Non-Linear Dynamic Analysis of Drill String System with Fluid-Structure Interaction

In this research, the non-linear dynamics of the drill string system model, considering the influence of fluid—structure coupling and the effect of support stiffness, are investigated. Using Galerkin’s method, the equation of motion is discretized into a second-order differential equation. On the basis of an improved mathematical model, numerical simulation is carried out using the Runge—Kutta integration method. The effects of parameters, such as forcing frequency, perturbation amplitude, mass ratio and flow velocity, on the dynamic characteristics of the drill string system are studied under different support stiffness coefficients, in which bifurcation diagrams, waveforms, phase diagrams and Poincaré maps of the system are provided. The results indicate that there are various dynamic model behaviors for different parameter excitations, such as periodic, quasi-periodic, chaotic motion and jump discontinuity. The system changes from chaotic motion to periodic motion through inverse period-doubling bifurcation, and the support stiffness has a significant influence on the dynamic response of the drill string system. Through in-depth study of this problem, the dynamic characteristics of the drill string can be better understood theoretically, so as to provide a necessary theoretical reference for prevention measures and a reduction in the number of drilling accidents, while facilitating the optimization of the drilling process, and provide basis for understanding the rich and complex nonlinear dynamic characteristics of the deep-hole drill string system. The study can provide further understanding of the vibration characteristics of the drill string system.

Review of Single Bubble Motion Characteristics Rising in Viscoelastic Liquids

The emphasis of this review is to discuss three peculiar phenomena of bubbles rising in viscoelastic fluids, namely, the formation of a cusp, negative wake, and velocity jump discontinuity, and to highlight the possible future directions of the subject. The mechanism and influencing factors of these three peculiar phenomena have been discussed in detail in this review. The evolution of the bubble shape is mainly related to the viscoelasticity of the fluid. However, the mechanisms of the two-dimensional cusp, tip-streaming, “blade-edge” tip, “fish-bone” tip, and the phenomenon of the tail breaking into two different threads, in some special viscoelastic fluids, are not understood clearly. The origin of the negative wake behind the bubbles rising in a viscoelastic fluid can be attributed to the synergistic effect of the liquid-phase viscoelasticity, and the bubbles are large enough; thus, leading to a very long relaxation time taken by the viscoelastic stresses. For the phenomenon of bubble velocity jump discontinuity, viscoelasticity is the most critical factor, and the cusp of the bubbles and the surface modifications play only ancillary roles. It has also been observed that a negative wake does not cause velocity jump discontinuity.

Peridynamics for Numerical Analysis

Discrete data analysis and numerical solutions to boundary and initial value problems of ordinary/partial differential equations are essential in almost every branch of science. Although the differentiation process is usually more direct than integration in analytical mathematics, the reverse is true in computational mathematics, especially in the presence of a jump discontinuity or a singularity. Integration is a nonlocal process because it depends on the entire range of integration. However, differentiation is a local process.

The effects of an abrupt increase in taxes on candy and soda in Norway: an observational study of retail sales

Background Fiscal policies are used to promote a healthier diet; however, there is still a call for real-world evaluations of taxes on unhealthy foods and beverages. We aimed to evaluate the effect of an abrupt increase, of respectively 80 and 40%, in the excising Norwegian taxes on candy and beverages on volume sales of candy and soda. We expected sales to fall. Methods We analyzed electronic point of sale data covering approximately 98% of volume sales of grocery stores in Norway. In two pre-registered models with weekly (log-)sales of taxed candy and soda from 3884 individual stores, we modeled the difference between the jump (discontinuity) in the trend around the time of the increase in taxes and the corresponding jump in the trend in a control season from the previous years (Model 1). In addition, we modeled the difference between the intervention and the control season in their changes in average sales (Model 2). Results Model 1 showed a 6.1% (one-sided 95% CI: not applicable (NA), 23.4, p-value = 0.26) increase and a − 3.9% (95% CI: NA, 4.9, p-value = 0.23) reduction in the differences in the jump in the trends, for candy and soda, respectively. The second model showed a relative decrease of − 4.9% (95% CI: NA, 1.0, p-value = 0.08) in the average sales of candy and an increase of 1.5% (95% CI: NA, 5.0, p-value = 0.24) in sales of soda. Supplementary analyses suggested that the results were sensitive to clustering on the time dimension. Conclusions When using two different quasi-experimental designs to model changes in volume sales of taxed candy and soda, we were not able to detect reductions in sales that coincided with an increase in the taxes. Variation across time makes it difficult to detect potentially small changes in sales even when using an entire country’s worth of sales data on the level of individual stores. We speculate that the tax increases were too modest to affect the prices to alter sales sufficiently.

The behavior of renormalizations of circle maps with rational rotation numbers and with Zygmund conditions

Let be one-parameter family of circle homeomorphisms with a break point, that is, the derivative has jump discontinuity at this point. Suppose satisfies a certain Zygmund condition which is dependent on parameter . We prove that the renormalizations of circle homeomorphisms from this family with rational rotation number of sufficiently large rank are approximated by piecewise fractional linear transformations in and -norms, depending on the values of the parameter and , respectively.

On a class of splines free of Gibbs phenomenon

When interpolating data with certain regularity, spline functions are useful. They are defined as piecewise polynomials that satisfy certain regularity conditions at the joints. In the literature about splines it is possible to find several references that study the apparition of Gibbs phenomenon close to jump discontinuities in the results obtained by spline interpolation. This work is devoted to the construction and analysis of a new nonlinear technique that allows to improve the accuracy of splines near jump discontinuities eliminating the Gibbs phenomenon. The adaption is easily attained through a nonlinear modification of the right hand side of the system of equations of the spline, that contains divided differences. The modification is based on the use of a new limiter specifically designed to attain adaption close to jumps in the function. The new limiter can be seen as a nonlinear weighted mean that has better adaption properties than the linear weighted mean. We will prove that the nonlinear modification introduced in the spline keeps the maximum theoretical accuracy in all the domain except at the intervals that contain a jump discontinuity, where Gibbs oscillations are eliminated. Diffusion is introduced, but this is fine if the discontinuity appears due to a discretization of a high gradient with not enough accuracy. The new technique is introduced for cubic splines, but the theory presented allows to generalize the results very easily to splines of any order. The experiments presented satisfy the theoretical aspects analyzed in the paper.

Analysis of Nonlinear Dynamic Characteristics of a Mechanical-Electromagnetic Vibration System with Rubbing

In this study, a rotor-bearing-runner system (RBRS) considering multiple nonlinear factors is established, and the complex nonlinear dynamic behavior of the coupling system is studied. The effects of excitation current, radial stiffness, and friction coefficient on dynamic characteristics are analyzed by numerical simulation. The research results show that the dynamic properties of the coupling system caused by different nonlinear factors are interactional. With the changes of different parameters, the RBRS presents multiple motion states, including periodic-n, quasi-periodic, and chaotic motion. The increase of the excitation current Ij has a certain inhibitory effect on the response amplitude of the system and makes the motion state of the system more complex, the chaotic motion wider, and the jump discontinuity enhanced. With the increase of radial stiffness kr, the motion complexity of the coupling system increases, the chaotic region increases, the response amplitude increases, and the vibration intensity increases. With the increase of the friction coefficient μ, the chaotic region increases first and decreases, the different motions alternate frequently, and the response amplitude gradually increases. This study can not only help to understand the dynamic characteristics of RBRS, but also help the stable operation of the generator set.