The present study uses a typical spinning flow pipeline model to demonstrate these findings. A dynamic representation of a pipeline with spinning flow with elastic limitations on both sides is started to be constructed. This phenomenon can be achieved by implementing an oil drilling pipeline in alignment with the Euler-Bernoulli beam theory. The subsequent analysis of the pipeline's stability is facilitated by discretising the coupled control equations and solving the eigenfrequency problem through the Galerkin method. The enhanced Hamilton principle is applied to generate partial differential equations governing the pipe's two transverse vibrations. The fourth-order Galerkin technique is then utilized to truncate these equations. Finally, the discrete complex modal functions are introduced to obtain the intrinsic frequency and period solutions of the system. It reveals the method through which some critical factors, including mass ratio, flow rate, and rotational velocity, affect the system's stability and vibration characteristics. The paper's findings establish a theoretical framework for vibration control and stability design of spinning pipes in moving fluid applications with complex restrictions in practical engineering contexts.

The low-frequency torsional vibration, which can not only reduce the power transmission efficiency of the shaft structures, but also threaten the operation safety of them, has been the research hotspot in the field of low-frequency vibration control. As the existing negative stiffness mechanism employed for low-frequency torsional isolation in shafts suffers from the strong nonlinearity and low negative stiffness, the design method of torsional vibration isolator with high magnetic torsional negative stiffness is proposed via magnetic charge superposition. The high magnetic torsional negative stiffness composed of tiles magnetized circumferentially is connected with plane spiral spring in parallel to analyze the low-frequency torsional isolation performance of the shaft structures. Referring to the magnetic charge model, the nonlinear torque and torsional negative stiffness of the High Magnetic Torsional negative Stiffness spring (HMTS) are derived, and then demonstrated via the numerical simulation of COMSOL finite element software in comparison with that of the traditional magnetic negative stiffness array. Besides that, the mechanical properties of plane spiral spring are also investigated using Ansys Workbench. With the effects of above analysis, the governing equations of the proposed isolator can be established, and relevant low-frequency isolation performance is studied with harmonic balance approach. A test rig of the isolator is set up to determine its low-frequency torsional isolation performance. The results show that the magnitude of high magnetic torsional negative stiffness spring is twice as high as that of the traditional magnetic negative stiffness ones, which can significantly broaden the isolation bandwidth as well.

Fluid-conveying pipes are extensively used in practical engineering in various industries and play an important role in industry and daily life. Under complicated working conditions, inevitable vibrations affect the stability and integrity of these pipes, drawing significant academic attention. Typically, the dynamic modeling of these pipes considers ideal rigid boundary conditions, including fixed support, simply support, and cantilever pipes, ignoring the effects of boundary elasticity. This paper investigates the effects of boundary elasticity on the harmonic excitation responses in sub-critical and super-critical regimes. The governing equations and boundary conditions are derived via the extended Hamilton's principle. Later, the non-trivial equilibrium configuration is analytically deduced, and the governing equations for fluid-conveying pipes with elastic supports are discretized into a set of nonlinear ordinary differential equations using the Galerkin method. The harmonic balance method (HBM) is employed to solve these differential equations, with its accuracy validated against the Runge-Kutta method. Finally, numerical examples are conducted in sub-critical and super-critical regimes to show the effects of boundary vertical stiffness, torsional stiffness, fluid velocity, and excitation on solution stability, natural frequencies, and amplitude of the steady-state response at the middle point. This paper provides important guidance for the design of boundary elasticity in sub-critical and sup-critical fluid-conveying pipes.

Axially moving devices are widely used in daily life, with the beam model being the most commonly used for analysis simplification. However, the inevitable transverse vibration phenomenon severely affects the stability and safety of the system. In certain devices, periodic velocity fluctuation may be observed, leading to parametric resonance. Furthermore, although the boundary conditions have an important influence, it is generally reduced to fixed or simply supported. However, such clear distinctions cannot be easily made in actual. Thus, this paper aims to analyze the principal and summation parametric resonance of a traveling beam considering boundary torsional stiffness, caused by varying velocity and tension. Natural frequencies and modes of the beam are derived based on complex modal method and validated using the differential quadrature element method (DQEM). Effects of boundary torsional stiffnesses and the variable velocity on natural frequencies of the traveling beam are discussed. To analyze the mechanism of steady-state amplitudes for both principal and summation parametric resonances, the method of multiple scales (MMS) is employed to perturb the nonlinear model. This allows for obtaining the linear homogeneous models with the modal revision method (MRM) at each time scale. Stability boundaries and its amplitude-frequency responses for principal and summation parametric resonances are derived. Furthermore, the analytical results are compared with the numerical results via the DQEM, verifying the feasibility and precision of MMS. Finally, a parametric study is performed to show the influence of some parameters on the stability boundaries of the beam and its amplitudes of different modes.

This paper provides numerical and exact solutions for an axially moving string system with variable length by a space–time finite element and a propagating wave model, respectively. Firstly, from the variational form, the dynamic problem for the continuum possessing changing mass is solved by a space–time finite element method. For the problem of a time-varying spatial domain, this finite element method discretizes the spatial and temporal domains simultaneously. Secondly, according to the regularity of propagating wave reflection, an exact solution for a variable-length moving string under uniform motion is derived by a propagating wave method. Subsequently, these two methods proposed are applied to a real-life example, i.e., a high-speed elevator cable. The vibration characteristics of the variable-length moving string with different boundary conditions are analyzed. Compared to the propagating wave method, the space–time finite element method has universality and low computational cost.

This paper investigates the vibration of an axially moving string with symmetrical nonclassical boundary conditions subjected to harmonic excitation. Instead of conventional fixed boundary, the boundary is modeled as a combination of a damper, a linear stiffness, and a cubic nonlinear stiffness to study the first primary resonance of the axially moving string. By applying the extended Hamilton principle, the governing equation and boundary conditions are obtained. The method of multiple scales (MMS) and the modal revision method are then utilized to perturb the governing equation and nonlinear boundary conditions into linear equations at different time scales. This enables analysis of transverse vibration at each corresponding time scale and an approximate analytical solution. The differential quadrature method (DQM) is adopted to demonstrate the feasibility and correctness of the employed method in this paper. Finally, a parametric study is carried out to indicate the effect of boundary parameters on the vibration response, taking into account rarely studied nonlinear boundaries.

The axially moving string model is widely used in engineering applications and is of great significance in research. To suppress transverse vibration and facilitate energy dissipation of the axially moving string with nonclassical boundaries, a bi-objective optimization model and methodology are proposed for its boundary parameters’ design. First, an approximate numerical model for an axially moving string with a nonclassical boundary is established, which is based on the finite element method (FEM) and Newmark-beta method. Then, a bi-objective model is proposed, including the average transverse vibration and the average system energy in a single traveling wave period, and a particle swarm optimization (BOPSO) algorithm is established for optimization. Finally, the proposed optimization model is applied in a numerical example, and the results are compared with NSGA-II, a multi-objective cuckoo search algorithm (MOCSA), and multi-objective flower pollination algorithm (MOFPA) to verify the feasibility of the proposed methodology.

以地铁B型车轴端接地线缆、接线端子、支架和线夹板组成的支架-线缆系统为研究对象,针对部件断裂问题进行系统性的结构特征分析,从支架结构、线缆固定方式等方面进行结构和部件分布的优化.基于支架-线缆系统的模态分析和谐响应分析,研究线缆的最大振幅点,对线缆的固定方式进行优化.优化后支架-线缆系统固有频率有所提高,能够尽量避免支架-线缆系统同轮轨和轴箱发生共振,提高了部件使用寿命.

The axially translating string has received wide attention due to its adverse effect of transverse vibration on security and stability in engineering. Most of the current literature focuses on classical boundary cases (e.g., fixed boundary, free boundary), while non-classical boundaries, such as damped boundary, spring-damped boundary, and mass-spring-damped boundary, are more relevant because they are in line with engineering practice. Boundary damping has a significant effect on system vibration, and the damping-damping boundary has rarely been studied. Thus, this paper is dedicated to the modeling, calculation and vibration passive control of a translating string with damping at both ends. First, the equations of motion and boundary conditions are deduced according to extended Hamilton's principle, with the boundary damping forces as the controlling forces. Second, the analytical solutions of vibration response and system energy expressions are derived using the reflected traveling wave superposition method (RTWSM). Next, to stabilize the system under the boundary damping forces, the boundary damping ranges that satisfy the exponential decay of the system energy are obtained. To further solve for optimal damping in the above ranges, RTWSM model and the boundary energy reflection are employed. Finally, the vibration responses of translating strings with different boundary damping values are simulated. The result shows that boundary damping in feasible intervals facilitates vibration attenuation effectively.

This paper provides wave solutions for the forced vibration response of a moving string system. Coupled vibration for different regions of the moving string system are considered. Firstly, due to the regularity of transmission and reflection, wave solutions are obtained by D’Alembert’s method incorporating forced waves. Secondly, the case of an applied control force provides a control strategy that changes the transmission of propagating waves to prevent the impact of the vibration travelling from one region of the string into another. Thirdly, the coupled vibration issue is handled from the point of view of propagating waves. The transmission and reflection of propagating waves at constraints are also studied. Finally, the theory proposed is applied to two real-life examples, i.e., the wiresaw manufacturing process and the hot-dip galvanizing process. Vibration characteristics of the system with a concentrated or uniform harmonic excitation are studied, and a good performance of the control strategy is demonstrated.

轴向移动绳系统广泛存在于工程设备中,因横向振动问题影响设备的正常运行而备受关注.针对具有非典型边界的轴向移动绳系统,应用行波反射叠加法,拓展了其在任意周期以及在给定初始条件均布简谐激励条件下的振动响应及能量解析解的求解.以边界控制进行振动抑制的方法具有简单、经济等优点.在轴向移动绳系统边界处设置质量-阻尼-弹簧的控制器以及控制力执行器,根据最优阻尼以及反射行波的振动抑制条件设计执行器的控制力,在第一个周期后快速抑制系统的横向振动,通过仿真体现自由和受迫振动时振动抑制的有效性.

An axially traveling string system, which is a kind of traveling material, attracts considerable attention owing to its broad applications. In this paper, an analytical wave solution for the vibration and energy of an axially traveling string with fixed and viscous damper (dashpot) boundaries in any propagation cycle is considered. Firstly, a novel recursive and simplified technique is proposed to expand the analytical solution for a traveling string to any propagation cycle, which was limited to only one propagation cycle due to complexity in previous work. As a kind of analytical solution, the traveling wave method has more accuracy and efficiency compared to numerical methods. Secondly, different from the previous result, the modified Hamilton’s principle is applied to the derivation of the dashpot boundary condition for the mass changing of the traveling string. Following the pipeline hydrodynamics theory, the energy gradient for the ‘control volume’ and the ‘system’ of traveling string are accurately obtained, respectively. Thirdly, from the point of view of vibration suppression, the optimal damping at the right end of the string is defined and the optimal damping value is derived, which is of considerable practical interest in vibration suppression at boundaries for axially traveling materials.

The finite length model of a traveling string can be used to study the lateral vibrations in many engineering devices. The vibrational energy exchange mechanism and its character-istics are very complex, due to the axial movement and the different boundary conditions. A finite length translating tensioned string model with mixed boundary conditions is considered here in order to study the exchange of vibrational energy during the reflection process. The boundary conditions are respectively at one end a spring-dashpot and the other a fixed boundary, together forming one kind of mixed boundary conditions. An analytical solution and energy expressions for the propagating wave are presented using a reflected wave superposition method. Firstly, a complete cycle of boundary reflections in the string is provided. To simplify the process for obtaining the response, each cycle is divided into three time intervals. Applying D'Alembert's principle and the reflection properties, expressions for the reflected waves under these mixed boundary conditions are derived with the vibrational response solved for three time intervals. The accuracy and efficiency of the proposed method are confirmed numerically by comparison to simulations produced using a Newmark-fl method solution. The comparison shows that the reflected wave superposition method solution is achievable for higher translational speeds, even the critical speed, which is not attainable from most numerical methods. The subsequent energy analytical expressions for a traveling string with these mixed boundary conditions are obtained in terms of the superposition of the traveling waves and their reflections. The properties of vibration energy exchange as a function of the translational velocity, the type of boundary and level of damping are discussed. Numerical simulation results proved that the viscous damper results in energy dissipation at the boundary, and the choice of the magnitude and direction of the translational string velocity can affect the energy of the traveling wave. (c) 2020 Elsevier Ltd. All rights reserved.

Impulse response function (IRF) and frequency response function (FRF) are the bases and preconditions for acquiring the parameters of a dynamic system and accurately obtaining the dynamic response of the system both in time and frequency domains. In the test of dynamic characteristics of a structural system, for some cases, it is not suitable to use the average power spectrum and cross-spectrum methods to obtain the FRF of the system. This paper studies the methods of extracting the IRF in the time domain, where the measured input and output signals contain white Gaussian noise. According to Duhamel's integral and the time-domain averaging technique, an efficient average recursive (AR) algorithm with anti-noise performance is proposed to obtain the impulse response function. In the AR method, it is assumed that the input and output data of the system are composed of white Gaussian noise with a mean value of zero. The proposed AR algorithm avoids the inversion of a larger matrix and improves the efficiency of calculation. Simulation and experimental results show that it has apparent advantages in computing efficiency and de-noising.

A reflected wave superposition method is proposed for an axially traveling string with classical and nonclassical boundaries, based on the reflection of the propagating wave on both sides of the string, combining its initial conditions and the continuity conditions in order to obtain the expressions for the reflected wave. The reflection process, in three phases, is deduced and a determinate expression for the transverse vibration is obtained. The correctness and superiority of the proposed method is verified by comparison with the Newmark- method for an axially moving string with a fixed and a spring-dashpot boundary.

An analytical vibration response in the time domain for an axially translating and laterally vibrating string with mixed boundary conditions is considered in this paper. The domain of the string is a constant, dependent upon the general initial conditions. The translating tensioned strings possess different types of mixed boundary conditions, such as fixed_dashpot, fixed_spring-dashpot, fixed_mass-spring-dashpot. An analytical solution using a reflected wave superposition method is presented for a finite translating string. Firstly, the cycle of boundary reflection for strings is provided, which is dependent upon the string length. Each cycle is divided into three time intervals according to the travelling speed and direction of the string. Applying D’Alembert’s principle and the reflection properties, expressions for the reflected waves under three different non-classical boundary conditions are derived. Then, the vibrational response of the axially translating string is solved for three time intervals by using a reflected wave superposition method. The accuracy and efficiency of the proposed method are confirmed numerically by comparison to simulations produced using a Newmark-β method solution. The energy expressions for a travelling string with a fixed_dashpot boundary condition is obtained and the time domain curves for the total energy and the change of energy at the boundaries are given.

A nonlinear equation describing the transverse vibration of an axially traveling string with constant and time-varying length is obtained by developing a new finite element model described by quadratic shape functions. A novel nonlinear coordinate transform is introduced with regard to its nonlinear terms. Subsequently, a new hybrid Newmark-beta/time varying degree of freedom method, which can adjust the element number automatically according to the change of string length, is proposed to improve accuracy. The proposed method as well as normal numerical methods are compared with an analytical solution. Results show that the proposed method is in good agreement with the Newmark-beta method for the case of small variations in string length, whilst it is superior in accuracy to the latter in the case of large length variations. Complex mode theory is adopted firstly to obtain the modal components as well as subsequently the modal energy for a traveling string. A phenomenon is observed where the free vibration energy leaks from one mode to the others in a traveling string. The higher the speed of translation and the modal order, the more energy that is leaked into the modes close to the initially excited mode.

Axially moving string system w hich is widely used in engineering equipment has attracted much attention for its vibration problems .In view of the calculation error and the divergence problem of transverse vibration of the high-speed moving string in the traditional finite element method and Galerkin method ,a calculation method for the transverse vibration of axially moving string system with finite length is presented based on traveling wave reflection superposition technology in different boundary conditions .Based on the initial and boundary conditions ,the expression of reflected wave can be obtained .Transverse vibration is equivalent to the superposition of the travelling wave with different speed and the reflected wave ,and its theoretical formula is derived .Compared with the New-mark-beta method and time-varying state space function method based on finite element discretization , the numerical example of axially moving string with both fixed ends and constant length shows that travelling wave reflection superposition method has higher precision and better stability in high-speed moving condition.

A guttering plough with two adjusting stages was designed in this paper, which can adjust its configure and position in two stages. With these two adjusting movements, the ploughshare of this guttering plough can be put in soil at a deep position, to dig out a deeper channel than normal ones. The boundary conditions including loading and constraint were obtained, when it work normally. Combined with it, and the transformed configure and position in two stages, and the structure and loading characteristics of the guttering plough, a mechanical model was established with finite element analysis method. Then its analysis and solution were carried out by using ANSYS software. Under normal working condition, the stress and strain distributions of each part of this guttering plough were obtained. The calculation results showed that the structure of this guttering plough can meet the requirement of strength, but the positions of the joints were slightly poor, so it should be properly enlarged. Finite element software can be used to analyze the spatial static of this guttering plough, which can be certified as a feasible method for the design and improvement of the plow frame structure.