In the present paper, we study a generalization of the initial-boundary problem for the inhomogeneous vibrating string equation. The initial conditions include the higher order derivatives of the unknown function. The problem is studied under homogen...
This paper is proposed for solving a partial differential equation of second order with a fractional derivative with respect to time (the vibration string equation), where the fractional derivative order is in the range from zero to two. We propose a...
The modeling of the one-dimensional wave equation is the fundamental model for characterizing the behavior of vibrating strings in different physical systems. In this work, we investigate numerical solutions for the one-dimensional wave equation empl...
The structural vibration of industrial droplet dispensers can be modeled by telegraph-like equations to a good approximation. We reinterpret the telegraph equation from the standpoint of an electric–circuit system consisting of an inductor and...
By integrating H∞ control into iterative learning boundary control (ILBC) with the method of lines (MOL), this paper suggests a novel scheme to reduce the vibrations of the uncertain vibrating string system in the presence of iteration-varying...
In order to address the issue of drill string stick–slip vibration, which leads to drill bit wear and reduces the drilling velocity, we conducted a study on the characteristics of stick–slip vibration using a proportional-integral-derivat...
The current study aims to study the drill string–casing system operating in an inviscid fluid under imbalanced and rubbing damage types. The Navier–Stokes equations were linearized to establish the hydrodynamic forces surrounding the dril...
Strings are common components in various mechanical engineering applications, such as transmission lines, infusion pipes, stay cables in bridges, and wire rope of elevators. The string vibrations can affect the stability and accuracy of systems. In t...
Self-vibrating systems based on active materials have been widely developed, but most of the existing self-oscillating systems are complex and difficult to control. To fulfill the requirements of different functions and applications, it is necessary...
The aim of our work was to investigate how electric guitar strings wear out. There are many myths about string wear. We decided to investigate what the wear process looks like in real life. In our work, sound processing methods such as DTFT and spect...
In this paper, the influence of the time variable preloading force on the vibration of an archetypal oscillator is investigated. The oscillator is modeled as a slider-string system which is mathematically described with a second order nonlinear diffe...
When drilling inclined and horizontal sections, a significant part of the drill string is in a compressed state which leads to a loss of stability and longitudinal bending. Modeling of the stress–strain state (SSS) of the drill string (DS), inc...
We consider an optimal boundary control problem for a one-dimensional wave equation consisting of two non-homogenous segments with piecewise constant characteristics. The wave equation describes the longitudinal vibrations of a non-homogeneous rod or...
In CO2 flooding technology, the injection tubing string is prone to intense fluid–structure interaction (FSI) vibrations and water hammer effects during transient start-up and shutdown processes, which seriously threaten injection safety. This...
Dynamic cable-tension is an important bridge-health indicator. However, it is difficult to be measured precisely and efficiently. A remote bridge dynamic cable-tension measurement method is proposed. It uses an interferometric radar sensor, a time-fr...
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 in...
In downhole drilling systems, self-excited torsional vibrations caused by the bit-rock interactions can affect the drilling process and lead to the premature failure of components. Especially self-excited oscillations of higher-order modes lead to cr...
In this study, a nonlinear mathematical model of a thin string oscillating in an isotropic viscoelastic medium is developed. The model addresses external and internal mechanical energy dissipation in the string using components described by nonlinear...
In this paper, we present a numerical scheme and alternating direction implicit scheme for the one-dimensional time–space fractional vibration equation. Firstly, the considered time–space fractional vibration equation is equivalently tran...
In the process of high flow rate fracture and high gas production, the sealing performance of the premium connection decreases due to the dynamic load and vibration of downhole tubing strings, which may cause accidents. Existing static analysis metho...
Axial harmonic excitation is an emerging method for enhancing drilling speed, yet its influence on the torsional dynamics of a drill string remains unclear. To investigate these effects, this study establishes a single-degree-of-freedom (SDOF) nonlin...
The wellbore of a sucker-rod pumping well experiences a multi-phase flow consisting of oil, gas, and water. The flow pattern and pump discharge pressure are greatly impacted by oil well production, which in turn significantly affects the simulation r...
During deepwater carbon capture, utilization, and storage (CCUS) riserless (open-loop) drilling, the drill string is directly exposed to a complex marine environment, resulting in mechanical behavior and failure mechanisms that differ from those unde...
Severe drill string vibrations, particularly stick–slip, significantly compromise drilling efficiency and tool longevity in deep hard formations. Compound percussive drilling (CPD) has emerged as a promising technique to mitigate these vibratio...
This paper presents a linear mathematical model of bass guitar string vibration with experimentally identified, frequency- and fret-dependent modal damping, aimed at high-fidelity generative sound synthesis. To identify the string damping parameters...
We consider a boundary control problem for the equation of string vibration with given initial and final conditions, given the deflection form at an intermediate moment of time. The control is carried out by displacement of one end with the other end...
In conventional band sawing, the long-span compression of the flexible saw blade often results in large fluctuations in cutting force, low cutting efficiency, and poor force predictability. To address these issues, this study investigates the dynamic...
This paper presents the design of an integrated micro-vibration isolation and pointing platform with a four-leg structure, incorporating pitch and yaw adjustment functions using voice coil motors. The primary objective is to mitigate the impact of sp...
During the drilling and repairing of wells, the pipe string transfer equipment has a high work frequency. The movement accuracy, response speed, and controllability of the equipment have significant impacts on the stability. In this paper, we propose...
In power transmission systems, conductor vibration may cause periodic variations in the axial load carried by composite suspension insulator strings. Such axial-load variations may induce parametric vibration, affecting the mechanical reliability of...
The present two-part paper concerns the active vibration suppression for the simplest damped continuous system, namely the transverse oscillations of an elastic string, with constant tension and mass density per unit length and friction force proport...
In high production gas wells, premium connections are subject to alternating loads and vibration excitation due to the change of fluid pressure exerted on the tubing string. The energy dissipation on the sealing surface of premium connections affects...
Recently, inertial mass dampers (IMDs) have shown superior control performance over traditional viscous dampers (VDs) in vibration control of stay cables. However, a single IMD may be incapable of providing sufficient supplemental modal damping to a...
In deepwater open-loop drilling of ultra-shallow high-build-rate horizontal wells, the drill string spans the exposed seawater section, the mudline transition, and the constrained downhole section. Existing studies have not yet established a unified...
Machine vision can prevent additional stress on yarn caused by contact measurement, as well as the risk of hairiness and breakage. However, the speed of the machine vision system is limited by image processing, and the tension detection method based...
In the present study, a semi-analytical model based on the small-amplitude wave theory is developed to describe the wave fields around a single gravity-type cylindrical open fish net cage. The cage may be submerged to different depths below the free-...
A pumping-while-tripping method is proposed to mitigate pressure swabs during tripping out in wells with a narrow mud density window and extended reach. In the proposed tripping-out process, the fluid circulation is started by using a special pump fr...
We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of th...
Conventional methods for calculating tension currently suffer from an excessive simplification of boundary conditions and a vague definition of effective cable length, both of which cause inaccurate cable tension calculations. Therefore, this study u...