Archive of Applied Mechanics最新文献

This study presents a fifth-order shear deformation theory for analyzing the displacement and stress of laminated and sandwich beams subjected to sinusoidal, uniformly distributed, and linearly varying loads. The theory's displacement field takes normal deformations and transverse shear effects into account. On both the upper and lower surfaces of the beams, the requirement of zero transverse shear stresses is fulfilled. Hence present theory does not require a shear correction factor. Governing equations and boundary conditions of laminated and sandwich beams are derived using the principle of virtual work. From the stress-equilibrium equations of the theory of elasticity, transverse shear stresses are recovered. Both the stress-free boundary conditions at the external surfaces and the continuity condition at the layer interface are satisfied by the transverse stresses that arise from this approach. Closed-form solutions for simply supported beams are obtained using Navier’s solution method. A MATLAB program is developed based on the present formulation to generate numerical results. A comparison result of present 5th OSDTs and those of the 3rd OSDTs, FSDT, and CBT are presented. The inclusion of transverse normal strain into the theory resulted in significant variation in the displacements and stresses of laminated and sandwich beams when compared to the results predicted from the lower-order theories discarding transverse normal strain.

Determination of the elastic field developed in a heterogeneous material provides useful information for calculating its overall elastic properties. When dimensions of inhomogeneities in such a material are comparable to the intrinsic length scale of its constituents, classical elasticity ceases to produce reliable solutions. Mindlin’s first strain-gradient elasticity, as an enhanced continuum mechanics theory, has proved its success in dealing with such a problem. Hence, this theory is utilized in the present paper to obtain an exact solution of the elastic displacement field induced in an infinite isotropic medium that contains a circular cylindrical inhomogeneity and is subjected to an anti-plane loading. The obtained solution demonstrates the size effect on the elastic field of the medium. On the other hand, an extended version of the equivalent inclusion method which is adapted to Mindlin’s first strain-gradient theory is developed to attack the same problem, leading to an approximate solution. Subsequently, by solving some numerical examples, a comparison between these exact and approximate solutions is provided in this paper.

In the study, we report the snap-through effect of a bistable beam by means of piezoelectric actuators. We first consider a bistable mechanism consisting of a buckled elastic thin beam. The latter is symmetrically equipped with two piezoelectric layers. The electric potential applied on the faces of the piezoelectric actuators is such as a moment at each end of the active layers is produced. The modeling of the elastic beam is based on the elastica theory. The main goal of the study is the investigation of the bistable response according to the applied electric voltage and the configurational parameters. A numerical study is proposed based on the equation of the beam model sandwiched by two piezoelectric layers, and a numerical validation of the model approach is performed using the finite element method. An optimization study is reported for the placement of the piezoelectric actuators as well as their dimensions (length and thickness). We look for the position of the piezoelectric actuators that minimizes the applied voltage to trigger the snap-through and maximize the beam deflection. The work is extended to the bistable actuation using two pairs of piezoelectric elements.

In the theory of anisotropic linear elasticity, there are different approaches to define the elasticity in a coordinate-dependent relation by matrices—commonly, the Voigt-notation—or tensorial expressions using fourth-order tensors. In view of numerical treatment, for example, the finite element method, the stress state is defined by the strain state via the fourth-order elasticity tensor, (textbf{T} = {pmb {mathcal {{C}}}} textbf{E}). In view of analytical considerations required, for instance, for parameter identification purposes, the inverse relation (textbf{E} = {pmb {mathcal {{C}}}}^{-1} textbf{T}) is necessary. In this paper, the inversion of the fourth-order representation is developed in a coordinate-free representation. using the concept of invariant theory, which is based on the principal invariants and the so-called mixed invariants of the strain tensor/stress tensor. The mixed invariants are defined in terms of the structural tensors, which represent the preferred directions of the material under consideration. The advantage here is that the constitutive equations for the anisotropic material (which are invariant under the elements of the material symmetry group) can be represented as isotopic tensor functions. Thus, the compliance tensor ({pmb {mathcal {{C}}}}^{-1}) can be obtained for any orientation of the anisotropy axes. We limit ourselves here to the case of transverse isotropy and orthotropy in a coordinate invariant representation.

This paper investigates the multimodal suppression of the vibroacoustic response of the composite laminated plate using negative capacitance shunts. By means of the energy method and the modified Fourier series method, a semi-analytical electromechanical coupled model is proposed to solve the vibroacoustic response of the laminated plate with multiple shunted piezoelectric patches and general boundary conditions. Three different forms of electromechanical coupled governing equations are derived based on Hamilton’s principle. The proposed model is proven accurate and versatile by comparing the results obtained by the present model with those from FEM and available references. Then, the strain function that directly determines the positions where piezoelectric patches are placed is derived. The influences of placement positions and the negative capacitance parameter on the suppression performance of the shunt are discussed. Finally, multiple shunted piezoelectric patches with the negative capacitance shunt are employed to suppress the multimodal vibroacoustic response of the composite laminated plate. Each shunted piezoelectric patch is placed at the position with large strain function values and is tuned to control a single corresponding mode. As a result, the multimodal vibroacoustic responses of the composite laminated plate with different boundary conditions are all significantly suppressed. The present study provides new insights into the issue of broadband vibration and noise control of composite laminated plate structures in industrial applications.

To investigate the mechanical and micro-failure behavior of stratified rock, a series of uniaxial compression and CT scanning tests of stratified limestone and sandstone at different bedding plane dip angles (α) were conducted. The experimental results showed that with the increasing α, uniaxial compressive strength (UCS), peak strain (ε_1p), Poisson’s ratio (μ) of stratified limestone and sandstone all first decreased and then increased, elastic modulus (E) of stratified limestone continuously increased, E of stratified sandstone first decreased and then increased. At different α, UCS and E of stratified limestone were larger than that of stratified sandstone, ε_1p and μ of stratified limestone were smaller than that of stratified sandstone. For stratified limestone, anisotropy coefficient of μ was the largest and anisotropy coefficient of E was the smallest. For stratified sandstone, anisotropy coefficient of ε_1p was the largest and anisotropy coefficient of E was the smallest. Anisotropy degree of stratified limestone and sandstone was approaching for UCS. Anisotropy degree of stratified limestone was larger than stratified sandstone for ε_1p and μ. Anisotropy degree of stratified limestone was smaller than stratified sandstone for E. The failure category of stratified limestone and sandstone at different α was quite different. Due to differences in failure mode, the morphology and distribution characteristics of micro-cracks along the sample height showed a significant difference. With the increasing α, volume fraction (VF) and the maximum area fraction (AF) first decreased and then increased for stratified limestone, and showed no obvious change trend for stratified sandstone. At α = 0º, 30º, 90º, VF and the maximum AF of stratified limestone were significantly larger than that of stratified sandstone. At α = 60º, VF and the maximum AF of stratified sandstone were larger than that of stratified limestone.

In light of the blood cells motion inside the vein or artery, there is no knowledge available about the importance of the flow of a non-deformable micropolar drop inside a circular cylindrical pipe filled with a micropolar fluid. This paper provides a two-fluid phase motion problem of an axially symmetrical quasisteady movement of a micro-structure fluid drop embedded in another micro-structure fluid of micropolar kind on the axis of an impermeable cylindrical pipe that is discussed under the low Reynolds number conditions. The interfacial tension between the immiscible fluid phases at the drop’s interface is assumed to be very large to ensure that the droplet remains spherical in shape. Also, the microrotation and couple stress relations at the droplet’s interface are used. The general solutions for the differential equations are fulfilled by the stream functions of the micropolar fluids, which are constructed by combining fundamental solutions in cylindrical and spherical coordinates, and then the conditions on the boundaries are fulfilled at the inner surface of the pipe by the Fourier-transform and also at the interface of the drop using collocation methods. The paper’s significance is to discuss and see the effectiveness of the pipe’s inner surface on the hydrodynamic normalised force influencing the drop sphere because of its filling with and existence in a micropolar fluid. Findings indicate that the hydrodynamic normalised force is increasing monotonically with the increase of the droplet-to-pipe radius ratio, and tends to infinity when the droplet’s interface touches the pipe’s inner surface. Additionally, the findings show that when the micropolarity parameters increase, so does the normalised drag force. Our findings for the normalised force agree well with the solutions that are provided in publications. The current study is also significant in the domains of industrial and biomedical operations like coagulation, sedimentation, and rheology of suspension, to name a few.

Vlasov theory of thin-walled beams neglects additional displacements induced by rotation of beam sections, which results in significant errors in calculating dynamic responses. In this study, additional lateral and vertical displacements and additional torques are introduced to modify Vlasov theory of thin-walled beams and a modified Vlasov beam model of asymmetric cross-sectional beams established. And then, a typical simply supported beam serves as a case in point to present a comprehensive analytical framework for the forced vibration analysis of beams with asymmetric sections. Subsequently, a beam element considering additional displacements is derived based on the principle of minimum potential energy. Notably, the proposed models and elements are versatile and applicable to various cross-sectional types. Finally, the impact of additional displacements on the forced vibration and the resonance of asymmetric cross-sectional beams is investigated under various boundary conditions. It is indicated that the impact of additional displacements becomes pronounced as boundary constraints are enhanced and should be considered in the dynamics analyses of beams. Moreover, as for an asymmetric cross-sectional beam, limiting torques can reduce its dynamic responses in the practical engineering. Additionally, additional displacements have a greater impact on torsional and lateral displacements instead of vertical displacements during vertical resonance.

Planet gear journal bearing (PGJB) is usually modeled by nonlinear film force or linear stiffness-damping coefficient in the dynamic modeling of wind turbine gearbox (WTG) with PGJB. The former has high simulation accuracy but a high computational cost; the latter has high computational efficiency but neglects time-varying film force and journal-sleeve eccentricity, leading to limited simulation accuracy. In this study, an improved dynamic modeling approach of PGJB is proposed considering the time-varying journal-sleeve eccentricity and additional eccentricity correction force based on the linear stiffness-damping coefficient. A rigid-flexible coupling dynamic model of WTG with PGJB is established, considering the structural flexibility of gearbox housing, carrier, ring gear, and shafts, as well as the dynamic supporting forces of PGJB. The influences of operating conditions and PGJB’s parameters on calculation accuracy and dynamic characteristics of WTG are studied and partially verified by an initial experiment. The results show that the dynamic meshing force fluctuation makes PGJB’s stiffness-damping coefficient and additional eccentricity correction force change periodically. The proposed model accurately predicts system response within boundary conditions, especially a prediction error of 10% in planet gear vibration displacements at the rated operating condition. Decreasing the width-to-diameter ratio and radial clearance of PGJB and increasing input torque improve the load-sharing performance of WTG.

Conformal mapping functions have significant applications in mechanics and other fields, and their computation methods have drawn considerable attention. We propose an iterative algorithm to compute the conformal mapping from the unit disk to physical domains with regular boundaries, defined by having only prime ends of the first kind. The mapping function is expanded into a Laurent series and use its truncated partial sum as an approximation. The Schwarz–Christoffel mapping formula provides the initial estimates for the series coefficients, which are then iteratively optimized. This algorithm efficiently handles complex domain shapes, such as winding orifices and slits, with high computational speed. Moreover, it offers valuable insights for designing algorithms to solve other types of conformal mapping problems and has practical significance in applications involving conformal mappings.