Elastic Bed Research Articles

DIFFERENCE BETWEEN MUSCLE ACTIVITIES DURING JUMPING MOTION IN DESCENT AND ASCENT PHASES ON A TRAMPOLINE

Trampoline bounces are performed on a bed of a jumping surface that is stretched over the trampoline apparatus. The jumping motion is divided into a descent phase, i.e., from the landing to the maximum depth, and an ascent phase, from the maximum depth to the takeoff. Most studies on muscle activity during jumping have investigated muscle activity during the same phase between groups or between landing and release; however, no studies have investigated muscle activity between phases. Therefore, this study aimed to investigate muscle activity during the descent and ascent phases and obtain basic data on the jumping motion. For the trials, participants were instructed to perform 15 consecutive jumps on the trampoline bed from a standing still position, as high as possible, straight and straight up in the center of the trampoline bed. The muscle activities of the rectus femoris, tibialis anterior, and lateral gastrocnemius revealed significant increases and larger effect sizes in the descent phase than in the ascent phase (p < 0.01). The muscle activities of the sternocleidomastoid, trapezius, and biceps femoris demonstrated significant increases and medium effect sizes in the descent phase in contrast to the ascent phase (p < 0.01). Pushing down the bed by the muscular activity of the lower extremities is most pursued in the descent phase. Then, participants maintain a straight vertical posture for the body to receive the rebound force from the maximum depth of the bed. This suggests that the sternocleidomastoid and trapezius muscles were significantly active in controlling the head position. A high jump is achieved by pushing the bed down for a deep descent and maintaining a straight posture at the maximum depth. The elastic bed is similar to an Open Kinetic Chain in the descent phase because the load incrementally increases, and to a Closed Kinetic Chain in the ascent phase because the load begins at the maximum depth of the bed. Separating the elements of the jumping motion required in the descent and ascent phases is important in athletic training

Analysis of the Dynamic Characteristics of Conical Shells of Variable Thickness on an Elastic Bed Under Unsteady Loading

Analysis of the Dynamic Characteristics of Conical Shells of Variable Thickness on an Elastic Bed Under Unsteady Loading

Comparison of the Structural Performance of Ballasted and Non-Ballasted Pavement of the Railway with the Help of Beam Models on Elastic Bed and Finite Element Model

Today, many countries are opting for ballast less paving of railways using concrete line slabs as an alternative. Ballast paving is particularly prevalent in high-speed lines, urban railways, as well as bridges and tunnels designed for high loads and speeds. The priority lies in ensuring that these lines are paved with proper structural performance, especially considering the mechanics of the line and the choice between ballast pavement and line slabs. This article delves into the structural modeling and analysis process of ballast and slabs for railway lines. Models for both ballast and slab lines under passage have been developed. The study investigates the train wheel load and the impact of bed conditions. Theoretical solutions, including the beam model on an elastic bed for ballast lines and the two-beam model for line slabs, have been presented. Multiple finite element models were explored using ABAQUS software, confirming the accuracy of the theoretical results with acceptable precision. This work establishes a suitable model for calculating the effects of vertical force on the line pavement structure and provides applications for comparing design performance between ballast and slab lines. The results highlight the optimal performance of the modeling and the superiority of the line slabs.

An Unfitted Method with Elastic Bed Boundary Conditions for the Analysis of Heterogeneous Arterial Sections

This manuscript presents a novel formulation for a linear elastic model of a heterogeneous arterial section undergoing uniform pressure in a quasi-static regime. The novelties are twofold. First, an elastic bed support on the external boundary (elastic bed boundary condition) replaces the classical Dirichlet boundary condition (i.e., blocking displacements at arbitrarily selected nodes) for elastic solids to ensure a solvable problem. In addition, this modeling approach can be used to effectively account for the effect of the surrounding material on the vessel. Secondly, to study many geometrical configurations corresponding to different patients, we devise an unfitted strategy based on the Immersed Boundary (IB) framework. It allows using the same (background) mesh for all possible configurations both to describe the geometrical features of the cross-section (using level sets) and to compute the solution of the mechanical problem. Results on coronary arterial sections from realistic segmented images demonstrate that the proposed unfitted IB-based approach provides results equivalent to the standard finite elements (FE) for the same number of active degrees of freedom with an average difference in the displacement field of less than 0.5%. However, the proposed methodology does not require the use of a different mesh for every configuration. Thus, it is paving the way for dimensionality reduction.

Influence Surface Coefficients of Plates Resting on Pasternak Foundation

In this study, internal force influence surface coefficients of plates resting on Pasternak foundation are obtained using the finite element method applying the classical Müller-Breslau Principle. The two-parameter elastic foundation is represented by the inclusion of the elastic bedding and shear parameter matrix terms of a 4-noded soil finite element to the corresponding stiffness matrix terms of the plate finite element used in the implementation. The loading matrices used to determine the influence surfaces directly are derived from the governing equations and the element matrices which are obtained using the Betti’s law. Internal force influence surface coefficients of plates with and without elastic foundation are given comparatively through numerical examples, confirming the values with another approach and the literature.

Vibration analysis of buried pipelines and piles using differential transformation method

Investigating the interaction between structures and their elastic foundations is essential in structures with elastic support conditions, such as buried pipelines and piles. Research investigation was carried out to find the frequency of a buried structure simulated by Euler–Bernoulli beam equations, with distributed damping and general boundary conditions on an elastic foundation. The elastic bed was modelled by a linear spring, and boundary conditions were changeable at two ends of the beam's support with variations in the stiffness of transitional and rotational springs. The differential transformation method (DTM) was then used to solve the equations by correlating the function and its derivatives. The frequency of the structure was obtained for various damping and stiffness values. The increase in the stiffness of the elastic support and the decrease in damping led to a higher frequency. The results of DTM agreed with the results of the exact method.

Calculation Method for Axisymmetric Bending of Circular and Annular Plates on a Changeable Elastic Bed. Part 2. Calculation Results for Continuous Circular Plates

Calculation Method for Axisymmetric Bending of Circular and Annular Plates on a Changeable Elastic Bed. Part 2. Calculation Results for Continuous Circular Plates

Thermal Buckling Analysis of Porous Conical Shell on Elastic Foundation

In this research, the thermal buckling analysis of a truncated conical shell made of porous materials on elastic foundation is investigated. The equilibrium equations and the conical shell`s stability equations are obtained by using the Euler`s and the Trefftz equations .Properties of the materials used in the conical shell are considered as porous foam made of steel, which is characterized by its non-uniform distribution of porous materials along the thickness direction. Initially, the displacement field relation based on the classical model for double-curved shell is expressed in terms of the Donnell`s assumptions. Non-linear strain-displacement relations are obtained according to the von Karman assumptions by applying the Green-Lagrange strain relationship. Then, performing the Euler equations leads obtaining nonlinear equilibrium equations of cylindrical shell. The stability equations of conical shell are obtained based on neighboring equilibrium benchmark (adjacent state). In order to solve the stability equations, primarily, due to the existence of axial symmetry, we consider the cone crust displacement as a sinusoidal geometry, and then, using the generalized differential quadrature method, we solve them to obtain the critical temperature values of the buckling Future. In order to validate the results, they compare with the results of other published articles. At the end of the experiment, various parameters such as dimensions, boundary conditions, cone angle, porosity parameter and elastic bed coefficients are investigated on the critical temperature of the buckling.

Calculation Method for Axisymmetric Bending of Circular and Annular Plates on a Changeable Elastic Bed. Part 1. Analytical Relations

Calculation Method for Axisymmetric Bending of Circular and Annular Plates on a Changeable Elastic Bed. Part 1. Analytical Relations

Refined Mathematical Model of the Stress State of Adhesive Lap Joint: Experimental Determination of the Adhesive Layer Strength Criterion

A new mathematical model of adhesive joint was developed and experimentally validated, in which the Vlasov–Pasternak two-parameter elastic bed model was used to simulate the stress state of the bonding layer. According to this elastic model, the adhesive layer was regarded as a membrane located in the middle of the adhesive layer thickness, between which and the bearing layers there were elastic elements. The outer bearing layers were regarded as beams in the Timoshenko approximation. The tangential stresses were considered to be constant across the thickness of the adhesive layer, and the normal (cleavage) stresses to be variable. This approach allows one to describe different types of boundary conditions for tangential stresses in the adhesive layer at the ends of the adhesive line, viz.: there are no tangential stresses at the edge of the adhesive joint if there are no adhesive spews, or the tangential stresses reach a maximum at the edge of the adhesive line if these spews exist. The problem was reduced to a system of ordinary differential equations in displacements and rotation angles of bearing layers. The system was solved by the matrix method. It was found that the sagging of the adhesive greatly reduced the maximum cleavage stresses in the adhesive layer. Tensile tests of adhesive lap-jointed metal rods were carried out. The proposed model was used to evaluate the strength criterion of the adhesive layer. It was shown that the best approximation of calculated and experimental data was provided by the maximum principal stress criterion. The proposed approach can be used to solve joint design problems.

Scattering of linear oblique water waves by an elastic bottom undulation in a two-layer fluid

A hydrodynamic model, with incorporation of elasticity, is considered to study oblique incident waves propagating over a small undulation on an elastic bed in a two-layer fluid, with the upper layer exposed to a free surface. Following the Euler–Bernoulli beam equation, the elastic bed is approximated as a thin elastic plate. The surface tension at the interface of the layers is completely ignored since its contribution will be minimal. While considering water waves passing over a deformable bottom, a significant change in the wave characteristics is observed due to the elasticity of the bottom which has an immense impact on the water wave kinematics and dynamics in addition to demonstrating the elastic behavior of the soil beneath. Time-harmonic waves propagate over an elastic bed with two different modes: the one corresponding to the smaller wavenumber propagates along the interface and the other one corresponding to the higher wavenumber along the free surface for any given frequency. Considering an irrotational motion in an incompressible and inviscid fluid, and applying perturbation technique, the first-order corrections to the velocity potentials are evaluated by an appropriate application of Fourier transform and, subsequently, the corresponding reflection and transmission coefficients are computed through integrals containing a shape function which depicts the bottom undulation. To validate the theory developed, one particular undulating bottom topography is taken up as an example in order to evaluate the hydrodynamic coefficients which are represented through graphs to establish the water wave energy conversion between those modes. The observation is that when the oblique wave is incident on the interface, energy transfer takes place to the free surface, but for free-surface oblique incident waves, no such energy transfer to the interface takes place because of the parameter ranges. It is noticed that reasonable changes in the elasticity of the bed have a significant impact when the propagating wave encounters a small elastic bottom undulation. Further, the values of reflection and transmission coefficients obtained for both the interfacial wave mode as well as the free-surface wave mode in the fluid are found to satisfy the important energy balance relations almost accurately. Such problems with a deformable bed, to be precise elastic here, will enable researchers to take up problems which take into account the characteristics of the infinite depth of soil beneath the bed, and the present study is expected to provide the necessary background.

On the dynamics of axially functionally graded CNT strengthened deformable beams

In this study, by functionally grading carbon nanotube (CNT) fibres through the axial direction of deformable beams, a new model for strengthening such structures is formulated. The strengthened deformable beam is additionally supported by a varying elastic foundation which is modelled via the Winkler–Pasternak elastic foundation. CNT distribution in the longitudinal direction is modelled using a power-law function presenting general forms of variation from linear to parabolic models. Equations of motion are determined using Hamilton’s principle and are solved by employing the generalised differential quadrature approach method. A comprehensive parametric investigation is presented in order to indicate the influence of having CNT fibres distributed functionally through the length. It is shown that grading CNT fibres axially have a significant effect in varying the natural frequency parameter. Moreover, the influence of having Winkler–Pasternak elastic bed on the free vibration of such structures is discussed considering different types of foundation stiffness variation through the length. A comprehensive comparison study is presented to verify the current methodology and formulation by using previous literature for foundation modelling and FE modelling for linearly varying CNT’s longitudinal distribution, which for all the cases, a good agreement between the results is observed.

Propagation of Oblique Waves Over a Small Undulating Elastic Bottom Topography in a Two-Layer Fluid Flowing Through a Channel

A hydrodynamic model, with the incorporation of elasticity, is considered to study oblique incident waves propagating over a small undulation on an elastic bed in a two-layer fluid, where the upper layer fluid is bounded above by a rigid lid, which is an approximation to the free surface. Following the Euler–Bernoulli beam equation, the elastic bed is approximated as a thin elastic plate. The surface tension at the interface of the layers is completely ignored since its contribution will be minimal. The behavior and properties of the roots of the dispersion relation are analyzed using counting argument and contour plot. In this case, time-harmonic waves propagate with only one wavenumber. Considering an irrotational motion in an incompressible and inviscid fluid, and applying perturbation technique, the first-order corrections to the velocity potentials are evaluated by an appropriate application of Fourier transform and, subsequently, the corresponding reflection and transmission coefficients are computed through integrals containing a shape function which depicts the bottom undulation. To validate the theory developed, two particular undulating bottom topography are taken up as examples in order to evaluate the hydrodynamic coefficients which are represented through graphs. It is noted that the reflection coefficient shows an oscillatory pattern, when the wavenumber of the undulating bed takes a value almost double the wavenumber of the incident wave. When the ratio of the wavenumber of the undulating bed and the wavenumber of the incident wave approaches 2, the theory predicts existence of resonance between the undulating elastic bed and the interface of the layers. It is worthwhile to note that reflected wave energy of the incident wave is higher if the number of ripples of the bottom undulation is large. It is further noted that the reflected energy increases in response to an increase in the values of the elastic parameters of the ocean bed. The results for a patch of sinusoidal ripples having different wavenumbers are found to be similar. Further, the reflected energy decreases for an increase in the angle of incidence. It is noted that reasonable changes in elasticity, ripple wavenumber and the number of the ripples of the bed have a remarkable effect when the propagating wave passing through a channel encounters a small bottom undulation. When results are compared with the available results, good agreement is observed.

Testing strategies and failure modes of dimpled laminate plates

Ground reinforcing plates are designed to facilitate the access of rescue vehicles and equipment in soft and muddy ground, e.g. for fire engines and cranes. Such plates have to be light and easy to handle, hence the use of composite materials is favourable. The investigated ‘dimpled plates’ are designed with glass fibre reinforced polymer (GFRP) and built to withstand high loads and to allow maximum deformation.Design parameters for the dimensioning of the plates are derived from standard ASTM laminate testing, and the values are used for the optimization of the plates by means of FEM (shape; composites layup). The verification of the component resistance and strength, however, requires adapted test configurations and procedures. Global loading of the structure has to replicate the situation in the field, and the resulting failure modes have to be identified for further optimization of the system.The scale of the plate bending tests had to be minimized due to large deflections. Mainly shear failure (delamination) and compressive failure (fibre buckling or crushing) were observed. Negative boundary effects had to be minimize in the tensile test, too. Fibre tensile failure followed after delaminations in the fillet of the knop base. Transverse compression: Testing against hard parallel plates provided high strength values, but the setup did not reproduce the situation of a soft bedding in the field, with mud. Different scenarios of elastic bedding over rubber plates were compared.The results provided the basis to optimize the material choice for the laminate (resin type, fibre reinforcement). The durability of the final composite laminates was verified with extensive aging tests in a later study.

An exact solution to the problems of flexo-poro-elastic structures rested on elastic beds acted upon by moving loads

This paper aims to examine flexural vibrations of fully saturated poroelastic structureson an elastic bed subjected to moving point loads via an analytical solution. Using aflexural beam model in conjunction with the Biot’s poro-elasticity theory, the equationsof motion of the porous structure are derived. Using assumed mode method and Laplacetransform, the explicit expressions of displacement and pore pressure are obtained carefully.For a particular case, the predicted results are also compared with those of another workand a reasonably good agreement is achieved. The influences of the moving load velocity,permeability ratio, transverse stiffness of the foundation, viscosity of the pore fluid, andporosity on the maximum elasto-dynamic fields and pore pressure are conclusively discussed.The velocity pertinent to the maximum possible dynamic response is graphically determinedand the roles of influential parameters on this crucial factor are displayed. The present modelcould be easily extended to multi-layered poroelastic structures under moving loads.

On the viscoelastic dynamics of fluid-conveying microtubes

This paper is the first to analyse the coupled fluid-structure viscoelastic dynamical characteristics of a fluid-conveying viscoelastic microtube resting on a nonlinear elastic bed subject to large rotations. None of the axial and transverse motions/accelerations is neglected in the modelling and simulations. The dissipation is modelled using the Kelvin–Voigt scheme for the deviatoric segment of the symmetric couple stress tensor and the stress tensor. Based on the Euler–Bernoulli theory, in which the microtube cross-section remains perpendicular to the centreline, and the modified couple stress theory (MCST), the energies and the work of external load and damping are formulated. Through use of Hamilton's principle, the coupled transverse-longitudinal equations governing the motion of the fluid-conveying viscoelastic microtube are developed. A weighted-residual-based discretisation method is applied to the continuous vibration model and the resultant reduced model is simulated via a continuation technique. The coupled fluid-structure dynamical characteristics of the fluid-conveying viscoelastic microtube are analysed by constructing the frequency-amplitude diagrams. It is shown that slight changes in the flow speed significantly affects the resonant response and modal interactions.

Effects of elastic bed on hydrodynamic forces for a submerged sphere in an ocean of finite depth

In this paper, we consider a hydroelastic model to examine the radiation of waves by a submerged sphere for both heave and sway motions in a single-layer fluid flowing over an infinitely extended elastic bottom surface in an ocean of finite depth. The elastic bottom is modeled as a thin elastic plate and is based on the Euler–Bernoulli beam equation. The effect of the presence of surface tension at the free-surface is neglected. In such situation, there exist two modes of time-harmonic waves: the one with a lower wavenumber (surface mode) propagates along the free-surface and the other with higher wavenumber (flexural mode) propagates along the elastic bottom surface. Based on the small amplitude wave theory and by using the multipole expansion method, we find the particular solution for the problem of wave radiation by a submerged sphere of finite depth. Furthermore, this method eliminates the need to use large and cumbersome numerical packages for the solution of such problem and leads to an infinite system of linear algebraic equations which are easily solved numerically by any standard technique. The added-mass and damping coefficients for both heave and sway motions are derived and plotted for different submersion depths of the sphere and flexural rigidity of the elastic bottom surface. It is observed that, whenever the sphere nearer to the elastic bed, the added-mass move toward to a constant value of 1, which is approximately twice of the value of added-mass of a moving sphere in a single-layer fluid flowing over a rigid and flat bottom surface.

Influence of Local Wetting of Loess Soil on the Redistribution of Reactive Pressures Under Foundations

An experimental-theoretical method is presented for tracking reactive soil pressures in a local wetted zone when solving problems of plate bending on an elastic bed with due regard for incomplete contact.

Interaction of surface gravity wave motion with elastic bottom in three-dimensions

A general three-dimensional hydroelastic model is developed to study the effect of elastic bottom on surface gravity wave motion in three-dimensions under the action of uniform compressive force based on linearized theory of water wave in finite water depth. The elastic bottom bed is modeled as a thin plate theory. The progressive wave characteristics in different wave modes are analyzed in both the cases of deep and shallow water waves. Further, the linearized long wave equation under shallow water approximation in a direct manner is derived and compared the results obtained based on the small amplitude wave theory. Three-dimensional Green's function associated with surface gravity wave motion with elastic bed is derived using the fundamental source potentials. Fourier-type expansion formula and corresponding orthogonal mode-coupling relations are derived in finite depth and finite/semi-infinite width in three-dimensions. Utilizing the expansion formula, two classical problems (i) forced motion and (ii) wave reflection by a rigid wall in a channel of finite width and finite/semi-infinite length are illustrated which will play significant role in the analysis of wave-structure interaction problems arising in ocean engineering.The effects of elastic bottom on surface gravity waves are analyzed by presenting several numerical results on reflection wave amplitudes in different cases. Further, the behavior of free motions and oscillations in a basin of finite width and finite/semi-infinite length with elastic bed under the action of uniform compressive force are discussed.

NUMERICAL METHOD FOR ESTIMATION OF TENSILE LOAD IN TIE-RODS

The work introduces a two-phase method for determination of axial loads in tie-rods. The method described here consists of an experimental activity and an automated numerical calculation. The influence of considering an elastic Winkler-type bed to model the tie-rod constraint inside the wall has been investigated. The algorithm used for calculation involves a solution of a functional minimization problem, where the tensile load and the stiffness of elastic foundation at the edges are used as optimization parameters and the error function, which describes the deviation between the frequencies measured and those calculated using finite element method, is minimized. Qualitative analysis of the results showed a significant reduction of the error compared to models with different boundary conditions. The method showed to be conservative for the strength evaluation of the rods, because the optimal values of tensile loads appeared to be higher than the load in perfect encastre conditions.