Solving Vibration Problems Research Articles

Lateral vibration reduction in vertically installed shafts by active control with LMS algorithm

Machines such as generators and electric motors that use vertical shafts must avoid noise and heat problems caused by vibration. Especially in the case of vertical hydro generators, vibrations caused by water flow through the turbine and imbalance of components can lead to poor performance, premature wear of components, and even system failure. Therefore, effective control of shaft vibration is very important for system maintenance and stable operation. To solve this problem, an active control method with Least Mean Squares(LMS) algorithm were applied to the lateral vibration. In the study, the vertical shaft and the active bearing were modeled using the Finite Element Method (FEM), and the external hydraulic force was employed with an unbalanced mass. Simulations were conducted and effectiveness of the simulation results was verified through the active control experiments. These results show that active bearings have the potential to solve vibration problems and extend the life of machines with vertical shafts, such as generators or electric motors.

초정밀 장비의 진동 저감을 위한 능동형 동조질량감쇠기

In an environment where ultra-high-precision equipment is used, vibration inevitably occurs due to various factors. These vibrations generate fatal effects, such as defect generation and reduced production yield, on ultra-high-precision production equipment. Among the multiple methods for solving vibration problems, a Tuned Mass Damper (TMD) is a useful technique that reduces vibration without changing the existing structure by attaching a passive dynamic system consisting of additional mass, spring, and damper. However, it is difficult to realize fine-tuning of the system parameters for optimal performance because the passive elements have structural limitations. An active TMD, which has a form wherein sensors, actuators, and a control device are added to the passive TMD structure, was introduced. It has higher performance than passive TMD because dynamic characteristics can be induced to stable and highly damped by a well-designed control algorithm realized by software in the control device. In this study, an active TMD was developed utilizing passive TMD with a voice coil actuator and attached to the center of both end fixed beam that assumed a single-degree-of-freedom structure. A dual-loop control algorithm using a non-minimum phase system was designed for a high-damped response while retaining stability. The modal test was performed for experimental evaluation and excellent performance of active TMD was verified.

Dynamic analysis of FG stepped truncated conical shells surrounded by Pasternak elastic foundations

This research presents a continuous element model for solving vibration problems of FG stepped truncated conical shells having various material properties and surrounded by Pasternak foundations. Based on the First Order Shear Deformation Theory (FSDT) and the equations of the FGM conical shells, the dynamic stiffness matrix is obtained for each segment of the shell having constant thickness. The interesting assembly procedure of continuous element method (CEM) is employed for joining those segments in order to analyze the dynamic behavior of the FG stepped truncated conical shells an assembly procedure of continuous element method (CEM) is employed for joining those segments. Free vibrations of different configurations of FG stepped truncated conical shells on elastic foundations are examined. Effects of structural parameters, stepped thickness and elastic foundations on the free vibration of FG stepped truncated conical shells are also presented.

Numerical study of the effect of viscoelastic properties of the material and bases on vibration fatigue of pipelines conveying pulsating fluid flow

The article presents the results of mathematical and computer modeling of the oscillatory processes of viscoelastic pipelines considering stationary external loads. A mathematical model of viscoelastic pipeline vibrations based on the theory of beams was developed when a pulsating fluid flows through it. Using the Bubnov-Galerkin method, based on a polynomial approximation of deflections, the problem was reduced to the study of a system of ordinary integro-differential equations, the solution of which was found numerically. A computational algorithm has been developed to solve vibration problems of composite pipelines conveying pulsating fluid. Stability and amplitude-time characteristics of vibrations of composite pipelines conveying pulsating fluid were studied at wide range of parameters variation of deformable systems and fluid flow. Critical fluid flow rates were found at which a viscoelastic pipe lost its rectilinear equilibrium shape. A singularity effect in hereditary kernels on vibrations of structures with viscoelastic properties was numerically studied. It was shown that with an increase in viscosity parameter of the pipeline material, the critical flow rate decreases. It was revealed that an increase in fluid pulsation frequency and excitation coefficient led to a decrease in the fluid flow critical rate. It was stated that an increase in Winkler bases parameters and the rigidity parameter of a continuous layer led to an increase in the critical flow rate.

Numerical modeling of vibration fatigue of viscoelastic pipelines conveying pulsating fluid flow

The effect of investigation results on viscoelastic properties of the material and bases on vibration fatigue of a pipeline conveying pulsating fluid flow is given in the paper. A mathematical model of viscoelastic pipeline vibrations based on the theory of beams was developed when a pulsating fluid flows through it. A computational algorithm has been developed to solve vibration problems of composite pipelines conveying pulsating fluid. Stability and amplitude-time characteristics of vibrations of composite pipelines conveying pulsating fluid were studied at wide range of parameters variation of deformable systems and fluid flow.

Implementation of Diagnostic Technique to Solve Vibration Problems in Sugar Industry: Some Case Studies

Predictive maintenance technique has been accepted worldwide for maintenance of rotating machines in process industries. Amongst a vast number of machine condition monitoring techniques, vibration monitoring and analysis is distinct and the most widely used method in detecting mechanical faults in common rotating machinery. Sugar industry is one of the important industries of many countries in which variety of rotating machines are linked together in order to carry out sugar production. Implementation of diagnostic technique through vibration monitoring and analysis can lead to effective predictive maintenance. This paper deals with a review of the state of the art of vibration condition monitoring and prognosis technique applied to the rotating machines in sugar industries. It also focuses on case studies of fault diagnosis and rectification of few rotating machines of this industry.

Effects of mount positions on vibrational energy flow transmission characteristics in aero-engine casing structures

The main goal of the study is to apply the structural intensity method to analyze the effects of positions of the main-mount and the sub-mount on the vibrational energy flow transmission characteristics in aero-engine casing structures, so as to attenuate the vibration of the casing and the whole aero-engine. Structural intensity method, indicating magnitude and direction of the vibrational energy flow, is a powerful tool to study vibration problems from the perspective of energy. In this paper, a casing-support-rotor coupling model subjected to the rotor unbalanced forces is established by the finite element method. Formulations of the structural intensity of a shell element and the structural intensity streamline are given. A simulation system consisting of the finite element tool and the in-house program is developed to carry out forced vibration analysis and structural intensity calculation. The structural intensity field of the casing is visualized in the forms of vector diagram and streamline representation. The vibrational energy flow behaviors of the casing at the rotor design rotating speed are analyzed, and the vibrational energy flow transmission characteristics of the casing with different axial positions of the main-mount and the sub-mount are investigated. Moreover, some measures to attenuate the vibration of the casing are obtained from the numerical results, and their effectiveness is verified in the frequency domain and the time domain. The results shed new light on the effects of the mount positions on the vibration energy transmission behaviors of the casing structure. The structural intensity method is a more advanced tool for solving vibration problems in engineering. Furthermore, it may provide some guidance for the vibration attenuation of the casing and the whole aero-engine.

A Wave-Based Analytical Solution to Free Vibrations in a Combined Euler–Bernoulli Beam/Frame and a Two-Degree-of-Freedom Spring–Mass System

In this paper, natural frequencies and modeshapes of a transversely vibrating Euler–Bernoulli beam carrying a discrete two-degree-of-freedom (2DOF) spring–mass system are obtained from a wave vibration point of view in which vibrations are described as waves that propagate along uniform structural elements and are reflected and transmitted at structural discontinuities. From the wave vibration standpoint, external forces applied to a structure have the effect of injecting vibration waves to the structure. In the combined beam and 2DOF spring–mass system, the vibrating discrete spring–mass system injects waves into the distributed beam through the spring forces at the two spring attached points. Assembling these wave relations in the beam provides an analytical solution to vibrations of the combined system. Accuracy of the proposed wave analysis approach is validated through comparisons to available results. This wave-based approach is further extended to analyze vibrations in a planar portal frame that carries a discrete 2DOF spring–mass system, where in addition to the transverse motion, the axial motion must be included due to the coupling effect at the angled joint of the frame. The wave vibration approach is seen to provide a systematic and concise technique for solving vibration problems in combined distributed and discrete systems.

An Electromechanical Co-Simulation Model Based on Lumped Parameter Model of Ball Screw Feed Drive System

The continuous search for efficiency put forward higher requests to the machine tool for high speed and high acceleration, which makes the large-size and lightweight-designed feed drive system more likely to produce vibration during high-speed and high-acceleration feed operation. Ball screw feed system is the most widely used linear drive system in the field of industrial automation. Electromechanical Co-Simulation for ball screw feed drive dynamics is an important technique for solving vibration problems occurs in the feed motion. In view of the shortcomings of the current dynamic simulation model in the study of vibration of ball screw feed drive system, taking a ball screw feed drive system test bench as an example, an electromechanical co-simulation model based on the lumped parameter model of ball screw feed drive system was built up in this paper. Firstly, based on the axial and rotation vibration integrated dynamic modeling method of ball screws, the lumped parameter model of ball screw feed system was established. Secondly, through the integration of the simulation model of semi-closed-loop cascade control system and the lumped parameter model of ball screw feed drive system, an electromechanical co-simulation model was built up. Simulation result shows that, the co-simulation model of ball screw feed drive system can predict the vibration occurs in the feed operation caused by the servo controller, ball screw feed system or the coupling between them.

Dynamic analysis of stepped composite cylindrical shells surrounded by Pasternak elastic foundations based on the continuous element method

This research presents a continuous element model for solving vibration problems of stepped composite cylindrical shells surrounded by Pasternak foundations with various boundary conditions. Based on the First Order Shear Deformation Theory (FSDT), the equations of motion of the circular cylindrical shell are introduced and the dynamic stiffness matrix is obtained for each segment of the uniform shell. The interesting assembly procedure of continuous element method (CEM) is adopted to analyze the dynamic behavior of the stepped composite cylindrical shell surrounded by an elastic foundation. Free vibrations and harmonic responses of different configurations of stepped composite cylindrical shells on elastic foundations are examined. Effects of structural parameters, stepped thickness and elastic foundations on the free vibration responses of stepped composite cylindrical shells are also presented. Comparisons with previously published results and finite element (FE) analyses show that the proposed technique saves data storage volume and calculating time, and is accurate and efficient for widening the studied frequency range.

Finite difference and Runge–Kutta methods for solving vibration problems

The vibration of a storey building can be modelled into a system of second order ordinary differential equations. If the number of floors of a building is large, then the result is a large scale system of second order ordinary differential equations. The large scale system is difficult to solve, and if it can be solved, the solution may not be accurate. Therefore, in this paper, we seek for accurate methods for solving vibration problems. We compare the performance of numerical finite difference and Runge–Kutta methods for solving large scale systems of second order ordinary differential equations. The finite difference methods include the forward and central differences. The Runge–Kutta methods include the Euler and Heun methods. Our research results show that the central finite difference and the Heun methods produce more accurate solutions than the forward finite difference and the Euler methods do.

Evaluation of the effect of stopping selected frames on noise in the cabin of a propeller airplane

A unified approach is proposed to solve vibration problems for stiffened plates, shells, and other arbitrary stiffened structures. The approach is applicable under the condition that independent solutions for the stiffened structure and the stiffening elements are known in the form of explicit expressions determining generalized displacements through generalized forces. The proposed universal equation is used to solve the problem of deterministic vibrations of a closed cylindrical shell with “smeared” stringers and irregular discrete frames. The solution is used to estimate the effect of noise suppression achieved in the cabin of a propeller airplane by stopping some of the frames positioned near the propeller.

On a problem of the vibration of functionally graded conical shells with mixed boundary conditions

This paper presents a theoretical approach to solve vibration problems of functionally graded (FG) truncated conical shells under mixed boundary conditions. The material properties of FG shell are assumed to vary continuously through the thickness of the conical shell. The fundamental relations, motion and strain compatibility equations of FG truncated conical shells are derived by means of the Airy stress function method. Two cases of mixed boundary conditions are investigated. The basic equations are solved by using Galerkin method and fundamental cyclic frequencies of FG truncated conical shells are obtained. The results are compared and validated with the results available in the literature. The detailed parametric studies are carried out to investigate the influences of radius-to-thickness ratio, lengths-to-radius ratio, material composition and mixed boundary conditions on the fundamental cyclic frequencies of truncated conical shells.

Analysis and compensation methods for time delays in an impact buffer system based on magnetorheological dampers

Magnetorheological dampers have been widely studied as versatile real-time actuators for solving vibration problems in various structures and systems. However, the inherent time delay problem of magnetorheological actuators may cause performance degradation of semi-active control systems. The primary purposes of this article are to provide a comprehensive analysis on the time delay of an impact buffer system based on a magnetorheological damper and to propose compensation methods to reduce the time delay. To this end, this study evaluated the electromagnetic circuit in the magnetorheological damper and designed an advanced correcting circuit to improve the response time. The simulation results show that the proposed circuit reduces the time delay by 5 ms. Using a magnetorheological buffer system setup, its force response times were tested. The experimental results show that the electromagnetic circuit plays a significant role in the time delay and it is highly dependent on the effectiveness of the electric parts of the control hardware. Furthermore, a proportional–integral–derivative controller is able to reduce the time delay and improve the dynamic performance of the magnetorheological impact buffer system.

모션프로파일의 주파수분석을 통한 웨이퍼 이송로봇의 진동성능 향상

This paper is study of solving vibration problem occurred in moving hand of wafer transfer robot in semiconductor manufacturing line. Long settling time for decreasing vibration makes low production rate, and moreover the excessive vibration of hand sometimes breaks the wafer in a cassette. The ways of reducing the moving speed and changing the type of motion profile did not help for lessening vibration. Therefore, we analyzed the mechanical property of the hand such as natural frequency, and frequency component of the motion profile currently used in the manufacturing line. In several conditions of motion profile, we found the best condition of which the frequency component in near of natural frequency of the hand is minimal and this induced small vibration in moving hand. The results were verified theoretically and experimentally using frequency analysis.

Wave propagation in electro‐magneto‐elastic solid plate of polygonal cross‐sections

PurposeThis paper aims to describe the method for solving vibration problem of electro‐magneto‐elastic plate of polygonal (triangle, square, pentagon and hexagon) cross‐sections using Fourier expansion collocation method (FECM).Design/methodology/approachA mathematical model is developed to study the wave propagation in an electro‐magneto‐elastic plate of polygonal cross‐sections using the theory of elasticity. The frequency equations are obtained from the arbitrary cross‐sectional boundary conditions, since the boundary is irregular in shape; it is difficult to satisfy the boundary conditions along the surface of the plate directly. Hence, the FECM is applied along the boundary to satisfy the boundary conditions. The roots of the frequency equations are obtained by using the secant method, applicable for complex roots.FindingsFrom the literature survey, it is clear that the free vibration of electro‐magneto‐elastic plate of polygonal cross‐sections have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of electro‐magneto‐elastic plates are based on the traditional circular cross‐sections only. So, in this paper, the wave propagation in electro‐magneto‐elastic plate of polygonal cross‐sections is studied using the FECM. The computed non‐dimensional frequencies are plotted in the form of dispersion curves and their characteristics are discussed.Originality/valueThe researchers have discussed the circular, rectangular, triangular and square cross‐sectional plates by the boundary conditions. In this problem, the author studied the vibrations of polygonal (triangle, square, pentagon and hexagon) cross‐sectional plates using the geometrical relation which is applicable to all the cross‐sections. The problem may be extended to any kinds of cross‐sections by using the proper geometrical relations.

Free and forced vibration analysis of uniform and stepped circular cylindrical shells using a domain decomposition method

This paper presents a domain decomposition technique for solving vibration problems of uniform and stepped cylindrical shells with arbitrary boundary conditions. Multilevel partition hierarchy, viz., stepped shell, shell segment and shell domain, is adopted to accommodate the computing requirement of high-order vibration modes and responses. The interface continuity constraints are enforced by using a modified variational principle and least-squares weighted residual method. The displacement components of each shell domain are expanded in the form of a double mixed series: Fourier series for the circumferential variable and polynomials/series (i.e., the Chebyshev orthogonal polynomials, Legendre orthogonal polynomials, and simple power series) for the axial variable. Free, steady-state and transient vibrations of uniform and stepped cylindrical shells are examined under different combinations of free, shear-diaphragm, simply-supported, clamped and elastic-supported boundaries. Comparisons with previously published results and finite element analyses show that the technique is computationally accurate and efficient. Effects of structural damping, stepped thickness and boundary conditions on the forced vibration responses of stepped cylindrical shells are also presented.

Higher-order accurate compact difference solutions for vibration problems of one dimensional continuous systems

In this paper, we present a fourth-order accurate and a seventh-order accurate, one-step compact difference methods. These methods can be used to solve initial or boundaryvalue problems which can be modeled by a first-order linear system of differential equations. It is then shown in detail how these methods can be used to solve vibration problems of onedimensional continuous systems. Natural frequencies of a cantilever beam in transverse vibrations are computed and the results are compared to analytical ones to prove the high accuracy and efficiency of both methods. A comparison was also made to a finite element solution and the results have shown that both compact-difference methods yield more accurate values even with a reduced number of intervals.

Higher-order accurate compact difference solutions for vibration problems of one dimensional continuous systems

In this paper, we present a fourth-order accurate and a seventh-order accurate, one-step compact difference methods. These methods can be used to solve initial or boundaryvalue problems which can be modeled by a first-order linear system of differential equations. It is then shown in detail how these methods can be used to solve vibration problems of onedimensional continuous systems. Natural frequencies of a cantilever beam in transverse vibrations are computed and the results are compared to analytical ones to prove the high accuracy and efficiency of both methods. A comparison was also made to a finite element solution and the results have shown that both compact-difference methods yield more accurate values even with a reduced number of intervals.

The use of He’s variational iteration method for obtaining the free vibration of an Euler–Bernoulli beam

This paper presents a way of using He’s variational iteration method to solve free vibration problems for an Euler–Bernoulli beam under various supporting conditions. By employing this technique, the beam’s natural frequencies and mode shapes can be obtained and a rapidly convergent sequence is obtained during the solution. The results obtained are the same as the results obtained by the Adomian decomposition method. It is verified that the present method is accurate and it provides a simple and efficient approach for solving vibration problems for uniform Euler–Bernoulli beams. A robust and efficient algorithm is also programmed using Matlab based on the present method, which can be easily used to solve Euler Bernoulli beam problems.