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— A new scheme of approximate solution of the problem of axial compression of an elastic cylinder with one movable and the other fixed end with a free lateral surface is presented and refines the known solution obtained using separation of variables when averaging conditions over stresses on the lateral surface of the cylinder. The refinement is made by successive removal of discrepancies: first, in the stress distributions on the lateral surface of the cylinder, then in the radial displacements along the ends and further in the axial displacement of the movable end. Comparison with the results of numerical solution of the problem by the finite element method for different values of the Poisson ratio and different combinations of overall dimensions of the cylinder has shown the effectiveness of the proposed approach.

This paper considers the inverse problem of determining the inhomogeneity laws of the coating of an elastic cylinder that provide minimum reflection of a plane acoustic wave in a particular angular sector and in a given frequency range. A functional that expresses the reflection intensity is constructed by direct solution of the direct problem, and an algorithm for minimizing this functional is proposed. Analytical expressions describing the mechanical parameters of the inhomogeneous coating are obtained.

Considered within the theory of small deformations superposed upon large is spatial behaviour for a prestressed laterally constrained elastic cylinder in equilibrium under zero body force and for sets of elastic coefficients that are not positive-definite. Certain cross-sectional integral measures are shown to be logarithmically convex implying at least exponentially increasing growth behaviour. For sufficiently long cylinders, this conclusion contradicts at most quadratic growth, and consequently the theory ceases to be valid indicating possible initiation of buckling and similar phenomena.

The paper investigates the dynamic behavior of a hollow elastic cylinder of finite length, placed in a rigid cylindrical shell, under a sharp change in internal pressure. A numerical solution of a two-dimensional dynamic problem is obtained using the method of spatial characteristics. The stress-strain state of an elastic cylinder is described by a system of hyperbolic equations with two circular conical surfaces as characteristic surfaces. The outer cones correspond to longitudinal waves; the inner ones correspond to transverse waves. The calculations were carried out under various conditions at the ends and the outer (contact) surface of the cylinder and shell. An analysis of the results for a cylinder with load-free ends shows that the absence of gluing the outer surface of the cylinder with the shell leads to a significant increase in the velocities of the points of the cylinder. Under the action of internal pressure, the ends move apart, resulting in a significant increase in the radial velocities of the internal channel. Qualitative patterns of behavior of the structures under consideration, which are widely used in mechanical engineering, on impact-type impacts, can be used to improve and optimize them at the design stage.

Root hairs are outgrowths of the epidermal cells of plant roots. They increase the root's exchange surface with the soil and provide it with good anchorage in the soil. Root hairs are an emblematic model of apical growth, a process also used by yeasts and hyphae to invade their environment. From a mechanical perspective, the root hair is considered as an elastic cylinder under pressure, closed by a dome that behaves like a yield fluid. We introduce here two innovative mechanical setups and protocols to characterize the mechanical properties of single growing root hairs in Arabidopsis thaliana . In the first setup, root hairs grow against an elastic obstacle until buckling. By measuring the critical buckling force, we determine the surface modulus and estimate the Young’s modulus of the cell wall, which aligns with previous measurements. Using a 1D elasto-viscoplastic model of root hair growth, we assess the excess pressure beyond the yield threshold (the driver of tip growth) and estimate the axial stiffness of the root hair, reflecting its elastic resistance to compression. For the second protocol, we designed a setup where a single root hair grows against a cantilever with variable stiffness, a technique adapted from our earlier work on rigidity sensing by animal cells. This method provides an independent estimate of the root hair's axial stiffness, confirming our initial findings and suggesting that this stiffness primarily involves tip compression and depends mainly on turgor pressure, at least within the low deformation regime explored. Graphical abstract

Purpose This study aims to investigate the effects of thermal buoyancy and flow incidence angles on mixed convection heat transfer and vortex-induced vibration (VIV) of an elastically mounted circular cylinder. The focus is on understanding how varying these parameters influences the vibration amplitudes in both the x and y directions and the overall heat transfer performance. Design/methodology/approach The research involves a numerical simulation of thermal fluid-structure interactions by integrating rigid-body motion equations with heat and fluid flow solvers. The cylinder operates at a lower temperature than the mainstream flow, and flow incidence angles range from 0° (opposing gravity) to 90° (perpendicular to gravity). The methodology is validated by comparing the results with established data on VIV for a cylinder vibrating in one direction under thermal buoyancy effects. Findings The study reveals that, without buoyancy (Ri = 0), increasing the flow angle from 0° to 90° decreases the vibration amplitude along the x-direction (Ax) while increasing it along the y-direction (Ay) across various reduced velocities (Ur). When buoyancy effects are introduced (Ri = −1), Ax peaks at specific Ur values depending on the flow angle, with significant variations observed. The maximum increase in Ax at Ri = −1 is over 15 times at Ur = 9 for a 0° angle, and Ay shows a more than 10-fold increase at Ur = 8 for a 30° angle. Additionally, adjusting the flow angle results in up to an 8% increase in the mean Nusselt number at Ri = −1. Originality/value This research provides novel insights into the combined effects of flow incidence angles and thermal buoyancy on VIV and heat transfer in an elastically mounted cylinder.

An exact analytical solution to the problem of large deformations of a multilayer cylindrical rod under multistage deformation is obtained for incompressible isotropic nonlinear elastic materials. At each step of deformation, another layer is attached to the rod, after which twisting and tension–compression of the cylinder along with the attached layer occur. The solution is obtained on the basis of the theory of multiple superposition of large deformations using one of the universal solutions of the problem of nonlinear elasticity. Numerical results are given. Nonlinear effects and effects associated with superposition of large deformations are analyzed.

AbstractThis study examines the propagation of shear waves on a highly inhomogeneous multi-layered elastic cylinder embedded in Winkler elastic foundations. The interface of the structure has been considered to bear generalized interfacial conditions, upon which the widely used perfect interfacial conditions turn out to be a special case. The harmonic wave solution has been deplored for the examination. Certainly, the discussion highlighted the roles of the Winkler foundation and layer thickness and the influence of material homogeneity versus non-homogeneity on the scaled phase velocity, dimensionless wave number, and scaled frequency, respectively, concerning layer thickness. In addition, it is observed that dimensionless vibrational displacements varied in response to changes in both the contact parameter and the angle . Moreover, this study is set to supplement the known literature concerning the emerging field of multi-layered construction and provide insights into constructing reliable materials in the field of material science.

Under the Hamilton system, the dual form governing equations of the cylindrical problem are established using displacements and stresses as the basic variables, and the problem is accordingly transformed into finding the eigenvalues and eigensolutions by adopting the method of separation of variables. Furthermore, solutions for zero eigenvalues and non-zero eigenvalues are systematic studied. The study shows that zero eigensolutions are composed of all the overall deformation solutions such as the traditional tension and bending problems, while non-zero eigensolutions include the torsion and bending groups charactered by local deformations.

This paper is concerned with the linear theory of inhomogeneous and orthotropic elastic materials with voids. We study the problem of extension and bending of right cylinders when the constitutive coefficients are independent of the axial coordinate. First, the plane strain problem for inhomogeneous and orthotropic elastic materials with voids is investigated. Then, the solution of the problem of extension and bending is expressed in terms of solutions of three plane strain problems. The results are used to study the extension of a circular cylinder with a special kind of inhomogeneity. The influence of the material inhomogeneity on the axial strain is established.