Acta Mechanica最新文献

The strain gradient elasticity theory and surface elasticity theory have been employed to describe the mechanical behavior of materials featuring microstructures within the interior and on the surface, respectively. In this paper, by using Hamilton’s principle, we established a combined model that takes into account both the effects of strain gradient and surface elasticity. Based on this combined model, we investigated the propagation of anti-plane and in-plane surface waves in an elastic half-space. For the anti-plane surface wave, we derived the dispersion equation of surface wave analytically. For the in-plane surface wave, we formulated the linear algebraic equations for the undetermined constants, with the elements of the coefficient matrix detailed in the appendix. We also obtained the range of values for the phase velocity of the anti-plane surface wave and the upper bound for the phase velocity of the in-plane surface wave. We examined the effects of strain gradient constants on the dispersion curves of both the anti-plane and in-plane surface waves. The results show that the dispersion behavior of surface waves becomes richer when both the effects of strain gradient and surface elasticity are considered compared to the case of considering only surface elasticity effect. In addition, we found that when the characteristic length associated with the kinetic energy is relatively large, anti-plane surface wave exists only at small wave numbers. When the wave number tends to zero, the phase velocity of the in-plane surface wave approaches that of the classical Rayleigh waves.

The current article is an innovative attempt to utilize the full layerwise (LW) finite element approach for investigating the nonlinear vibrations of sandwich plates with functionally graded graphene nanoplatelets (GPLs)-reinforced face sheets. The fundamental novelty of this research is the employment of the full LW theory, which provides accuracy equivalent to three-dimensional (3D) elasticity while reducing computational cost, simplifying mesh modification, and enabling faster attainment of the element stiffness matrix by maintaining the 2D structure. The uniform or functionally graded distributions of GPLs within the face sheets are considered. The effective material properties of face sheets are estimated according to the rule of mixtures and the Halpin–Tsai model. Subsequent to confirming the convergence and validity of the numerical approach and formulation, thorough parametric analyses are executed to assess the effects of various factors involving the thickness ratio of the core-to-face sheet, edge constraints, and geometric parameters, together with dispersion pattern, volume fraction, and the dimension of GPLs on the nonlinear vibration conducts of the sandwich plate. The findings demonstrate that as the core-to-face sheet thickness ratio of the sandwich plate rises, the linear and nonlinear-to-linear frequency (NTL) display opposite trends. Furthermore, the NTL ratio is not notably altered by the configuration type of the face sheets.

Most research currently is limited to isotropic or porous materials reinforced by graphene platelets (GPLs). However, functionally graded materials (FGMs) made of two different material constituents offer many advantages in terms of durability, strength, high-temperature resistance, and design flexibility. Therefore, a new FGM model reinforced by GPLs (GPL-reinforced FGM) is proposed to enhance the performance of nanoplate structures. This paper presents analytical solutions for buckling and static bending problems of the GPL-reinforced FGM nanoplates with surface stress effects placed on a Pasternak elastic foundation. Three variation laws of the FGM (i.e., P-FGM, E-FGM, and S-FGM) combined with four GPL patterns (i.e., UD, FG-O, FG-X, and FG-V) are studied. The governing equations of the nanoplate resting on the elastic foundation are derived based on the principle of minimum total potential energy, Reddy’s third-order shear deformation theory (TSDT), nonlocal strain gradient (NSG) theory (NSGT), and Gurtin–Murdoch surface elasticity theory (SET). The Navier technique is then utilized to determine the critical buckling load, deflection, and stress components of the nanoplate. The influence of material parameters, NSG parameters, surface energy parameters, and elastic foundation parameters on the static buckling and bending behaviors of the GPL-reinforced FGM nanoplate is investigated.

The dispersion and attenuation characteristics of Rayleigh waves in a non-uniform viscoelastic half-space with a covering layer are studied in this paper. The half-space and the covering layer are modeled by the fractional-order Zener viscoelastic solid. Compared with the traditional integer-order viscoelastic model, the viscoelastic model with fractional-order derivative is more flexible in describing the complicated history-dependent mechanical behavior. Legendre and Laguerre orthogonal polynomials are used to approximate the displacement field of surface waves. The rectangular window function is used to merge the surface boundary conditions. The complicated problem of solving the complex wave number in the complex region is ultimately transformed into an eigenvalue problem. The correctness of the method is verified by comparing our outcomes with those in the literature. It is found that the present spectrum method avoids the complicated iterative process of root-finding and the pseudo-root and root-missing problem compared to the traditional root-finding method. Moreover, the uneven gradient distribution of the cover layer and half-space has opposite effects on the propagation of Rayleigh waves at low and high frequencies, and the same influence applies to fractional-order effects. The present study has important theoretical significance and application potential in the geophysical exploration and earthquake engineering.

The objective of this paper is to present a mathematical model for examining the response of capacitive MEMS with elastomeric microstructured gaps, to mechanical shock pulses. This type of MEMS has attracted increasing attention in recent years due to its enhanced sensitivity, particularly in healthcare systems. Although the literature successfully develops experimental analysis, it lacks a comprehensive mathematical model to predict behavior, as well as necessary analysis. This paper presents a model that focuses on the response of a half-sine shock. The capacitor gap has been filled with a micro-pillar array made of polydimethylsiloxane (PDMS) as a microstructured layer. Three sets of coupled nonlinear differential equations have been obtained to govern the transverse vibrations of the beam, and the axial and bending vibrations of the pillars. PDMS has been assumed to follow the Kelvin–Voigt model, along with the nonlinear strain. A comparison was made between the air and PDMS gap systems, revealing that the former experiences a response amplitude several times smaller than the latter due to the added stiffness of the pillars in the absence of an electrostatic field. Nevertheless, when the electrostatically actuated beam is subjected to shock, the opposite results may be observed. This is due to the opposing effects of the added stiffness of the pillars and the gap’s higher permittivity. The results demonstrate that the provided model is capable of accurately predicting the response of the microstructured-gap capacitor to mechanical shocks and other external stimuli.

A passive flow control device, Clark-Y airfoil-shaped vortex generator (VG) on NREL Phase VI turbine blade, which has s809 airfoil section, is investigated. Both qualitative oil flow visualization from wind tunnel experiments and quantitative measures of aerodynamic coefficients using steady-state CFD with OpenFOAM are reported. Airfoil-shaped VGs are proposed and compared with traditional rectangular and triangular VGs. The use of airfoil-shaped VGs to delay separation, improving aerodynamic efficiency, inducing local pressure peaks and augmenting vorticity in the flow field are reported in detail. Results show that blades equipped with airfoil-shaped VGs provide a (5%) lift coefficient increase and a (27.68%) drag coefficient reduction compared to clean blades at a stall angle of (alpha = 11^circ ). Airfoil-shaped VGs also generate more vorticity downstream compared to conventional VGs, contributing to maximum increase in peak vorticity inducing an additional momentum to the flow to delay separation without significant drag penalty. Thus, airfoil-shaped VGs offer a promising alternative to traditional VG designs.

The paper deals with the problem of design of unit in auxetic metastructure. The unit is modeled as a two-part spring-like system where each part is with individual stiffness. To overcome the problem of analyzing of each of parts separately, the equivalent spring is suggested to be introduced. In the paper, a method for obtaining the equivalent elastic force of the unit is developed. The method is the generalization of the procedure suggested for substitution of a hard and a soft spring in series with an equivalent one. The nonlinearity of original springs is of quadratic order. As a results, it is obtained that the equivalent elastic force for two equal springs remains of the same type as of the original springs (soft or hard). For two opposite type springs in series with equal coefficients, the equivalent force is soft. The method is applicable for any hard and soft nonlinear springs or spring-like systems. Thus the hexagonal auxetic unit which contains a soft and a hard part in series is analyzed. In the paper, a new analytic method for determination of the frequency of vibration for the unit under action of a constant compression force acting along the unit axis is introduced. The method is applied for units which contain two parts: hard–hard, soft–soft, hard–linear, soft–linear and opposite. The obtained approximate vibration results are compared with numerically obtained ones and show good agreement. The advantage of the method is its simplicity as it does not require the nonlinear equation of motion to be solved.

In this paper, the free vibration analysis of hybrid laminated thin-walled cylindrical shells is investigated based on Sanders’s thin shell theory and artificial spring technology. The hybrid laminated shells are made of graphite fiber reinforced composite (GFRC) and multilayer functionally gradient carbon nanotube-reinforced composite (FG-CNTRC) plies. The influence of Coriolis and centrifugal forces on the shell's strain and kinetic energy, resulting from rotation, has been considered. The orthogonal polynomials are selected as the admissible function and the Rayleigh–Ritz method is employed to obtain the natural frequency. The results of the study are validated against the results of open literature. The influences of CNT distribution patterns, number of plies, stacking sequences, CNT volume fraction, boundary constraints(BCs), rotating speed, and the orientation angle on the natural frequency of the cylindrical shells. The results show that specific stacking configurations can significantly enhance the fundamental frequency of the shell. It provides a reference for the design and optimization of hybrid laminated cylindrical shell structures.

The current work investigates the aerothermoelastic behavior of control fins with nonlinear deployable joints connected to a nonlinear actuator. The fin is attached to a cylindrical body with a hemispherical bow, and the fin–body configuration is subjected to Mach 6 hypersonic flow with a nonzero angle of attack. A Navier–Stokes flow model-based computational fluid dynamics (CFD) solver is coupled to a finite element thermoelastic solver using mapping-based coupling technique. Diffusion function-based smoothing method is used for the CFD grid deformation. The fin is assumed to be connected to a finite stiffness actuator at the root, and the effects of actuator stiffness, actuator freeplay as well as freeplay at the deployable joint are investigated. Flow field, structural and thermal quantities are evaluated and reported for various fin configurations. A complex coupling between different modes of deformation is observed and it is shown that the actuator rotation or angle of attack, and hence torque, strongly depends on the actuator and joint freeplays. The obtained results indicate a significant increase in instabilities in the fin oscillation with increasing joint and root freeplay.

Planar phased array antennas have significant applications in fields such as space communication, electronic reconnaissance, navigation, remote sensing and deep space exploration. This study focuses on the active vibration control of a novel on-orbit assembled large-scale two-dimensional planar phased array antenna. The novel structure and assembly method of the antenna are introduced. Using the finite element method, we develop the dynamic model of antenna structure. Due to the low and dense natural frequency characteristics of the structure, the distributed cable actuators are used to suppress the vibration. Considering the unilateral and saturated constraints of the cable force, the control law is designed by combining the linear quadratic regulator with the Bang–Bang regulator. The controllability criterion and particle swarm optimization algorithm are adopted to optimize the actuator distribution. We validate established dynamic model and control method by numerically simulating. The simulation results indicate that the dynamic model can describe the dynamic behavior as accurately as ABAQUS; the controller can effectively suppress the vibration of the antenna structure.