Acta Mechanica最新文献

This paper presents a novel locally resonant metamaterial structure and proposes a method to analyze its elastic wave dispersion properties. The structure is conceived as a multiple beam system with parallel beams transversely interconnected by periodic arrays of small resonators, each consisting of a spring-mass-spring subsystem in parallel with a couple of springs. Inserting the resonators between the beams, instead of attaching them as external appendages like in some alternative examples of locally resonant beams in the literature, makes the structure appealing for practical realization and use; furthermore, hosting several arrays of resonators gives the possibility to open multiple band gaps. The proposed method is a homogenization approach for flexural wave dispersion analysis, which removes the equations for the resonators from the set governing the dynamics of the system and reverts the original structure to an equivalent one featuring a tri-diagonal effective mass matrix with frequency dependent terms. The advantage of the homogenization approach is twofold: (1) it demonstrates that the band gaps arise in the frequency ranges where the effective mass matrix is negative definite, generalizing the well-established concept of band gaps attributable to negative mass effects in single locally resonant beams; (2) it provides dispersion curves and band gaps very efficiently, and the band gaps are identified upon calculating the eigenvalues of the tri-diagonal effective mass matrix. Analytical expressions of the band gap edges are obtained for the baseline case of a double beam system, to be readily used for design. Additionally, the exact transfer matrix method in conjunction with the Bloch theorem is formulated as alternative to the homogenization approach for wave dispersion analysis. Finally, the proposed concept of locally resonant structure and pertinent homogenization approach are validated by calculating the transmittance properties of the corresponding finite structure, via the standard finite element method.

The recent uniaxial micron-compression experiments exhibit the size effect and stochastic phenomenon such as stair-like fluctuation of the strain for the plasticity deformation of the single-crystal micropillars. Nevertheless, the current crystal plasticity theories fail to predict and characterize these phenomena due to lack of consideration of the related physical mechanisms. To compensate for such deficiency, this paper mainly aims to establish a dislocation-based crystal plasticity model for the single-crystal micropillars in the micro-compression to characterize the jerky fluctuation features by considering variational and stochastic micro-boundary conditions, which are controlled the dislocation source length. The new model is applied to investigate the size effect and stair-like fluctuation of the strain for single-crystal Ni with size from 2 to 20 μm by the finite element analysis. The predicted intermittent flows match well with those by experimental observations during the plastic flow. The simulation results reveal that the stress and the amplitude of the strain burst show obvious size effect and stochastic behavior.

The equilibrium of two rigidly connected elastic half-planes made of different materials, with a thin rigid inclusion placed on the border of their separation, is considered. One side of the inclusion is connected to one of the half-planes, and the other is exfoliated with the formation of a crack. The frictional contact of the crack faces near its tips is taken into account. Using the Wiener–Hopf method, the solution of the system of integral equations of the problem is obtained in a closed form. The dimensions of the areas of contact of the crack faces, stress distributions in the areas of contact, at the boundary of the separation of the half-planes outside the crack and at the junction of the inclusion with the half-plane, asymptotic distributions of stresses and displacements in the vicinity of the end of the inclusion were found.

This paper aims to derive the motion equations for a small-scale flexoelectric-multilayer plate and move deep through its vibrational response to several determining variable variations. Flexoelectricity indicates the electrical polarization induction in response to the non-uniform strain gradient. As moving toward small scales, the importance and the role of this property comes more to the picture. The under-examination structure is fabricated of three layers; a mid-layer which is assumed to be composed of the porous exponential and power law-functionally graded materials, two flexoelectric face sheets, and the Vlasov foundation. The motion equations are derived mathematically based on the new EP of porous material, Hamilton’s principle, and modified couple stress theory. Utilizing the new EP power law besides evaluating the influence of the variables, length scale parameter, materials composition, geometrical characteristics, porosity, foundation parameter, and boundary conditions (B.C.s) on the dimensionless natural frequency (DNF) of such a sandwich model is the novelty of this paper. It is revealed that the lateral ratio enhancement causes DNF and stiffness reduction in the model. Furthermore, among all considered B.C.s, simply support and clamped support refer to the lowest and the highest DNF, respectively. The content of the recent paper serves as a good source to provide a better understanding of the vibrational response of high stiffness-to-weight ratio structures to different variable variations.

Compared to homogeneous beams, metamaterial-based sandwich beams are known to be lighter and provide better mechanical characteristics. However, their application has mainly been limited to large-scale structures, and their potential for granting small-scale structures enhanced characteristics has not been fully explored yet. The present manuscript aims to investigate nonlinear vibration in size-dependent metamaterial-based sandwich microbeams with hexagonal and triangular lattice cores. To do so, well-known homogenization techniques based on modeling the representative volume element (RVE) of the lattice have been utilized to find the equivalent properties of the nonlinear cores. Moreover, the modified strain gradient theory is used to obtain the governing equation of motion for a small-scale microbeam and the multiple scales method is adopted to investigate the free vibration and primary resonance of the discretized system. Further, size effects and the effect of geometry on the free and forced nonlinear vibration of lattice sandwich beams are examined. In addition to highlighting the size effects, the results indicate that properly implementing nonlinear metamaterials in microbeams can enhance and tune vibrational performance across various length scales. The results of the present paper can provide a more detailed perception of the concept of nonlinear metamaterial-based microbeams and their application in MEMS/NEMS devices.

This paper presents the delamination impact over the dynamic response of the variable angle tow (VAT) composite plates. The VAT plates with various fiber angles are constrained to different boundary conditions for parametric investigation, while delamination is made to present over two different locations with varying sizes. A comparative stochastic vibration study is performed to evaluate the contribution of composite properties to delaminated and intact plates. The randomness in the material properties is modeled with the efficient Latin hypercube sampling method. The polynomial neural network-based surrogate model, considered an efficient substitute for computationally expensive Monte Carlo simulation, is employed in the present work to examine the stochastic behavior of VAT plates. The contribution of the composite properties on the uncertain vibration characteristics is evaluated. It is observed from the investigations that the sensitivity of the composite properties varies significantly with the delamination. Lastly, a failure probability estimation is carried out with a developed polynomial neural network-based surrogate model to provide safe design estimation for various cases.

The different approximating assumptions used in deriving models for structural analysis by dimensional reduction of a 3d continuum to structural components like beams and plates or shells limit the applicability of these models by geometrical constraints. Hence, caution should be exercised when transitioning from the application range of one type of structure model to another one. This should be taken into account especially when stability analyses are performed. In order to demonstrate this, in this note, buckling of annular plates under tensile loading at the inner edge is treated as an example. The ratio between inner and outer radius is varied. For ratios approaching 1.0, plate buckling turns into buckling of circular beams. This is not only a question of accuracy of the solution but can lead to a substantial qualitative change of the character of buckling. Such considerations might be interesting from a theoretical point of view; in any case they are important from the engineering point of view.

The sixth-order basic differential equation of axisymmetric bending model for modified gradient elastic Kirchhoff–Love plates (MGEKLPs) subjected to both transverse and in-plane loads in cylindrical coordinate system is derived on the basis of the simplified deformation gradient theory and general MGEKLP model in Cartesian coordinates, which incorporates two length-scale parameters related to strain gradient and rotation gradient. Using the variational method, five distinct types of axisymmetric boundary conditions (BCs) corresponding to the basic equation are simultaneously obtained. Specifically, there are two modified classical BCs and one non-classical higher-order BC for each boundary. Applying the axisymmetric MGEKLP model, we present a general solution for size-dependent bending deflection and conduct a specific analysis of axisymmetric bending examples in circular and annular thin plates under transverse loads. The study presents two types of (i.e., singly and doubly) clamped and simply supported BCs and delves into the impact of two distinct higher-order BCs on axisymmetric deflection by examining clamped and simply supported circular thin plates. In addition, based on the axisymmetric bending of an annular thin plate with simply supported inner edge and free outer edge under the action of uniform bending moment, the special case of influence of strain gradient and rotation gradient parameters on axisymmetric deflection are discussed. This study enhances the comprehensiveness of axisymmetric bending deformation of gradient elastic thin plates and can offer theoretical guidance for the microstructure design of bending materials.

Lightweight, high-strength, conductive carbon nanocomposites are widely used in axial moving systems, and the primary parametric resonance and primary resonance due to variable axial velocity and tension are quite disturbing when they work in complex electromagnetic environments. In this paper, a theoretical model for predicting Young’s modulus and electrical conductivity of graphene nanocomposites is developed by combining equivalent medium theory, shear-leg theory, and Mori–Tanaka theory. The magnetoelastic vibration equations of axially moving graphene nanocomposite current-carrying beam with variable speed and axial force are then derived and solved analytically and numerically. The amplitude-frequency response equations are derived to describe the parametric resonance of the nanocomposite beam with different graphene volume concentrations. The coupled effect of graphene fillers, electric–magnetic field, and external citation on the system’s primary parametric resonance are deeply investigated. The results showed that the concentration of graphene filler could significantly affect the amplitude response of the system by controlling Young’s modulus and electrical conductivity of the nanocomposite. It can provide a theoretical basis for structure design and vibration control in engineering applications.

In this article, we apply the sensitivity analysis method to capture the influence of various parameters on the inflation pressure, axial force, and the deformation for an inflated and axially stretched cylinder. The material consists of an isotropic ground substance material reinforced with fibers that undergo a continuous and mechano-sensitive remodeling process. The input parameters of the mechanical system are assumed to be distributed according to the uniform probability distribution function. In the sensitivity analysis, we apply the Sobol method to determine how the variations of input parameters affect the inflation as well as the axial force in the cylinder. Special attention is given to the fiber remodeling process associated with a homeostatic balance between the constant fiber creation process and the strain-stabilized fiber dissolution. The results may help to understand the importance of the effect of material parameter changes, for example, due to remodeling processes in the context of diseases or recovering processes, on the overall tissue behavior.