FORCE DRIVEN VIBRATIONS OF NONLINEAR PLATES ON A VISCOELASTIC WINKLER FOUNDATION UNDER THE HARMONIC MOVING LOAD

In the present paper, the forced driven nonlinear vibrations of an elastic plate in a viscoelastic medium and resting on a viscoelastic Winkler-type foundation are studied. The damping features of the surrounding medium and foundation are described by the Kelvin-Voigt model and standard linear solid model with fractional derivatives, respectively. The dynamic response of the plate is described by the set of nonlinear differential equations with due account for the fact that the plate is being under the conditions of the internal resonance accompanied by the external resonance. The expressions for the stress function and nonlinear coefficients for different types of boundary conditions are presented.

Stability of the critical equilibrium of a compressed column on a Winkler foundation

In this paper, the critical equilibrium of a simply supported compressed column on a Winkler foundation is analyzed based on Koiter’s theory. The exact expression of the potential energy functional is presented. By the Fourier series of the disturbance deflection, the second-order variation of the potential energy is expressed as a quadratic form. At critical equilibrium, the second-order variation of the potential energy is semi-positive definite, so that the stability of the critical equilibrium is determined by the sign of the fourth-order variation or sixth-order variation. It can be seen that only in two small ranges of elastic-foundation stiffness is the corresponding critical state stable and the bifurcation equilibrium upward. Then, the theoretical results of this paper are compared with previous experimental and theoretical results.

Stability Analysis of Rib Pillars in Highwall Mining Under Dynamic and Static Loads in Open-Pit Coal Mine

The highwall miner can be used to mine the retained coal in the end slope of an open-pit mine. However, the instability mechanism of the reserved rib pillar under dynamic and static loads is not clear, which restricts the safe and efficient application of the highwall mining system. In this study, the load-bearing model of the rib pillar in highwall mining was established, the cusp catastrophe theory and the safety coefficient of the rib pillar were considered, and the criterion equations of the rib pillar stability were proposed. Based on the limit equilibrium theory, the limit stress of the rib pillar was analyzed, and the calculation equations of plastic zone width of the rib pillar in highwall mining were obtained. Based on the Winkler foundation beam theory, the elastic foundation beam model composed of the rib pillar and roof under the highwall mining was established, and the calculation equations for the compression of the rib pillar under dynamic and static loads were developed. The results show that with the increase of the rib pillar width, the total compression of the rib pillar under dynamic and static loads approximately decreases in an inverse function, and the compression of the rib pillar caused by static loads of the overlying strata and trucks has a decisive role. Numerical simulation and theoretical calculation were performed in this study. In the Numerical simulation, the coal seam with a buried depth of 122 m and a thickness of 3 m was mined by the highwall miner. According to the established rib pillar instability model of the highwall mining system, it is found that when the mining tunnel width is 3 m, the reasonable width of the rib pillar is at least 1.3 m, and the safety factor of the rib pillar is 1.3. The numerical simulation results are in good agreement with the results of theoretical calculation, which verifies the feasibility of the theoretical analysis of the rib pillar stability. The research results can provide an important reference for the stability analysis of rib pillars under highwall mining.

An Analytical Model for Almost Conformal Spherical Contact Problems: Application to Total Hip Arthroplasty with UHMWPE Liner

Due to its high relevance for designing ball joints in mechanical engineering and (artificial) hip joints in biomechanics, the almost conformal elastic contact between a sphere and a spherical cup represents an important contact problem of current research. As no closed-form analytical solution to the problem has been found to date, full computational methods such as the finite element method are needed for analysis. However, they often require incredibly long, unacceptable calculation times, making parameter studies hardly practicable. For this reason, approximate analytical and semi-analytical models are applied, capable of predicting quantities of interest with sufficient accuracy. In the present work, a very simple model based on a radially directed Winkler foundation is presented, which provides (approximate) closed-form analytical solutions for both the pressure distribution and the dependencies between macroscopic contact quantities such as normal force and indentation depth. To ensure an optimal mapping of a specific contact problem, only the foundation modulus must be defined in a suitable way. As an example, the proposed model has been successfully adapted to adequately simulate the frictionless normal contact for hard-on-soft hip implants. For this purpose, the foundation modulus was approximated with the aid of a finite element analysis instead of adopting it from already well-established models, as the latter produce clearly erroneous results for large liner thicknesses and large Poisson’s ratios. By a comparison with extensive parameter studies of finite element simulations, it is demonstrated that the proposed model provides acceptable results for all commonly used hard-on-soft hip implants. On this basis, the influence of geometrical changes of the femoral head and the acetabular cup on the maximum pressure as well as the half-contact angle is discussed, and consequences on the wear behavior are deduced.

“Mechanistic Analysis of Rigid Pavement for Wheel Load Stresses By Finite Element Method Considering Different Sub-Grade with Different Percentage of Metal Fibre”

In the present work, analysis of concrete pavements using ANSYS software has been attempted. ANSYS is a finite element method-based software. The concrete slab has been modeled with solid 45 brick element and spring elements for soil. Analysis was carried out for a wide range of load and slab soil combination. The soil as “Winkler type” represented by elastic springs and their stiffness was derived from modulus of sub-grade reaction. The influence of any particular base or sub base on edge stresses was not studied here. The model will be then subjected to number of varying input parameters like the change in the thickness of pavement slab, sub-grade material to winkler foundation, modulus of elasticity by adding metal chips in different percentage like 10%, 20%, 30% and also intensity of loads. It is aimed to compare the stresses of the model study with classical approach of Westergaards and IRC 58- 2002 method. Westergaards equation under estimate edge wheel load stresses when compared with those obtained from ANSYS. For generating the charts, edge loading condition was considered which is critical case for wheel load stresses. Also, it was aimed to compare the results with those given by IRC 58 – 2002 design charts. Design charts were developed in thesis work yield the same value of pavement thickness as that of IRC 58 – 2002 method.

“Mechanistic Analysis of Rigid Pavement for Wheel Load Stresses By Finite Element Method Considering Different Sub-Grade with Different Percentage of Metal Fibre”

In the present work, analysis of concrete pavements using ANSYS software has been attempted. ANSYS is a finite element method-based software. The concrete slab has been modeled with solid 45 brick element and spring elements for soil. Analysis was carried out for a wide range of load and slab soil combination. The soil as “Winkler type” represented by elastic springs and their stiffness was derived from modulus of sub-grade reaction. The influence of any particular base or sub base on edge stresses was not studied here. The model will be then subjected to number of varying input parameters like the change in the thickness of pavement slab, sub-grade material to winkler foundation, modulus of elasticity by adding metal chips in different percentage like 10%, 20%, 30% and also intensity of loads. It is aimed to compare the stresses of the model study with classical approach of Westergaards and IRC 58- 2002 method. Westergaards equation under estimate edge wheel load stresses when compared with those obtained from ANSYS. For generating the charts, edge loading condition was considered which is critical case for wheel load stresses. Also, it was aimed to compare the results with those given by IRC 58 – 2002 design charts. Design charts were developed in thesis work yield the same value of pavement thickness as that of IRC 58 – 2002 method.

Photothermoelastic Interactions in Silicon Microbeams Resting on Linear Pasternak Foundation Based on DPL Model

In this work, the photothermal interactions in semiconductor microbeams during the photo-thermo-elastic process have been investigated using the generalized photothermal theory. The proposed mathematical model is constructed based on the Euler–Bernoulli model, the heat equation with two-phase lag and coupled plasma wave equation that indicates the prediction of thermal, elastic and photovoltaic effects in the microbeam resonators. Based on the introduced model, the dynamic influence of thermoelastic photovoltaic microbeam resting on an elastic foundation medium with two parameters has been studied. The Winkler foundation parameter is one of these parameters while the second is the shear foundation parameter. In the field of Laplace transform, the governing equations have been solved while the inverse transforms are found numerically using a tried-and-true approximation technique based on Fourier transform series. The numerical calculations of thermophysical field variables have been discussed and graphically presented. The effects of the magnetic field, Winkler and shear foundation parameters, and lifetime of photogenerated electron have been investigated and studied in detail. Comparisons have been made between the proposed model and previous models that have been derived as special cases from the presented results.

An Exact Solution to the Free Vibration Analysis of a Uniform Timoshenko Beam Using an Analytical Approach

This study presents an exact solution to the free vibration analysis of a uniform Timoshenko beam using an analytical approach, a harmonic vibration being assumed. The Timoshenko beam theory covers cases associated with small deflections based on shear deformation and rotary inertia considerations. In this paper, a moment-shear force-circular frequency-curvature relationship was presented. The complete study was based on this relationship and closed-form expressions of efforts and deformations were derived. The free vibration response of single-span systems, as well as that of spring-mass systems, was analyzed; closed-form formulations of matrices expressing the boundary conditions were presented and the natural frequencies were determined by solving the eigenvalue problem. Systems with intermediate mass, spring, or spring-mass system were also analyzed. Furthermore, first-order dynamic stiffness matrices in local coordinates were derived. Finally, second-order analysis of beams resting on an elastic Winkler foundation was conducted. The results obtained in this paper were in good agreement with those of other studies.

Fracture Characteristics and Zoning Model of Overburden during Longwall Mining

The fracture characteristics and zoning model of overburden during longwall mining are the basis of coal mine disaster prevention. However, the existing theoretical model is inconsistent with the field measurement. In order to further research into the strata’s fracture characteristics and optimize the overburden’s zoning model, we used the elasticity and Winkler foundation theory to establish first fracture and periodic fracture mechanics models of clamped boundary supported by an elastic foundation with a key stratum as the research object. We analyzed the stress distribution characteristics and fracture evolution pattern of the mining-induced key stratum. We analyzed the zoning characteristics of mining-induced overburden and established the zoning model according to different fracture mechanisms. The results show that the key stratum formed a double “O-X” shaped interconnected fracture zone after the first fracture. The key stratum formed a double “C-K” shaped interconnected fracture zone after the periodic fracture. We divided the mining-induced overburden into three zones along the horizontal direction: the original rock zone, the inverted triangular compression-shear fracture zone, and the trapezoidal tensile fracture zone. The study revealed the mechanism of inverted step fracture in the separation zone, explained the fracture mechanism of the coal pillar support zone, and has significant theoretical value for the prevention and control of water disasters, gas outbursts, and strata movement.