criterion of Budiansky–Roth. The large effects of material parameters, geometrical parameters, and nonlinear viscoelastic foundation on dynamic responses of considered structures are investigated and discussed in many numerical examples.

In the present study, a series of lattice structures with Gyroid minimal surfaces were meticulously designed to incorporate linear density gradients and two distinct trigonometric function-based density gradients. These advanced architectures were subsequently compared and contrasted with a uniform lattice sandwich structure. The mechanical behavior and energy absorption characteristics of the four lattice sandwich structures were rigorously investigated through a combination of experimental testing and finite element analysis (FEA). The results of this comprehensive analysis revealed that during compression, all four gradient lattice structures exhibited varying degrees of shear slip, which manifested as discernible discrepancies in their respective stress–strain curves. Relative to the uniform lattice structure, the linear gradient lattice sandwich structure exhibited an enhancement in elastic modulus by 1.69%, while the square sine function gradient lattice sandwich structure showed a significant increase of 14.45% in elastic modulus. Conversely, the square cosine function gradient lattice sandwich structure experienced a reduction in elastic modulus by 9.61%. Employing either a linear gradient or a square sine function density gradient design was found to augment the load-bearing capacity of the uniform lattice structure. Notably, when the strain in the uniform structure reached densification strain, it absorbed energy exceeding 5.842 MJ/m³, indicating superior energy absorption capabilities among the four structures examined, thus rendering it particularly suitable for applications where high energy absorption is imperative. Furthermore, finite element simulations were conducted to validate the experimental findings, and the simulation results demonstrated a high degree of correlation with the experimental data, with discrepancies less than 6%, thereby confirming the reliability of the FEA model in predicting the performance of these intricate lattice structures.

The reduced multibody system transfer matrix method is a completely recursive method utilizing joint coordinates and applicable for evaluating the generalized accelerations of a multibody system at any given moment, provided that the generalized coordinates and velocities are known. For an open-loop multi-rigid-body system, the generalized coordinates of the system are composed of the generalized relative coordinates of the joint elements. Typically, for each joint element, the dimension of the generalized relative coordinates is equal to its relative motion degrees of freedom, leading to minimum dimension of the generalized coordinates of the system, which is equal to the degrees of freedom of the system. However, this may result in singularity for a ball-and-socket joint element when evaluating its generalized accelerations if any triad of Euler angles is utilized as its generalized relative coordinates. The tetrad Euler parameters are an alternative to Euler angles to resolve such a singular problem, which is a common practice in the dynamics approaches using body coordinates as generalized coordinates; nevertheless, it has not been observed in the completely recursive methods with joint coordinates. In this paper, the self-constraint equations of Euler parameters are taken into account to establish the corresponding reduced transfer equations characterized by a symmetric generalized inertial matrix, which are in completely recursive form. Fundamental numerical stability analyses are conducted via condition numbers of corresponding matrices, demonstrating that employing Euler parameters to describe the relative kinematics of a ball-and-socket joint element enhances numerical stability compared to Euler angles.

The aim of the present work is to discuss the fractional mass-spring system with damping and driving force, considering a simple modification to the fractional derivatives with a non-singular kernel of the Atangana–Baleanu and Caputo–Fabrizio types. We introduce two novel modified fractional derivatives that offer advantages when the fractional differential equations involve higher-order fractional derivatives of order (1+alpha ) or (alpha +1), with (0<alpha <1). Previous definitions of fractional derivatives with non-singular kernel do not have a unique definition, leading to significant inconsistencies. One of the main results of the present work is that the proposed modifications provide a unique result for the fractional-order derivatives (1+alpha ) and (alpha +1). Additionally, we apply these two novel fractional derivatives to the fractional mass-spring system with damping and driving force. In the case of the modified Caputo–Fabrizio fractional derivative, novel analytical solutions have been constructed, showing interesting oscillating time evolution with a transient term not previously reported. This transient term features an initial nonzero oscillating return away from the equilibrium position. For the modified Atangana–Baleanu fractional derivative, the numerical solutions also exhibit this nonzero oscillating return away from the equilibrium position. These results are not present when using the Caputo singular kernel derivative, as demonstrated in the comparison figures reported here.

The control of the drag, noise, and vibration of underwater vehicles has always been a hot topic, causing the study of skin with multiple functions to become a development trend. In the present paper the vibration isolation and sound radiation reduction characteristic of a multiple functions skin, micro-floating raft array skin (MFRAS), are assessed by a mathematical model. The mathematical model is developed based on the thin plate theory and the effective medium theory and validated by the finite element model and reference. The structural parameters of MFRAS have been discussed and optimized by orthogonal experiment design with the evaluation index, the average value of the mean square velocity level. The results show that the MFRAS can isolate the vibration transmission of internal equipment by mismatched impedance between MFRAS and plate, and then reduce the sound radiation. The optimized MFRAS can reduce the mean square velocity level by 1.35 dB and the sound radiation power level by 2.47 dB within the frequency range of 10–2000 Hz compared with the equal weight free damping layer.