Transverse Vibration Analysis Research Articles

Transverse vibration analysis of generally laminated two-segment composite shafts with a lumped mass using generalized differential quadrature

The use of composite materials for weight reduction of shaft drivelines has positive impacts in different applications. The driveshafts design is mostly dictated by its natural frequencies. In order to maximize the natural frequencies, shafts are built in one, two or more segments. Analysis of such components has complexities in dealing with two-segments, shear deformation, and material coupling effects. This paper presents a theory that includes shear deformation and rotary inertia along with coupling effects to analyze transverse vibration behavior of generally laminated shafts with intermediate joints. Equivalent modulus of elasticity is used instead of traditional stiffness terms to account for material coupling. The equations of motion are solved using generalized differential quadrature. Results were compared with those published in the literature and finite element simulations, and it has been shown that the present method can accurately predict transverse vibration behaviors of generally laminated two-segment shafts with a lumped mass.

A new modeling approach for the dynamics of a micro end mill in high-speed micro-cutting

This study presents a distributed parameter model for the transverse vibration analysis of a micro end mill. Owing to its geometrical nonuniformity, the micro end mill is spatially sub-structured into three distinct spinning elastic systems. With the application of the extended Hamilton’s principle to the energy expressions of the spinning elastic systems, the governing equations of each sub-structured system are obtained. The overall analytical model incorporates a number of nonclassical structural effects that range from rotary inertia, shear deformation, taper ratio, to the rate of twist. For detailed frequency analyses, systematic solution of the elastodynamics governing equations is provided with the spectral finite element method. To assess the accuracy of the presented method, the frequency values of each of the spatial sub-structure are validated through available results in the literature. In the same vein, the solution of the entire ensemble of the distributed parameter system compares well with ANSYS® simulation. The investigation reveals the spinning rate to have the most significant effect on the frequency value of the micro tool followed by the taper ratio and the complex geometry of the micro flute.

Estimation of the dynamic elastic properties of wood from Copaifera langsdorffii Desf using resonance analysis

Analysis of transverse vibrations has been identified as a simple, inexpensive, fast and effective method of characterizing the elastic properties of several materials, including wood. The objective of this study is to evaluate the dynamic elastic properties of wood from Copaifera langsdorffii through resonance analysis. A linear correlation was observed, with a coefficient of determination of 0.88, between the dynamic modulus of elasticity (Ed), as determined by BING (resonance analysis), and the static modulus of elasticity (E), as determined by a universal testing machine, for wood samples of Copaifera langsdorffii. A moderate correlation was observed (0.69) between the Ed and the apparent density (D) of the samples. The shear modulus (G) was negatively correlated with D, E, and Ed, yet not significantly. The specific modulus, which is the stiffness to density ratio, was linearly correlated with the internal damping. This viscoelastic correlation is rarely reported in literature and indicates, for instance, wood quality for the manufacture of musical instruments. The BING system provided fast, reliable results for estimation of elastic properties, particularly stiffness, in wood of Copaifera langsdorffii.

Transverse Vibration Analysis of Buried Pipeline under Fluid-Solid Coupling Interaction

The pipe model is simplified as elastic foundation beam model of Euler-Bernoulli, the form of pin rocker bearing in the analysis of transverse vibration in the paper. According the principle of Hamilton, after a series of variation, exchanging the order of integral and integration by parts, the transverse vibration differential equation of pipe is obtained without fluid. Considering different boundary consitions, the solving process is carried out. By utlization of MALAB language, the numerical example is analyzed, considering fluid and foundation. Thus, the fluid-solid coupling interaction is not ignored in transverse vibration in the buried pipeline.

Free transverse vibration analysis of a toothed gear

Analysis of transverse vibration of the gear found in a high-speed gearbox considered as an annular plate reflecting gear geometry is the subject of this paper. How gear angular velocity affects the deformation of normal modes of transverse vibration of the system under consideration is analysed. Models considered were discretized by the finite elements method. Numerical computations have been performed in the ANSYS environment. The algorithm to identify the proper distorted mode shapes is presented. The Campbell diagram for the system under consideration is elaborated. The problems discussed here can be useful for engineers dealing with dynamics of rotating machine systems.

Establishment of Mathematical Model of Buried Pipeline on Nonlinear Soil Dynamic Model

The pipe model is simplified as elastic foundation beam model of Euler-Bernoulli in the paper, the supported form of pin rocker bearing in the analysis of transverse vibration. Kelvin viscoelastic foundation model is adopted and the dynamic model of soil spring is regarded as nonlinearity. Applying the principle of Hamilton, the differential equation of vibration is deduced. By utilization of the first three-order modal and the orthogoality of main vibration mode, the equations are discreted and transformed into state formulas. The critical flow velocity is obtained using the Matlab software in a typical numerical example.

Transverse Free Vibration Analysis of Buried Pipeline under Simply Supported Restraint

The pipe model is simplified as elastic foundation beam model of Euler-Bernoulli in the paper. Considering the effect of fluid flow in the pipe and outer soil constraint, the transverse vibration differential equation of buried pipeline is derived by using of Hamilton principle. By utilization of the first three-order modal and the orthogoality of main vibration mode, the equation is deduced and transformed into state formulas. The typical numerical example is analyzed by Matlab software. It is found that the natural frequency of pipe conveying fluid usually decreases along with flow velocity improving and the effect of foundation on the pipe stability is apparent.

Transverse Free Vibration Analysis of Buried Pipeline under Simply Supported Restraint

The pipe model is simplified as elastic foundation beam model of Euler-Bernoulli in the paper. Considering the effect of fluid flow in the pipe and outer soil constraint, the transverse vibration differential equation of buried pipeline is derived by using of Hamilton principle. By utilization of the first three-order modal and the orthogoality of main vibration mode, the equation is deduced and transformed into state formulas. The typical numerical example is analyzed by Matlab software. It is found that the natural frequency of pipe conveying fluid usually decreases along with flow velocity improving and the effect of foundation on the pipe stability is apparent.

Transverse Vibration of Non-Uniform Euler-Bernoulli Beam, Using Differential Transform Method (DTM)

Analysis of transverse vibration of beams is presented in this paper. Unfortunately, complexities which appear in solving differential equation of transverse vibration of non-uniform beams, limit analytical solution to some special cases, so that the numerical method is presented. DTM is a numerical method for solving linear and some non-linear, ordinary and partial differential equations. In this paper, this technique has been applied for solving differential equation of transverse vibration of conical Euler-Bernoulli beam. Natural circular frequencies and mode shapes have been calculated. Comparing results with the cases which exact solution have been presented, shows that DTM is a strong method especially for solving quasi-linear differential equations.

Transverse Vibration Analysis of Buried Pipeline under Earthquake Interaction

The vibration of buried pipeline is influenced by inner fluid and outer constrained soil. Euler-Bernoulli beam is analyzed in the vibration model of buried pipeline, using the Hamilton principle. In addition, the differential equations of transverse vibration of buried pipeline deduced by the mechanical model are transformed into basic form of dynamics equations, considering earthquake excitation as random wave. Using the method of the elasticity time-travel analysis to programming, the pipe element, the soil parameter and the earthquake dynamic parameter are analyzed in the Matlab software. With soil from soft to hard, the response of piping displacement becomes smaller and smaller. In the same soil, the earthquake damage rate of the piping becomes increaser and increaser with earthquake intensity increasing.

Dynamic Characteristics Analysis and Simulations of Transverse Vibration of Axially Moving Electrode Wire in WEDM

Many factors influence WEDM (Wire-cut Electrical Discharge Machining) processing precision, and the influence of various factors on the processing precision are expressed by wire electrode dynamic form ultimately. In this paper, the transverse vibration theoretical model of the axially moving electrode wire coupled with thermal stresses is established by the principle of Hamilton. The influence of various processing parameters on wire vibration are analyzed and simulated. This study provides a relevant theoretical basis for optimizing processing parameters, reducing the wire vibration and improving machining precision.

Analysis of Transverse Vibration of Axially Moving Viscoelastic Sandwich Beam with Time-Dependent Velocity

Transverse vibration of an axially moving viscoelastic sandwich beam is investigated in this paper. Based on the Kelvin constitutive equation, transverse controlling equation is established. First of all, the multiple scales method is applied to obtained steady-state response. Elimination of scales terms will give us the amplitude of vibrations. Additionally, the stability conditions of trivial and non-trivial solutions are analyzed using Routh-Hurwitz criterion. Eventually, numerical results are obtained to show the thickness of core layer, mean velocity, the amplitude of fluctuation effects on natural frequencies and response curves.

Transverse Vibration Measurement and Analysis of a Three-Point Supported Dual-Span Rotor System with Angle Misaligned Flexible Coupling

The angular misalignment of a three-point supported dual-span rotor system is discussed. Vibration measurement for coupling misalignment is taken in this paper by using the model test rig, and the rotor vibration response characteristics with different misalignment quantities and different rotating speed are compared. Based on the finite element method, researches on the three-point supported dual-span rotor system are made, and then the simulation and experimental results are compared. Both the simulation and the measurement are compared to show the features. The results show that the amplitudes of the misaligned rotor vary with rotating speeds and misalignment angles, and the center orbits of the misaligned rotor change into ellipses with the increase of misalignment, together with double harmonic responses.

Analysis of Transverse Vibration of Circular Plates with an Elastically Mounted Mass Based on Combination of GDQM and FEM

The generalized differential quadrature method (GDQM) developed recently is more and more widely used in structural analysis, but that is restricted by some conditions. The finite element method (FEM) is a conventional numerical method, but the calculational work is very great. In this paper, the GDQM and the FEM are combined together to analyze the transverse vibration of circular plates with an elastically mounted mass. The results show that this combination is a new way first proposed in this paper to solve the problems with complex domains in structural analysis. And it is a rapid, efficient, accurate and flexible numerical method with both the advantages of the GDQM and the FEM. Comparison with the existing literature has proved that the results obtained by this method are very accurate.

Mathematical analysis of transverse vibration of conical spiral tube bundle with external fluid flow

The conical spiral tube bundle is a new type of heat transfer elements used to enhance heat transfer through flow-induced vibration. The effect of the external fluid flow on the transverse vibration of the conical spiral tube bundle is investigated with a mathematical method proposed in this article. Firstly, the natural vibration of the tube bundle is obtained by the hammering excitation method and the mode shapes of the transverse vibration are discussed. Then the effect of the external fluid flow on the transverse vibration of tube bundle is analyzed by a combination of experimental data, empirical correlations and FEM. The results show that in the frequency range from 0 Hz to 50 Hz, there exist six transverse vibrations. The external fluid flow has a significant effect on the frequency of the tube's transverse vibration, which are decreased by about 18% to 24% when the external fluid flow speed is 0.3 m/s.

Exact solutions for free flexural vibration of Lévy-type rectangular thick plates via third-order shear deformation plate theory

In this paper, exact closed-form solutions in explicit forms are presented for transverse vibration analysis of rectangular thick plates having two opposite edges hard simply supported (i.e., Lévy-type rectangular plates) based on the Reddy’s third-order shear deformation plate theory. Two other edges may be restrained by different combinations of free, soft simply supported, hard simply supported or clamped boundary conditions. Hamilton’s principle is used to derive the equations of motion and natural boundary conditions of the plate. Several comparison studies with analytical and numerical techniques reported in literature are carried out to demonstrate accuracy of the present new formulation. Comprehensive benchmark results for natural frequencies of rectangular plates with different combinations of boundary conditions are tabulated in dimensionless form for various values of aspect ratios and thickness to length ratios. A set of three-dimensional (3-D) vibration mode shapes along with their corresponding contour plots are plotted by using exact transverse displacements of Lévy-type rectangular Reddy plates. Due to the inherent features of the present exact closed-form solution, the present findings will be a useful benchmark for evaluating the accuracy of other analytical and numerical methods, which will be developed by researchers in the future.

Transverse Vibration Analysis of Euler-Bernoulli Beams Carrying Concentrated Masses with Rotatory Inertia at Both Ends

Transverse vibration analysis is presented for Euler-Bernoulli beams carrying concentrated masses and taking into account their rotatory inertia at both ends. The dimensionless eigenfunctions for the problems are first obtained using the differential equations of motion and considering translational and rotatory springs at both ends. A numerical technique, the Newton–Raphson algorithm, is then used to solve vibration eigenfunctions of the beams. Finally, the influences of different non-dimensional parameters on frequencies are discussed.

Modal perturbation method for transverse vibration analysis of prestressed beams

Modal perturbation method for transverse vibration analysis of prestressed beams

DSC-element method for free vibration analysis of rectangular Mindlin plates

A novel DSC-element method is proposed to investigate the free vibration of moderately thick plates based on the well-known Mindlin first-order shear deformation plate theory. The development of the present approach not only employs the concept of finite element method, but also implements the discrete singular convolution (DSC) delta type wavelet kernel for the transverse vibration analysis. This numerical algorithm is allowed dividing the domain of Mindlin plates into a number of small discrete rectangular elements. As compared with the global numerical techniques i.e. the DSC–Ritz method, the flexibility is increased to treat complex boundary constraints. For validation, a series of numerical experiments for different meshes of Mindlin plates with assorted combinations of edge supports, plate thickness and aspect ratios is carried out. The established natural frequencies are directly compared and discussed with those reported by using the finite element and other numerical and analytical methods from the open literature.

MECHANISM AND ENERGY RANDOM ANALYSIS OF TRAIN DERAILMENT ON RAILWAY BRIDGES

In this paper, the mechanism of train derailment on bridge is developed by applying the system dynamics stability concepts. The theory of energy random analysis for train derailment on bridge is put forward. The contents of the theory are as follows: (1) establishing vibration equation set for the train–bridge system; (2) determining exciting source of transverse vibration of the system; (3) method of energy random analysis of transverse vibration of the system; (4) geometric rules of derailment; (5) calculation of the whole process of train derailment on bridge; (6) criteria of energy increment for judging train derailment on bridge. Finally, three cases concerning train derailment on bridges are treated that coincide with actual conditions. Some main conclusions obtained are: (1) insufficient transversal rigidity of bridge is the reason causing train derailment on bridge and (2) enhancing transversal rigidity of bridge is the main preventive measure against train derailment on bridge.