Mechanical Vibration Problems Research Articles

Network-based System of Mechanical Vibration Fault Diagnosis

Nowadays researchers are investing in electrical machines fault diagnosis area. The users and manufacturers are strong for containing diagnostic features for reliability and scalability improvement. The regular monitoring enables machine faults early detection and hence helpful for automation by providing process control. The fault detection performance and machine-learning algorithms classification are highly dependent on features involved. The aim of this paper is to solve the network mechanical vibration problem and for that a research on mechanical vibration fault diagnosis is proposed. The first is to use the vibration signal receiving device to record the vibration signal of the target device. In the process of receiving the signal, the measurement point is related to the accuracy of the received signal, so it is necessary to prepare the measurement point. Secondly, the principle of fault detection based on vibration detection is introduced. The main purpose of this method is to identify the fault characteristics, simulate the fault with MATLAB, and obtain the error time-frequency diagram behavior. The feature vector dimension obtained by the idling confirmation example is the same as that of the rotor, which is 14, including 8 relative wavelet packet intensity entropy feature indexes and higher values, minimum value, peak-to-peak value, mean value, mean square error and variance. Finally, the deficiencies of the detected vibration faults are identified and similar improvements are proposed. Improvements only reduce signal vibration, disrupting feature isolation and identifying patterns.The observed percentage accuracy for classification of faults through proposed approach is 98.2%.

Incremental harmonic balance method for multi-harmonic solution of high-dimensional delay differential equations: Application to crossflow-induced nonlinear vibration of steam generator tubes

Diverse science and engineering problems are governed by delay differential equations (DDE). Seeking periodic solutions of DDEs is crucial for many nonlinear dynamic systems. The incremental harmonic balance (IHB) method is an efficient semi-analytical approach for periodic solutions of DDE. Among various DDE systems, flow-induced vibration (FIV) of tube bundles with loose support is unique, in the sense that the added damping cancels out structural damping in the vicinity of critical velocity, making it extremely slow to retain a convergent solution if numerical integration (NI) is utilized. Despite the efforts of developing IHB for various mechanical vibration problems with time-delay, no attempt has been made to employ IHB to nonlinear FIV problems. Here we fill this blank by separately combining two spatial discretization strategies, i.e., discretization via linear vibration modes or via finite element method (FEM), with IHB to capture limit cycle solutions after the onset of instability. Within the range of gap velocity of interest, the IHB demonstrates excellent convergence by increasing harmonic terms, and good agreement is obtained between IHB results and the results by NI method. An 18 degree-of-freedom (DOF) nonlinear DDE system was readily dealt by integrating FEM and IHB, each DOF being approximated by three harmonics. This is the first attempt to employ IHB for multi-harmonic solution of high-dimensional FIV problems, which opens a door for solutions of other DDEs. All the codes used in this paper could be downloaded via: https://github.com/XJTU-Zhou-group/IHB.

Influence of Bistable Plunge Stiffness on Nonlinear Airfoil Flutter

Abstract Aeroelastic systems have nonlinearities that provide a wide variety of complex dynamic behaviors. Nonlinear effects can be avoided in practical applications, as in instability suppression or desired, for instance, in the energy harvesting design. In the technical literature, there are surveys on nonlinear aeroelastic systems and the different manners they manifest. More recently, the bistable spring effect has been studied as an acceptable nonlinear behavior applied to mechanical vibration problems. The application of the bistable spring effect to aeroelastic problems is still not explored thoroughly. This paper contributes to analyzing the nonlinear dynamics of a typical airfoil section mounted on bistable spring support at plunging motion. The equations of motion are based on the typical aeroelastic section model with three degrees-of-freedom. Moreover, a hardening nonlinearity in pitch is also considered. A preliminary analysis of the bistable spring geometry's influence in its restoring force and the elastic potential energy is performed. The response of the system is investigated for a set of geometrical configurations. It is possible to identify post-flutter motion regions, the so-called intrawell and interwell. Results reveal that the transition between intrawell to interwell regions occurs smoothly, depending on the initial conditions. The bistable effect on the aeroelastic system can be advantageous in energy extraction problems due to the jump in oscillation amplitudes. Furthermore, the hardening effect in pitching motion reduces the limit cycle oscillation (LCO) amplitudes and also delays the occurrence of the snap-through.

On interactive fuzzy solutions for mechanical vibration problems

Fuzzy initial value problems describing classical mechanical vibrations are the focus of this paper. In particular, this work considers systems described by nth-order linear ordinary differential equations whose initial conditions are uncertain and given by interactive fuzzy numbers. The concept of interactivity arises from the concept of joint possibility distribution (J). An approach based on the sup-J extension principle, which is a generalization of Zadeh’s extension principle, is presented. This theory is applied to two major examples of oscillatory systems: the forced vibration of an uncoupled mass-spring-damper system and the free vibration of a coupled undamped mass-spring system. In both cases, we have that the solution via sup-J extension, where the fuzzy initial conditions are given by linearly correlated fuzzy numbers, is contained in the solution via Zadeh’s extension.

A Move Recent Review of The Integral Equations and Their Applications

In many branches of pure analysis, Integral Equations are one of the most useful techniques, such as functional analysis theories and stochastic processes. It is one of the most significant branches of mathematical analysis, in many fields of mechanics and mathematical physics,. In this research, we will address the integral equations in many physical issues and their applications. They are also associated with mechanical vibration problems, analytic function theory, orthogonal systems, quadratic form theory of infinitely many variables.

An educational software suite for comprehensive learning of Computer‐Aided Engineering

AbstractThe learning of Computer‐Aided Engineering (CAE) usually involves practical computer lessons on the use of CAE software. Software packages suitable for learning should be user‐friendly and accessible, with an affordable cost. However, the CAE freeware and proprietary software available in the market are relatively difficult to use for novices. Furthermore, most proprietary software packages are very costly, hindering the access of learners. In this study, a CAE freeware suite, CAE 3D, has been developed for supporting the learning of CAE technology. CAE 3D contains four modules for analyzing 3D solid mechanics, heat transfer, and mechanical vibration problems by the finite element method, and 3D fluid dynamics problems by the finite volume method. Unlike most CAE freeware applications, the user interface of CAE 3D is a purely graphical user interface instead of containing some text‐based user interfaces. As CAE 3D is user‐friendly and capable of analyzing various types of engineering problems, it is suitable for use as a learning tool of CAE. For example, learners can adjust parameters, such as geometry, material properties, and/or boundary conditions, to explore the effects of a given setting on the CAE results. This article explains the CAE learning process, development of CAE 3D software and application of CAE 3D to university classrooms. The classroom feedback indicates that the students were highly satisfied with CAE 3D in terms of the usability, the reliability of results and the contribution toward learning. These responses support the applicability of CAE 3D in CAE education.

Dynamic Response Bound Estimation of Structures with Interval Parameters

This study aims to evaluate the result of mechanical vibration problems in presence of an interval of values for parameters such as mass, length, modulus of elasticity, moment of inertia. A possibility and computationally efficient method is proposed to obtain the limits of natural frequency of systems with interval parameters. The interval eigenvalue problem is formulated by the Finite Element Method (FEM) which stiffness and mass matrices are submitted to disturbance by Perturbation Theory of Matrices (PTM). At each stage of the analysis, the existence of uncertainty in matrix formulation is considered as the presence of disorder in a pseudo-deterministic system capable of providing technically reliable and efficient results. Numerical results are presented using a tool developed by the author in MATLAB ®. This program works with dynamic structures with interval uncertainty. The numerical results are compared with the literature and with a Monte Carlo simulation. Experimental tests were conducted to validate the results of the proposed method.

The use of normal forms for analysing nonlinear mechanical vibrations.

A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent variant of the normal form method, that respects the specific structure of such models, is recalled. It is shown how this method can be placed within the context of the general theory of normal forms provided the damping and forcing terms are treated as unfolding parameters. The approach is contrasted to the alternative theory of nonlinear normal modes (NNMs) which is argued to be problematic in the presence of damping. The efficacy of the normal form method is illustrated on a model of the vibration of a taut cable, which is geometrically nonlinear. It is shown how the method is able to accurately predict NNM shapes and their bifurcations.

Asymptotic Behavior of Solutions of Neutral Difference Equations Dealing with Mechanical Vibration Problems

Asymptotic behavior is studied for solutions of neutral difference equations dealing with mechanical vibration problems and other related topics, and some theorems have been obtained.

Eigenanalysis in structural acoustics.

Determination of characteristic frequencies and solutions (mode shapes) for vibrating systems is a staple of linear dynamics in engineering, so it should be no surprise that analysts strive for the same in coupled structural-acoustic systems. Computation of these eigensolutions confers not only physical insight into the behavior of the system, but also a means to reduce the mathematical dimension of frequency-response and other engineering computations. As in other mechanical vibration problems, the eigensolutions of coupled systems form a nearly optimal space for the approximation of the forced-response solutions. However, the coupled structural-acoustic eigenproblem is not trivial, and can be prohibitively expensive if not handled properly; this is particularly true for exterior problems. Notably, identification of a physically pertinent self-adjoint operator for the system of interest is a critical challenge. Here we will discuss the coupled structural-acoustic eigenproblem, various approximations common in practice, as well as alternative approaches to model reduction.

A Coupled Analysis of Mechanical Vibration Problem and Transfer Process

Electrostatic printing process is an assembly of electrostatic, mechanical and optical process. It includes controlling such a variety of physics. It involves materials that can be electro-staticly charged, or vibrate in and deform mechanically. While the dimensions of physical parts are in centimeters, the accuracy of the process is measured and controlled in microns.In general, the overall printing process is analyzed in terms of series of individual processes, e.g. transfer of toner to paper or vibration of the rollers. The design of a new printer concept is followed by investigation of the performance against a series of design parameters. The components of a laser printer are tested to verify the desired performance of each of these processes.If one considers a printer as a system, it may be beneficial to look at the relationship between the individual processes and identify the interrelation between the components and processes of the entire system. In this paper, we will attempt to demonstrate, the coupling between a specific electrostatic process: transferring toner from a photo-conductor roller to paper and a mechanical process: vibration of the OPC roller, paper and belt. This approach can be extended to include many other processes and components.

Blind source separation of internal combustion engine piston slap from other measured vibration signals

Internal combustion engines have several vibration sources, such as combustion, fuel injection, piston slap and valve operation. For machine condition monitoring or design improvement purposes, it is necessary to separate the vibration signals caused by different sources and then analyse each of them individually. However, traditional frequency analysis techniques are not very useful due to overlap of the different sources over a wide frequency range. This paper attempts to separate the vibration sources, especially piston slap, by using blind source separation techniques with the intention of revealing the potential of the new technique for solving mechanical vibration problems. The BSS method and the Blind least mean square algorithm using Gray's variable norm as a measure of non-Gaussianity of the sources is briefly described and separation results for both simulated and measured data are presented and discussed.

Parametric estimation of the cross-power spectral density

A new cross-spectral analysis procedure is proposed for the parametric estimation of the relationship between two time sequences in the frequency domain. In this method, the two observable outputs are modeled as a pair of autoregressive moving-average and moving-average (ARMAMA) models under the assumption that the two outputs are driven by a common input and independent ones simultaneously. Cross- and auto-power spectral densities (PSDs) of a pair of ARMAMA models can be derived as forms of rational polynomial functions. The coefficients of these functions can be estimated from the cross-correlation function or the auto-correlation functions of the two observed sequences by using the method presented in this paper. The main advantage of the present procedure is that the physical parameters of an unknown system can be easily estimated from the coefficients of the cross- and auto-PSD functions. To illustrate the effectiveness of the proposed procedure, numerical and practical examples of a mechanical vibration problem are analyzed. The results show that the proposed procedure gives accurate cross- and auto-PSD estimates. Moreover, the physical properties of the unknown system can be well estimated from the obtained cross- and auto-PSDs.

Identification of Nonlinear Systems by Synchronization in Chaotic Systems. Parametric Identification by Autosynchronization.

This paper studies a practical method for parametric identification of one degree of freedom forced Duffing system by the chaotic autosynchronization. Our previous paper discussed a method evaluating modeling errors of a chaotic system by the chaotic synchronization and showed that the proposed index approaches its minimal value as a modeling error reaches zero. The next step of our approach is to develop a practical method to obtain a model which synchronizes with a target chaotic system (consequently becomes identical to the target system). To achieve this, we develop an application of an autosynchronizing chaotic system. The basic theory of our method have been developed by Parlitz. However, his work dealt only with an autonomous system such as Lorenz system, which rarely arises in mechanical vibration problems. First, we develop a method constructing an autosynchronizing system for a parametric identification of mechanical vibration systems. We then perform a parametric identification of the forced Duffing system by the autosynchronizing system. The precise values of system parameters of the forced Duffing system are dynamically estimated even if these parameters are time-varying.

ANALYSIS OF OPTICAL WAVEGUIDES USING AN ANALOGY TO A MECHANICAL VIBRATION PROBLEM

Many waveguide problems in integrated optics may mathematically be described by a scalar Helmholtz equation. In this paper it will be shown, that the same equation arises in the analysis of a mechanical vibration problem (elastically bedded membrane). One can utilize this analogy for calculating the propagation characteristics and field distribution of optical waveguides by one of the wide spread mechanics Finite‐Element codes, which are available on many computer systems, including personal computers in recent years. As an example this computation by analogy method is employed for the computation of the propagation characteristic of a symmetric film waveguide.

The effect of superimposed Rankine and forced vortices on conical diffuser performance

It is not always possible for a designer to accommodate a conical diffuser giving the greatest possible pressure recovery for a given area ratio because this usually involves a long version with a total conical angle of about 7 degrees. Considerable efforts have therefore been made to improve the performance of diffusers with total conical angles up to at least 30 degrees by adopting various techniques listed in Ref. 1. One suggestion was the addition of whirl to the flow in the inlet pipe; that is, to superimpose a vortex coaxial with the pipe and diffuser axis. However, Refs. 1 and 2 show the amount of published research on this topic to have been meagre.A previous paper has dealt with the case of adding a forced vortex whirl velocity distribution to the incoming flow and showed that improvements were possible, certainly in static pressure recovery and even in so-called efficiency, using a restricted definition of the latter. Because of mechanical vibration problems, the maximum swirl angle that could be added to the flow was about 15 degrees, corresponding to a forced vortex rotation rate of about 28 rad/s. This led to a beneficial redistribution of axial velocity components and a diminished tendency for flow separation from the walls.

The Finite Element Analysis of Shocks and Acceleration Waves in Nonlinearly Elastic Solids

Application of the finite element method to timedependent problems, particularly mechanical vibration problems of complex structures, dates back to the early 1960's. The use of consistent mass matrixes was proposed by Archer in 1965, and mode superposition techniques became popular in the late 1960's for the analysis of vibration problems. During the last half-decade, the need for studying transient dynamic phenomena in complex structures, particularly wave phenomena, has risen sharply. Prejudices that developed while studying vibration phenomena still persist, and modern engineering literature on finite element applications to wave problems is still filled with discussions of various implicit schemes which had proved to be efficient for low frequency response or linear structures. In very recent times, application of finite element methods to nonlinear dynamic problems have begun to appear, but one rarely finds the mention or shocks or of numerical schemes capable of handling them.

A generalization of Kron's eigenvalue procedure

Kron's eigenvalue procedure in its original form applies only to systems having real eigenvalues and the simple orthogonality properties associated with mechanical vibration problems which may be formulated in terms of two symmetric real matrices. In this paper, the method is extended to cover more general eigenvalue problems—for example, the complex eigenvalue problems which arise naturally in studies of damped mechanical systems. A computational algorithm for composite-system eigenvalues is developed in terms of Newton's method.

Generalized Vibration Analysis by Means of the Mechanical Transients Analyzer

Abstract This paper presents the results of a general study that has been made of a linear system having 2 deg of freedom. This is representative for many mechanical vibration problems as well as for problems of other physical systems. The system is described specifically in terms of the mechanical parameters of translational motion and consists of one mass, spring, dashpot system mounted on another. Three types of generalized solutions are given for the maximum motion of the first system relative to the second, or the maximum stress developed in the spring of the first system. One of these is for known sinusoidal forces applied to the second system, one is for the whole system striking a fixed base at a known velocity without rebound, and one is for such an impact and one rebound. The solutions were obtained on the mechanical transients analyzer which employs the principle of electric-circuit analogy. The solutions are given in dimensionless curve form for a wide range of all parameters.

Vibrations in Aircraft

THE present series of articles is intended to cover in a general manner the whole subject of vibration in aircraft. The study of aircraft vibration is a specialized branch of engineering science, calling for considerable practical skill and experience in the design and use of measuring equipment, as well as the ability to carry out the mathematical analyses which render test results intelligible and lead to the successful solution of vibration problems. The leading features of all mechanical vibration problems are, however, of such a nature as to be readily understood, and the aim of this series is to describe these leading features so as to facilitate the appreciation of the broad principles governing the avoidance of unpleasant or dangerous vibrations.