Vibration Of String Research Articles

Research on the Integration Teaching Mode of Traditional Music Elements and College Piano under the Background of Information Technology

Abstract With the deep integration of information technology and music education, how to integrate traditional music to innovate college piano teaching mode has become a problem that must be solved for the development of the times. Based on the scaffolding teaching method, this paper integrates traditional music elements with college piano in-depth and realizes the innovation of college piano integration teaching mode by adopting online pre-study before class, offline teaching during class and timely reflection and evaluation after class. In the teaching process, traditional music signals are represented by time-frequency domain features so as to realize the digital pre-processing of traditional music signals, and traditional music fundamental tone contours are transformed by using the fundamental tone feature extraction method. Then, based on the principles of physics, we explored the string vibration equation of the piano-generating principle and constructed a mathematical model for the piano music signal. To verify the effectiveness of this paper’s method in piano teaching in colleges and universities, relevant algorithms and teaching practices are used. The results show that the GNSDR of this paper’s method on vocals is improved by 6.58% compared with Unet, and its SDR is 4.25dB and 5.21dB when separating the two music source signals of Piano and Vocals, which is improved by 0.36dB and 0.14dB compared with SHN-4, respectively. The college piano scaffolding teaching model that integrates traditional music elements has enhanced sight-reading ability by 116.44%. Under the background of information technology, it is necessary to fully combine the relevant technology to extract the characteristics of traditional music elements so as to help teachers better carry out the design of piano music teaching programs and improve the quality of colleges and universities to cultivate piano talents who inherit traditional music.

A non-local problem with integral conditions of the first kind for the string vibration equation

A non-local problem with integral conditions of the first kind for the string vibration equation

The Problem of Two-Dimensional String Vibrations with a Nonlinear Condition

We study a model of small spatial transverse vibrations of a string where the deviation of any of its points from the equilibrium is characterized by two coordinates. It is assumed that in the course of vibrations one end of the string is inside a bounded closed convex set С belonging to a plane @ perpendicular to the segment along which the string is stretched. In turn, the set C can move in the plane @, with its motion given by a mapping. The end of the string remains free until it touches the boundary of the set. After coming into contact, they move together. A formula representing the solution of the initial–boundary value problem describing this vibration process is obtained. The problem of boundary control of the vibration process is considered.

Hole Cleaning during Drilling Oil and Gas Wells: A Review for Hole-Cleaning Chemistry and Engineering Parameters

Efficient hole cleaning during drilling operations is critical to maintain a high rate of penetration and smooth drilling, leading to minimum drilling problems and economical drilling efficiency. This process involves several important factors, including pipe-sticking incidents, higher cuttings concentrations in the annulus, noisy vibration of the drill string, erratic equivalent circulating density, lost circulation incidents, well control incidents, geomechanical hole section instability, tight spots during tripping operations, and excessive usage of chemical additives for conditioning hole sections and mud. Various approaches, including correlations, methodologies, developments, algorithms, equipment, charts, field experience, chemicals, and studies involving experiments, can be used to enhance the efficiency of hole cleaning. The development of hole-cleaning models is important for use as hole-cleaning indicators to ensure optimized drilling efficiency. This paper presents a comprehensive overview of the complex field of hole cleaning in the oil and gas industry. It includes techniques, tools, models, and chemical additives. It also encompasses drilling engineering, operations, and chemistry. To facilitate the transit of drill cuttings, maintain hole section stability, cool and lubricate the drill bit, and transmit hydraulic horsepower, this article outlines the important roles of drilling fluids. The significance of chemical additives, including nanoparticles, natural and modified polymers, and synthetic polymers, in preserving wellbore stability, improving drilling efficiency, and lowering drill bit wear is also covered in the study. It concludes by making recommendations for further study to clarify hole cleaning for the reader to facilitate and boost drilling efficiency.

Investigation of field scenarios using a 4n degrees of freedom transient torque and drag model

A coupled drill string dynamics model presents an opportunity to understand, replicate and potentially control the vibrations occurring along a drill string in a deep well. This paper describes a 4n degrees of freedom (4nDOF) model of the axial, torsional and lateral dynamics, consisting of coupled wave equations and lumped elements, which include modeling of the contact between the drill string and wellbore with a stiff string assumption. The model accounts for the bit-rock interaction, structural damping, and hydraulic forces acting on the lumped elements. The 4nDOF model is compared with three field scenarios from a drilling operation in the North Sea: a three-stage top drive start-up procedure, a drilling sequence starting from off-bottom conditions, and a backreaming operation at low rotational speed. The selected cases include instances of stick–slip and higher modes of torsional vibrations, which persist despite the use of a surface vibration mitigation system. High-frequency data recorded by a downhole measurement sub placed near the drill bit are used to verify the simulated downhole rotational speed and triaxial accelerations. The model is useful for analyzing torsional stick–slip events, which are replicated with a similar period and amplitude as in the downhole measurements. Furthermore, the model accurately reproduces the transition between first and second mode torsional oscillations upon the activation of a tuned top drive vibration mitigation system. The model can also be used to analyze lateral deformations and whirling of the drill string at various depths. The field case simulations show that the lateral dynamics can undergo significant changes at certain points in the drill string during torsional stick–slip and higher-mode torsional oscillations. The proposed model can be used to run simulations in close to real-time on a standard personal workstation, thus making it a valuable tool for devising and testing new drill string vibration mitigation solutions.

Perceptual and cognitive infiltration of piano lessons for college students under the concept of digital health

Abstract In this paper, firstly, according to mental health education, the research on the perception penetration of the piano course is illustrated from the two directions of body perception and mind perception. Secondly, it researches the music feature extraction in the piano course, obtains the amplitude, wavelength and frequency of the music feature according to the piano string vibration equation, then applies the short-time Fourier analysis to identify the music feature and reconstructs the piano timbre by using the identification result, which provides technical support for the design and realization of the piano course teaching system. Then, the overall design direction of the piano course teaching system is determined according to the teaching needs of the piano course in colleges and universities, and then the core module of the piano course system is realized. At the same time, the teaching of piano courses is empirically analyzed through statistical analysis. The results show that there is a significant difference between piano course teaching and the degree of perception and cognition in piano course teaching (F=4.194, p<0.05), there is a significant difference between piano course teaching and the degree of cognition (F=4.243, p<0.05), and there is a significant difference between piano course teaching and interpersonal relationship (F=5.391, p<0.05). This study not only has a promoting effect on piano teaching in colleges and universities but also improves the guiding value of piano curriculum reform in colleges and universities.

Vibrational modal-based characterization and pitch measurement of Pipa

Abstract Pipa fretting and pitch measurement are crucial aspects of playing. In this paper, Pipa’s string vibration is simplified to bounded string vibration, and a simplified structural model of Pipa is built. Transverse free vibration is used to establish the vibration equations of Pipa strings, and differential analysis is used to analyze the standing waves. Meanwhile, the vibration of the resonance panel of the Pipa was abstracted into a dynamic model, and the modal analysis was performed using coordinate transformation. In the actual test, the sound signal generated by the vibration was also processed with the help of the Fourier transform, and the pitch of the Pipa was measured by analyzing the time and frequency domains. The vibration of the Pipa panel is complex but regular, with the vibration pitch line at 32.5 hz being a central axis and the vibration pitch line at the frequency of 85 hz being on the upper side, while the vibration corresponding to the frequencies of 32.5 hz and 85 hz can be regarded as a synthesis of the vibration corresponding to the frequency of 175.5 hz. Under the viewpoint of vibration modal analysis, the performance effect of the Pipa has a more refined expression.

Multivariable control of the undesirable axial vibrations of the horizontal drill string

Multivariable control of the undesirable axial vibrations of the horizontal drill string

Vibration Control for a Three-Dimensional Variable Length Flexible String With Time-Varying Actuator Faults and Unknown Control Directions

In this study, actuator faults and unknown control directions are taken into account concurrently for a three-dimensional variable length flexible string system modeled by partial differential equations (PDEs). Different from the unknown fault parameters being restricted to just positive constants in the previous fault-tolerance research on PDEs systems, the time-varying actuator faults are considered, which is more practical but challenging. Additionally, the control directions of the system are unknown which can also be different in three directions. To overcome the difficulties, adaptive control laws employing the Nussbaum function are designed, and some auxiliary control signals are intended for service. Under the proposed boundary control scheme, uniform ultimate boundedness of the closed-loop system is guaranteed, and the deflections of the flexible string can be suppressed to a small neighborhood of zero. Finally, the simulations are implemented to indicate the control effect. <i>Note to Practitioners</i>&#x2014;String structural systems are widely used in fields of indoor and outdoor industrial and mining enterprises, ports, wharves, and seabeds. To improve work efficiency and safety, effectively suppressing the vibration of the flexible string is a crucial problem to be solved. This paper proposes a novel adaptive boundary control scheme to reduce the deflections of the flexible string system subject to time-varying actuator faults and unknown control directions in three-dimensional space. The control scheme is designed without simplification, which can provide a theoretical basis and a feasible solution for the control of flexible string systems in practical engineering. In the future, we will address the modeling and control problems of moving three-dimensional variable length flexible string systems.

PDE modelling and switch strategy controller design for a flexible detection system with output constraint and actuator failure

A novel approach for modelling a mine detection robot system is presented in this paper using partial differential equations and Hamilton’s principle. The system comprises a rigid arm, a detecting sensor module, and a flexible string. The paper addresses the challenges of boundary deflection constraint and actuator fault. To overcome these challenges, a unique controller is developed using Barrier Lyapunov function and switching strategy. This controller enables the robot system to achieve the desired position and eliminate the vibration of flexible string. The superiority of the designed control law is demonstrated through simulation results. Furthermore, the asymptotic stability of the closed-loop flexible system is established by the use of extending LaSalle’s Invariance principle to an infinite dimensional system. This principle ensures that the system will eventually reach a stable state over time.

Optimal Boundary Control of String Vibrations with Set Values of Deflection Functions and Point Velocities at Different Intermediate Time Instants

Optimal Boundary Control of String Vibrations with Set Values of Deflection Functions and Point Velocities at Different Intermediate Time Instants

A new approach for real-time prediction of stick–slip vibrations enhancement using model agnostic and supervised machine learning: a case study of Norwegian continental shelf

Efficient and safe drilling operations require real-time identification and mitigation of downhole vibrations like stick-slip, which can significantly diminish performance, reliability, and efficiency. This pioneering research introduces a robust machine learning approach combining model-agnostic regression techniques with Bayesian Optimized Extra Trees (BO_ET) to accurately predict stick-slip events in real-time using downhole sensor data. The model is rigorously tested and validated on a substantial offshore dataset comprising over 78,000 data points from a Norwegian continental shelf (NCS) oil field. The key input features encompassing real-time downhole and surface drilling parameters are carefully selected, including critical variables such as collar rotational speed, shock risks, annular pressure, torque, mud flow rate, drill string vibration severity, and other relevant measurements. These parameters offer significant insights into the occurrence of harmful stick-slip vibrations. Among several sophisticated machine learning models, the Extra Trees (ET) algorithm demonstrates superior performance with the lowest errors of 5.5056 revolutions per minute (r/min) Mean Absolute Error (MAE) and 9.9672 r/min Root Mean Square Error (RMSE) on out-of-sample test data. Further hyperparameter tuning of the ET algorithm via Bayesian Optimization dramatically reduces errors down to 0.002156 MAE and 0.024495 RMSE, underscoring the significant innovation and advantages of the proposed approach. By seamlessly incorporating real-time downhole sensor data and drill string mechanics, the model enables reliable identification of stick-slip events as they occur downhole. This grants opportunities to optimize critical drilling parameters including revolutions per minute (RPM), weight-on-bit (WOB), mud flow rates, and more to effectively mitigate stick-slip severity and improve the rate of penetration (ROP). Integrating the approach into automatic driller systems on offshore rigs offers immense benefits for drilling operations through substantially increased efficiency, fewer premature failures, lower costs, and significantly improved productivity and safety. Overall, this research strongly emphasizes the immense transformative potential of advanced data analytics and machine learning in enabling more efficient, economical, and sustainable drilling practices. The proposed model demonstrates clear superiority over existing methods and establishes a robust and reliable platform for real-time stick-slip prediction and mitigation, maximizing drilling performance.Graphical abstract

On the effect of space dimension and potential on the multiplicity of positive and nodal solutions for Kirchhoff equations

The paper is concerned with the multiplicity of positive and nodal solutions for the following Kirchhoff equation arising in the study of string or membrane vibrations−(a+b∫RN|∇u|2dx)Δu+λV(x)u=|u|p−2u,inRN, where N≥3, a,b and λ are positive parameters, the potential V(x)∈C(RN,R+), and 2<p<min⁡{4,2⁎=2NN−2}. Because the complicated competition between nonlocal Kirchhoff term and sub-cubic nonlinearity, the standard nodal Nehari manifold method does not work. As we shall see, under some suitable assumptions on potential V(x), we prove that the above problem admits at least two positive solutions and two nodal solutions, where a novel constraint manifold and some analytical tricks are introduced to overcome this obstacle. An interesting finding is that the space dimension and potential have a strong influence on the number of positive or nodal solutions. Moreover, we also give the asymptotic behavior of solutions as λ→+∞ and b→0+. These results improve and generalize the previous results in the literature.

Evaluation of distributed damping subs with active control for stick–slip reduction in drilling

Drill string vibrations can cause damage to the equipment and reduce drilling performance. There are two primary methods to address this issue: top drive control or the use of specialized tools near the bottom hole assembly (BHA). Another previously published idea is to have several torsional damping sleeves along the drill string, adding viscous damping to the system. The sleeves are designed to be non-rotating, held in place by static friction, but if the combination of braking coefficient and relative pipe velocity gets too high, the sleeve will slip. This paper examines the effectiveness of active control of the braking coefficient, using an On–Off-based control scheme with proportional control. Stability maps are employed to assess the effects of this control scheme on the system for various combinations of top drive feed rates and revolutions per minute (RPM) set points. Such maps allow for a performance comparison of passive sleeves and active sleeves. The results show that active control can improve the drill string behavior both when drilling and when rotating off-bottom, by reducing the slippage of the sleeves. The settling time is reduced to up to a third of the settling time of the passive sleeves.

The damped vibrating string equation on the positive half-line

In this paper, the existence of a solution to the problem describing the small vertical vibration of an elastic string on the positive half-line is investigated in the case when both viscous and material damping coefficients are present. The result is obtained by transforming the original partial differential equation into an appropriate abstract second-order ordinary differential equation in a suitable infinite dimensional space. The abstract problem is then studied using the combination of the Kakutani fixed point theorem together with the approximation solvability method and the weak topology. The applied procedure enables obtaining the existence result also for problems depending on the first derivative, without any strict compactness assumptions put on the right-hand side and on the fundamental system generated by the linear term. The paper ends by applying the obtained result to the studied mathematical model describing the small vertical vibration of an elastic string with a nonlinear Balakrishnan–Taylor-type damping term.

Implicit and explicit schemes for energy-stable simulation of string vibrations with collisions: Refinement, analysis, and comparison

Collisions play an important role in the sound production mechanism of musical string instruments. Impactive contact modelling must therefore be incorporated in energy-stable time-stepping schemes for simulation and sound synthesis. Recently, explicit and linearly implicit schemes based on energy quadratisation have emerged as a means of numerical modelling of nonlinear string vibrations that avoids the need for iterative solvers, which significantly enhances the applicability to real-time sound synthesis. However when applied to modelling collisions, spurious oscillations and artefacts have been reported, which can be linked to the one-sided nature of the contact force. To investigate whether and how these limitations can be avoided, this paper proposes refined numerical scheme variants for both lumped and distributed contact configurations, and assesses their accuracy and efficiency. For reference, two nonlinearly implicit schemes are also included in the comparisons. Guaranteed correctness of the sign of the numerical contact force is proven for several of the scheme variants. Numerical experiments across three case studies indicate that each of the proposed schemes converges towards the exact solution, and that for sufficiently small time steps, explicit schemes generally perform well compared to implicit schemes.

The Problem of Two-Dimensional String Vibrations with a Nonlinear Condition

The Problem of Two-Dimensional String Vibrations with a Nonlinear Condition

Analysis of the Influence of Downhole Drill String Vibration on Wellbore Stability

Most studies related to aspects of wellbore stability, such as wellbore breakage, block dropping, and wellbore expansion, revolve around the physicochemical interaction between drilling fluid and surrounding rock, but relevant studies show that drill string vibration during drilling also has a crucial and even decisive influence on wellbore stability. In order to thoroughly explore the influence mechanism of drill string vibration on wellbore stability, our research group established a finite element flexible simulation model of drill string dynamics and used a storage downhole vibration measurement device to collect downhole real drilling vibration data to verify the correctness of the simulation model. Then, based on the critical conditions of wellbore breakage, a wellbore stability evaluation method was established, and the wellbore stability under different drilling parameters and drilling tool combination conditions was evaluated and analyzed. The research results play an important role in revealing the influence mechanism of drill string vibration on wellbore stability and can provide theoretical guidance for engineering problems such as wellbore instability risk assessment.

Particle Origins for String Vibrations

Considering the origin of the particles an approach has been provided to show the origin of Bosons, Fermions along with supersymmetry (SUSY) from string vibrations in g \(\ge\) 1 genus of a hypercomplex manifold through \(\eta\) X \(\eta\) matrix for the generator \(\nabla\)(p,q).

Study on water hammer effect and tubing string vibration in high-pressure high-production gas wells

The transient internal flow in high-pressure high-production gas wells generates severe water hammer and tubing string vibration, which accelerates fatigue damage, joint wear, thread loosening, and other wellbore integrity problems. Based on the analysis of transient flow in gas wells, a mathematical model for fluid pressure surge and the induced tubing string vibration is developed and validated by similarity experiments. This method considers fluid-structure interaction, initial loads of tubing string, and compressibility of natural gas, and can fill the gap in quantification of water hammer pressure and tubing sting dynamic load in high-pressure high-production gas wells. On this basis, the effects of valve closure time, production rate, liquid content, and tubing string structure on transient flow and tubing string characteristics are analyzed systematically. The calculations show that wellhead pressure increases rapidly, and pressure wave propagates along tubing string to induce vibrations in the string after an instantaneous shut-in at the wellhead. During this transient process, fluid pressure and axial stress at wellhead reach their maximum valves. Owing to the fixed constraint effect of wellhead and downhole packer, the lack of restrictions on tubing distant from wellhead and packer enhances the severity of axial vibration. As valve closure time increases, the maximum wellhead pressure, tubing vibration displacement, and velocity gradually decrease. Therefore, the most direct way to control water hammer effect and tubing string vibration is to extend the shut-in time or prevent a rapid shut-in of gas well. The methods used in this study and the results obtained therein can serve as both a theoretical framework and practical foundation for the prediction and control of water hammer effect and tubing string vibration in high-pressure high-production gas wells.