Mechanics of Solids最新文献

The SH waves in a rotating functionally graded system comprising an elastic substrate and functionally graded magneto-electro-elastic layer are studied analytically. The bonding of layer and substrate are well contact with corrugation as well as upper boundary taken as corrugated with stress free. Dispersion relations have been obtained for four cases of electrically open and magnetically open, electrically short and magnetically short, electrically open and magnetically short, and electrically short and magnetically open situations with corrugated interface. Based on the numerical results, the properties of SH waves through the proposed framework and the conditions depending on various physical and geometrical parameters have been examined. The study examines the simultaneous simulated results of several physical parameters, including inhomogeneity, layer thickness, rotation, and amplitudes of corrugation, which were created using Mathematica 7. The examined model could be helpful for the development of surface acoustic wave (SAW) devices.

This study utilizes a multiple scales perturbation approach to analyze the nonlinear wave propagation characteristics of a doubly curved sandwich composite piezoelectric shell with a flexible core under hygrothermal conditions. Stress and strain computations for the flexible core and face sheets are conducted employing Reddy’s third-order shear deformation theory (TSDT) and third-order polynomial theory, respectively. The investigation delves into the combined effects of a multilayered shell, flexible core, and magneto-rheological layer (MR) in elucidating the nonlinear behavior of both in-plane and vertical moments within the core. The Halpin-Tsai model is employed to derive the properties of polymer/Carbon nanotube/fiber (PCF) and polymer/Graphene platelet/fiber (PGF) three-phase composite shells. The governing equations for the multiscale shell system are derived using Hamilton’s formulation. The study explores temperature fluctuations, diverse distribution patterns, curvature ratios, and electric fields through numerical analysis, with graphical presentation of results. Previous research has validated the accuracy of these methodologies. Notably, these factors significantly impact the frequency-amplitude curves of the smart structure.

The problem of dispersed failure of isotropic and cylindrical-anisotropic rods made of damageable materials during torsion has been investigated. Non-linear differential equations have been formulated, representing the expansion of dispersion front during torsion of rod transmitting power under a constant torque. For the development of dispersed failure process, formulas have been obtained to identify incubation period and, the problem has been resolved.

The reasons for the occurrence of failures are considered, the consequence of which can be considered the progressive collapse of structures and the consideration of structural safety in more expanded concepts than when assessing the first and second groups of limit states for low-rise buildings built from local materials.

Problem of sliding of a periodic system of asperities along the boundary of a viscoelastic half-space with a coating is under consideration. The coating is modeled by a layer with flexural rigidity. The solution is based on reducing the problem to the contact of a limited system of asperities with the action of others being replaced by distributed pressure; the accuracy of such approach is evaluated. The numerical-analytical solution is based on double integral Fourier transforms, the boundary element method and the iterative procedure. The influence of the shape of asperities, sliding velocity, and coating thickness on the deformation component of the friction force and on the effect of mutual influence of asperities has been analyzed. To identify the effect of mutual influence, a comparison of the results (distribution of contact pressure and friction force) obtained for multiple contacts and for the isolated asperity has been made. For comparison, the results of solving a similar problem for viscoelastic half-space without a coating have been obtained and analyzed.

There are a number of cases of operation of structures in which external influences are of a random oscillatory nature. These are, first of all, transportation cases – rail and road transportation.

Therefore, when forming loading modes to assess the service life strength of structures in these cases, a probabilistic-statistical approach is used. The basic principles of this approach are presented in the formation of cyclic loading spectra for testing and analyzing the service life of products. The levels of cyclic loading were assessed and proposals were made for using the developed approach in assessing the service life strength of structures.

A new closed solution of the non-axisymmetric coupled unsteady problem of thermoelectroelasticity for a long piezoceramic cylinder is constructed while satisfying the boundary conditions of thermal conductivity of the 1st and 3rd kind. The cylindrical surfaces of the element are electroded and connected to a measuring device with a high input resistance. Limiting the rate of change of the temperature field on the inner surface of the cylinder allows us to include the equations of equilibrium, electrostatics and thermal conductivity in the mathematical formulation of the problem. To study the resulting non-self-adjoint system of equations and construct a closed solution, a generalized biorthogonal finite integral transformation is used. The obtained dependencies make it possible to determine the temperature, electric and elastic fields in the piezoceramic cylinder, as well as the potential difference between its electrode surfaces under the action of a non-stationary non-axisymmetric temperature “exposure”.

A schematic diagram and mathematical model of the functioning of a new piezoelectric membrane (MDS) actuator with double spirals (DS) electrodes on the upper and/or lower surfaces of a thin piezoelectric layer with axisymmetric and periodic (small period) reciprocal electric polarization along the radial coordinate are presented. The polarization of the layer is carried out as a result of connecting the polarizing value of the electrical voltage to the outputs of the double spirals of the electrodes. The electrodes of each (upper and lower) double helix of the MDS actuator are made in the form of electroded tape coatings on the surfaces of the piezoelectric layer in close proximity to each other (due to the small pitch of the helix) to create high electric field strengths along the field lines in local areas of the piezoelectric layer between them when connecting an alternating or direct control electrical voltage to the electrodes, in particular, with positive and negative values of electrical potentials. It is important that the electric field lines and, as a consequence, the polarization of the piezoelectric layer of the MDS actuator are oriented mainly along (i.e., towards or against) the radial coordinate of the membrane, in contrast to many traditional actuator schemes. The results of numerical simulation for a round elastic membrane with piezoelectric actuators installed on its upper and lower surfaces confirmed the effectiveness of the proposed piezoelectric MDS actuator when operating according to the “bimorph” scheme, including using the proposed new structural element (section) - piezoelectric MDS- “compression rings” for various geometric and control parameters. The effect of a significant increase in the deflection of the membrane with installed piezoelectric MDS actuators was revealed compared to the use of traditional homogeneous plate piezoelectric actuators of the bimorph type for various conditions of fastening the membrane, in particular, stationary (rigid) fastening of its center. For a hybrid piezoelectric MDS actuator, including independent concentric circular and annular (i.e., “pressure ring”) sections, a non-monotonic character was revealed and a numerical analysis was carried out of the nonlinear dependence of the largest deflection in the center of a membrane hinged and fixed at the edge on the radius ratio its circular and annular MDS sections. Cases have been identified in which the “pressure ring” effect manifests itself, i.e. when the maximum deflection of a membrane with a “pressure ring” exceeds the best possible deflection of this membrane without using it according to the traditional “bimorph” scheme. The new piezoelectric MDS actuator can be used in micromechanics, controlled optics, sensor technology, acoustics, in particular, in the manufacture of piezoelectric acoustic or membrane-type sensor elements, electromechanical transducers for collecting vibration energy.

The article is an analytical review and is devoted to the theory of thin, isotropic elastic plates. The basic relations of the theory based on the kinematic hypothesis are presented, according to which tangential displacements are distributed linearly over the thickness of the plate, and its deflection does not depend on the normal coordinate. As a result, a system of sixth-order equations was obtained for two potential functions: the penetrating potential, which determines the deflection of the plate, and the edge potential, which makes it possible to set three boundary conditions on the edge of the plate and eliminate the well-known contradiction in the theory of Kirchhoff plates. Problems that do not have a correct solution within the framework of Kirchhoff’s theory are considered - cylindrical bending of a plate with a free edge, bending of a rectangular plate with a non-classical hinge, torsion of a square plate by moments distributed along the contour, bending of a plate with a rigid stamp. In conclusion, a brief historical review of works devoted to the theory of plate bending is presented.

An exact solution to the contact problem of indentation of an absolutely rigid stamp with a straight base, taking into account friction, into one of the edges of a finite crack located in a homogeneous elastic plane is constructed. It is assumed that tangential contact stresses are directly proportional to normal contact pressure. In this case, it is believed that the friction coefficient is directly proportional to the coordinates of the contacting points of the contacting surfaces. The defining system of equations for the problem is derived in the form of an inhomogeneous Riemann problem for two functions with variable coefficients and its closed solution in quadratures is constructed. Simple formulas for contact stresses and the normal dislocation component of displacements of crack edge points are obtained. The patterns of changes in contact stresses and crack opening depending on the maximum value of the friction coefficient have been studied.