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This is a review on models for dynamic analyses of various drilling systems suitable for application in oil and gas industry. The rotary and also rotary–percussive drilling systems, vertical, horizontal and inclined, are physically and mathematically modeled. The basic physical model for analysis of the drilling system is the Timoshenko beam. Torsional, axial, transversal and combined vibrations of the drill string are considered. Special attention is given to bit–rock interaction models. Various mathematical expressions for bit–rock torque and force are suggested. Inclusion of these mathematical models in the drilling system consideration is expected in the future. In the paper advantages and disadvantages of drilling systems are also discussed. Finally, the aim of this review is to give direction for future research and improvement in drilling systems. [ABSTRACT FROM AUTHOR]

The present paper deals with the analytical study of Love-type wave propagation in a fiber-reinforced viscoelastic layer sandwiched between an orthotropic viscoelastic layer of finite thickness and an inhomogeneous viscoelastic half-space. A dispersion equation for Love-type wave propagation has been obtained using suitable boundary conditions. Some particular cases have also been calculated, and it is seen that the dispersion equation is reduced to the classical Love wave equation, which validates the present mathematical model. Numerical computations were carried out for involved parameters and illustrated with the help of graphs. The effects of viscoelastic parameters, thickness ratio, reinforced parameters, inhomogeneity parameters, and order of the depth variation in the dispersion curves are highlighted. The present study may be beneficial in geophysical applications and earthquake engineering to understand the nature of seismic wave propagation. [ABSTRACT FROM AUTHOR]

In this paper, the structural vibration control of short-period systems by a sliding model of a tuned liquid column damper (herein referred to as STLCD) is investigated from both theoretical and experimental points of view. The proposed STLCD is essentially composed of a U-tube container with liquid inside, which can slide on a linear guide rail and is connected to the structure by a spring-dashpot system. Unlike traditional fixed TLCDs, this type of arrangement allows the proposed STLCD to be tuned to short-period structural systems since the spring can be used for tuning while the dashpot provides additional damping. Details on the selection of the optimal design parameters of the STLCD are provided, and the validity of the introduced mathematical model is verified both in time and frequency domains through experimental tests conducted at the Laboratory of Experimental Dynamics at the University of Palermo, Italy. For the experimental tests, a scale model of an STLCD-controlled structure is considered, focusing on the reduction of the roof accelerations. Finally, for comparison purposes, the control performance of the proposed control strategy for the vibration suppression of stiff structures is evaluated by analyzing its structural responses in contrast with the corresponding uncontrolled structure under harmonic excitations. [ABSTRACT FROM AUTHOR]

The imperfection at the interface among two materials exists to various reasons such as thin inter phase, chemical action or interface damage. The interfaces such as mechanical, thermal and electrical significantly affect the performance of structural component that are utilized in various fields. The present mathematical study analyzes the reflection and transmission phenomenon of thermo-elastic wave being incident at the distinct types of separating interfaces in an initially stressed rotating structure with two different type half-spaces comprised of piezo-thermo-elastic (PTE) materials. The mathematical model of this study is performed under three-phase-lag model of generalised thermo-elasticity for normal stiffness interface (NSI), transverse stiffness interface (TSI), thermal conductance interface (TCI), electric imperfect interface (EII), and welded contact interface (WCI). The mathematical expressions for the amplitude and energy ratios are derived for the reflected and transmitted qP, qSV, qT and EA waves. The effects of initial stresses, rotation, phase lag and bonding parameters on amplitude ratios are performed, and energy balance law is established to validate the model. The validation of the result has been made with an existing problem for the correctness of the results. Numerical computations have been executed to demonstrate the mathematical findings by the graphical mean. [ABSTRACT FROM AUTHOR]

Mathematical models of planar physically nonlinear inhomogeneous plates with rectangular cuts are constructed based on the three-dimensional (3D) theory of elasticity, the Mises plasticity criterion, and Birger's method of variable parameters. The theory is developed for arbitrary deformation diagrams, boundary conditions, transverse loads, and material inhomogeneities. Additionally, inhomogeneities in the form of holes of any size and shape are considered. The finite element method is employed to solve the problem, and the convergence of this method is examined. Finally, based on numerical experiments, the influence of various inhomogeneities in the plates on their stress–strain states under the action of static mechanical loads is presented and discussed. Results show that these imbalances existing with the plate's structure lead to increased plastic deformation. [ABSTRACT FROM AUTHOR]

In this article, we consider a variant of the Simo–Reissner theory for a rod but restrict the study to two-dimensional motion where the rod undergoes flexure, shear and extension but not torsion. Linear elastic behaviour is assumed to formulate constitutive equations; the constitutive equations of the Timoshenko theory adapted for extension and large rotation. We call the model the local linear Timoshenko rod model. We show that this model serves as a framework for a class of simpler mathematical models for slender solids in various applications. The advantage is that the more general model can be used to evaluate and compare the simpler models. [ABSTRACT FROM AUTHOR]

In this work, we present the mathematical formulation and the numerical implementation of a new model for initially straight, transversely isotropic rods. By adopting a configuration space that intrinsically avoids shear deformations and by systemically neglecting the energetic contribution due to torsion, the proposed model admits an unconstrained variational statement. Moreover, as the natural state of the rod is the trivial one and the mechanical properties are homogeneous on the cross section, the need for pull-back and push-forward operations in the formulation is totally circumvented. These features impose, however, some smoothness requirements on the stored energy function that need to be carefully considered when adopting general constitutive models. In addition to introducing the rod model, we propose a spatial discretization with the finite element method, and a time integration with a hybrid, implicit scheme. To illustrate the favorable features of the new model, we provide results corresponding to numerical simulations for plane and three-dimensional problems that are investigated in the static and dynamic settings. Finally, and to put the presented ideas in a suitable context, we compare solutions obtained with the new model against a rod model that allows for torsion and shear. [ABSTRACT FROM AUTHOR]

In this work, mathematical models of physically nonlinear plates and beams made from multimodulus materials are constructed. Our considerations are based on the 3D deformation theory of plasticity, the von Mises plasticity criterion and the method of variable parameters of the theory of elasticity developed by Birger. The proposed theory and computational algorithm enable for solving problems of three types of boundary conditions, edge conditions and arbitrary lateral load distribution. The problem is solved by the finite element method (FEM), and its convergence and the reliability of the results are investigated. Based on numerical experiments, the influence of multimodulus characteristics of the material of the beam and the plate on their stress–strain states under the action of transverse loads is illustrated and discussed. [ABSTRACT FROM AUTHOR]