Showing papers in "Journal of Sound and Vibration in 2001"

A local radial point interpolation method (lrpim) for free vibration analyses of 2-d solids

Abstract: A local radial point interpolation method (LRPIM) is presented to deal with boundary-value problems for free vibration analyses of two-dimensional solids. Local weak forms are developed using weighted residual method locally from the partial differential equation of free vibration. A technique to construct shape functions using radial function basis is proposed. The shape functions so formulated possess delta function property. Essential boundary conditions can be implemented with ease as in the finite-element method. Some important parameters on the performance of LRPIM are also investigated thoroughly. Numerical examples for free vibration analyses of two-dimensional solids to demonstrate the validity and efficiency of the present LRPIM are presented.

Standardized general-purpose noise reaction questions for community noise surveys: research and a recommendation

Abstract: Differences in survey questions' wordings and weakness in some questions used to measure noise annoyance have interfered with accumulating knowledge about the factors that affect different communities' responses to noise. In 1993 an ICBEN team, Community Response to Noise, set the goal of creating high-quality survey questions that would yield internationally comparable measures of overall reactions to noise sources. After 7 years of discussions and research the team has developed and tested a method that attempts to meet those goals. The team recommends the use of a pair of multi-purpose questions in community noise surveys. The wording of the questions is presented for the nine languages for which a standardized empirical study protocol has been followed to select annoyance scale words. The team's protocol can be used to create comparable questions for additional languages in the future.

The Harmonic Balance Method with arc-length continuation in rotor/stator contact problems

Abstract: There are a variety of abnormal running conditions in rotating machinery which lead to rotor/stator interaction dynamics which, in turn, can cause a rich mixture of effects associated with rub-related phenomena. These effects manifest themselves in the occurrence of multiple solutions for steady state vibration response scenarios, including amplitude jumps during rotor acceleration, and vibration responses at different/multiple frequencies of excitation forces such as unbalance. This paper describes a numerical algorithm based on the harmonic balance method to calculate the periodic response of a non-linear system under periodic excitation. The algorithm also calculates the stability of the periodic solutions found, marks turning and bifurcation points, and follows a solution branch over varying system parameters via arc-length continuation.

Vibration of a beam with a breathing crack

Abstract: A continuous cracked beam vibration theory is used for the prediction of changes in transverse vibration of a simply supported beam with a breathing crack. The equation of motion and the boundary conditions of the cracked beam considered as a one-dimensional continuum were used. The eigenfrequency changes due to a breathing edge-crack are shown to depend on the bi-linear character of the system. The associated linear problems are solved over their respective domains of definition and the solutions are matched through the initial conditions. The changes in vibration frequencies for a fatigue-breathing crack are smaller than the ones caused by open cracks. The method has been tested for the evaluation of the lowest natural frequency of lateral vibration for beams with a single-edge breathing crack. Experimental results from aluminium beams with fatigue cracks are used for comparison with the analytical results.

Structural damage detection using artificial neural networks and measured frf data reduced via principal component projection

Abstract: This paper deals with structural damage detection using measured frequency response functions (FRFs) as input data to artificial neural networks (ANNs). A major obstacle, the impracticality of using full-size FRF data with ANNs, was circumvented by applying a principal component analysis (PCA)-based data reduction technique to the measured FRFs. The compressed FRFs, represented by their projection onto the most significant principal components, were then used as the ANN input variables instead of the raw FRF data. The output is a prediction for the actual state of the specimen, i.e., healthy or damaged. A further advantage of this particular approach was found to be the ability to deal with relatively high measurement noise, which is of common occurrence when dealing with industrial structures. The methodology was applied to the measured FRFs of a railway wheel, each response function having 4096 spectral lines. The available FRF data were grouped into x, y and z direction FRFs and a compression ratio of about 400 was achieved for each direction. Three different networks, each corresponding to a co-ordinate direction, were trained and verified using 80 PCA-compressed FRFs. Twenty compressed FRFs, obtained from further measurements, were used for the actual damage detection tests. Half of the test FRFs were polluted further by adding 5% random noise in order to assess the robustness of the method in the presence of significant experimental noise. The results showed that, in all cases considered, it was possible to distinguish between the healthy and damaged states with very good accuracy and repeatability.

Identification of damping: Part 1, viscous damping

Abstract: Characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics. The most common approach is to use “viscous damping” where the instantaneous generalized velocities are the only relevant state variables that affect damping forces. However, viscous damping is by no means the only damping model within the scope of linear analysis. Any model which makes the energy dissipation functional non-negative is a possible candidate for a valid damping model. This paper, and its companion (see pp. 63–88 of this issue), are devoted to developing methodologies for identification of such general damping models responsible for energy dissipation in a vibrating structure. This paper considers identification of viscous damping under circumstances when the actual damping model in the structure is non-viscous. A method is presented to obtain a full (non-proportional) viscous damping matrix from complex modes and complex natural frequencies. It is assumed that the damping is “small” so that a first order perturbation method is applicable. The proposed method and several related issues are discussed by considering numerical examples based on a linear array of damped spring-mass oscillators. It is shown that the method can predict the spatial location of damping with good accuracy, and also give some indication of the correct mechanism of damping.

Proper orthogonal decomposition (pod) of a class of vibroimpact oscillations

Abstract: This study employs the method of proper orthogonal decomposition (POD), also known as the Karhunen–Loeve (K–L) method, to extract dominant coherent structures (modes that approximate the system behavior) from time-series data. These mode shapes can be used in a Galerkin reconstruction process to obtain lower dimensional models for the structural systems under consideration. The mode shapes and the energies obtained by this process can also be used to predict certain kinds of periodic or non-periodic non-linear motions. The K–L method has been applied successfully to fluid dynamical, thermal processes and signal processing. However, only a handful of works exist in the area of vibration analysis and structural mechanics. An extensive K–L analysis is performed numerically for two vibroimpacting systems: a beam and a rotor. Lower dimensional models are created and used to study non-linear energy transmission from low to higher K–L modes. Extensive reconstructions are also performed to prove the efficacy of the K–L method to provide accurate low-dimensional dynamical models. In addition, experimental investigations are presented for the case of the overhung impacting rotor and qualitative comparisons with the theoretical analysis are presented.

Vibration analysis of thin cylindrical shells using wave propagation approach

Abstract: The vibration analysis of cylindrical shells using wave propagation method is presented. Results obtained using the method have been evaluated against those available in the literature. Comparison of the results by the present method and numerical finite element method is also carried out. It is possible to conclude through the comparisons that the present method is convenient, effective and accurate. The method can be easily extended to complex boundary conditions and fluid-loaded shell structures

Free field vibrations during the passage of a thalys high-speed train at variable speed

Abstract: During homologation tests of the high-speed train (HST) track between Brussels and Paris, free field vibrations and track response have been measured during the passage of a Thalys HST at speeds varying between 223 and 314 km/h. These experimental data are complementary to the other, but scarce, data sets published in the literature. Apart from illustrating the physical phenomena involved, this data set can be used for the validation of numerical prediction models for train-induced vibrations.

Construction of an active suspension system of a quarter car model using the concept of sliding mode control

Abstract: This paper is concerned with the construction of an active suspension system for a quarter car model using the concept of sliding mode control. The active control is derived by the equivalent control and switching function where the sliding surface is obtained by using Linear quadratic control (LQ control) theory. The active control is generated with non-negligible time lag by using a pneumatic actuator, and the road profile is estimated by using the minimum order observer based on a linear system transformed from the exact non-linear system. The experimental result indicates that the proposed active suspension system is more effective in the vibration isolation of the car body than the linear active suspension system based on LQ control theory and the passive suspension system.

Reconstruction of acoustic transfer matrices by instationary computational fluid dynamics

Abstract: Thermoacoustic combustion instabilities are a frequently encountered problem in the operation of combustion equipment. The “brute-force” application of computational fluid dynamics to the analysis of thermoacoustic instabilities is estimated to be forbiddingly expensive for many systems of technical interest due to the high computational demands of a time- and space-accurate simulation of a (low Mach number) compressible reacting flow in a complex geometry. Thermoacoustic systems can be modelled efficiently as networks of acoustic multi-ports, where each multi-port corresponds to a certain component of the system, e.g., air or fuel supply, burner, flame, combustor and suitable terminations, and is represented mathematically by its transfer matrix. For some multi-ports, the transfer matrix can be derived analytically from first principles: i.e., the equations of fluid motions and suitable approximations. However, the acoustic behavior of more complicated components, e.g., a burner or a flame, has to be determined by empirical methods, by using a “black box” approach common in communications engineering. In this work, a method is introduced which allows one to reconstruct the transfer matrix of an acoustic two-port from an instationary computation of the response of the two-port to an imposed perturbation of the steady state. Firstly, from the time series data of fluctuating velocity and pressure on both sides of the two-port, the auto- and cross-correlations of the fluctuations are estimated. Then, the unit impulse responses of the multi-port are computed by inverting the Wiener–Hopf equation. Finally, the unit impulse responses are z -transformed to yield the coefficients of the transfer matrix. The method is applied to the one-dimensional model of a heat source with time delay placed in a low-Mach-number compressible flow, for which an analytical description can be derived from first principles. Computational predictions of the transfer matrix have been validated successfully against these analytical results. Furthermore, a comparison of the novel approach presented in this paper with a method for computing the frequency response of a flame by Laplace-transforming its step response is carried out.

Determination of crack location in beams using natural frequencies

Abstract: In this paper, we describe a numerical method for determining the location of a crack in a beam of varying depth when the lowest three natural frequencies of the cracked beam are known. The crack is modelled as a rotational spring and graphs of spring stiffness versus crack location are plotted for each natural frequency. The point of intersection of the three curves gives the location of the crack. Earlier work in this area involved the use of the Frobenius technique for solving the governing differential equation analytically and then using a semi-numerical approach to obtain the crack location. In this work, we use the finite element approach to solve the same problem. The beam is modelled using beam elements and the inverse problem of finding the spring stiffness, given the natural frequency, is shown to be related to the problem of a rank-one modification of an eigenvalue problem. Examples outlining the accuracy and ease of using this method are shown. The results are compared with those from semi-analytical approaches. The biggest advantage of this method is the generality in the approach; different boundary conditions and variations in the depth of the beam can be easily modelled.

Identification of a crack in a rod based on changes in a pair of natural frequencies

Abstract: This paper deals with the identification of a single crack in a vibrating rod based on the knowledge of the damage-induced shifts in a pair of natural frequencies. The crack is simulated by an equivalent linear spring connecting the two segments of the bar. The analysis is based on an explicit expression of the frequency sensitivity to damage and enables non-uniform bars under general boundary conditions to be considered. The inverse problem is generally “ill-posed”, because even if the system is not symmetrical, cracks in different locations can still produce identical changes in a pair of natural frequencies. In spite of this, it is found that there are certain situations concerning uniform rods in which the effects of the non-uniqueness of the solution may be considerably reduced by means of a careful choice of the data. The theoretical results are confirmed by a comparison with dynamic measurements on steel rods with a crack. Some of the results are also valid for cracked beams in bending.

Vibration analysis by discrete singular convolution

Abstract: This paper explores the utility of a discrete singular convolution algorithm for vibration analysis. A number of different realizations of singular convolution kernels are selected to illustrate the present algorithm. Vibration analysis of strings, rods, beams, diatomic molecules, membranes, waveguides and thin plates are utilized to test numerical accuracy and speed of convergence of the present approach. Numerical experiments indicate that the discrete singular convolution is a simple and reliable algorithm for vibration analysis.

A simplified method for natural frequency analysis of a multiple cracked beam

Abstract: A new method for natural frequency analysis of beam with an arbitrary number of cracks is developed on the bases of the transfer matrix method and rotational spring model of crack. The resulted frequency equation of a multiple cracked beam is general with respect to the boundary conditions including the more realistic (elastic) end supports and can be constructed analytically by using symbolic codes. The procedure proposed is advanced by elimination of numerical computation of the high order determinant so that the computer time for calculating natural frequencies in consequence is significantly reduced. Numerical computation has been carried out to investigate the effect of each crack, the number of cracks and boundary conditions on the natural frequencies of a beam.

A numerical and experimental investigation of the dissipation mechanisms of resonant acoustic liners

Abstract: In a recent investigation, it was found by direct numerical simulation that sound waves at high intensity can induce vortex shedding at the mouths of the resonators of an acoustic liner. Measurements from their numerical simulations indicate that the rate at which kinetic energy is transferred to the shed vortices can be much higher than the viscous dissipation rate. Thus vortex shedding is a dominant dissipation mechanism of resonant acoustic liners. This paper reports the results of a co-ordinated investigation aiming at validating the observations and measurements of direct numerical simulation experimentally. The experiment uses a normal incidence impedance tube. Good agreements are found between the measured absorption coefficients of the physical experiment and direct numerical simulation over a broad range of frequencies and sound pressure levels. A separate visualization experiment confirms the observation of shed vortices at high incident sound intensity.

Analytical description and optimization of the dynamic behaviour of passively suspended road vehicles

Abstract: A simple two-degree-of-freedom linear model is used to derive a number of analytical formulae describing the dynamic behaviour of passively suspended vehicles running on randomly profiled roads. Two different power spectral densities are considered for modelling the road irregularity. The derived analytical formulae can be used either during preliminary design or for other special purposes, especially when approximated results are acceptable. An optimization method, based on Multi-Objective Programming and Monotonicity analysis, is introduced and applied for the symbolic derivation of analytical formulae featuring the best compromise among conflicting performance indices pertaining to the vehicle suspension system, i.e., discomfort, road holding and working space. The optimal settings of the relevant vehicle suspension parameters (i.e., tyre radial stiffness, spring stiffness and damping) are derived either symbolically and/or numerically.

Predicting the acoustical radiation of finite size multi-layered structures by applying spatial windowing on infinite structures

Abstract: A new technique based on a spatial windowing of plane waves is presented in order to take into account the finite size of a plane structure in sound radiation and sound transmission calculation. This technique leads to predicted results which are much closer to experimental measurements than the classical wave approach applied to an infinite structure. In the first part, the principle of the technique is described as well as the derivation of the modified sound radiation efficiency. In the second part, some predicted results, including the sound transmission index of an aluminium plate, a double glazing panel and a multi-layer panel, and the radiation efficiency of a mechanically excited metal plate, are presented and compared to experimental results in order to validate the spatial windowing technique. The effect of the structure size on both sound transmission (acoustical excitation) and sound radiation (mechanical excitation) is also discussed.

a Combined Modal/finite Element Analysis Technique for the Dynamic Response of a Non-Linear Beam to Harmonic Excitation

Abstract: In this paper, a method is proposed for modelling large deflection beam response involving multiple vibration modes. Significant savings in computational time can be obtained compared with the direct integration non-linear finite element method. The deflections from a number of static non-linear finite element test cases are transformed into modal co-ordinates using the modes of the underlying linear system. Regression analysis is then used to find the unknown coupled non-linear modal stiffness coefficients. The inclusion of finite element derived modal masses, and an arbitrary damping model completes the governing non-linear equations of motion. The response of the beam to excitation of an arbitrary nature may then be found using time domain numerical integration of the reduced set of equations. The work presented here extends upon the work of previous researchers to include non-linearly coupled multi-modal response. The particular benefits of this approach are that no linearization is imposed, and that almost any commercial finite element package may be employed without modification. The proposed method is applied to the case of a homogeneous isotropic beam. Fully simply supported and fully clamped boundary conditions are considered. For the free vibration case, results are compared to those of previous researchers. For the case of steady-state harmonic excitation, results are compared with the direct integration non-linear finite element method using ABAQUS. In all cases, excellent agreement is obtained.

Finite element vibration analysis of rotating timoshenko beams

Abstract: The stiffness and mass matrices of a rotating twisted and tapered beam element are derived. The angle of twist, breadth and depth are assumed to vary linearly along the length of beam. The effects of shear deformation and rotary inertia are also considered in deriving the elemental matrices. The first four natural frequencies and mode shapes in bending–bending mode are calculated for cantilever beams. The effects of twist, offset, speed of rotation and variation of depth and breadth taper ratios are studied.

Vibration and buckling of multilayered composite beams according to higher order deformation theories

Abstract: Natural frequencies and buckling stresses of laminated composite beams are analyzed by taking into account the complete effects of transverse shear and normal stresses and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a one-dimensional higher order theory for laminated composite beams subjected to axial stress is derived through Hamilton's principle. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported laminated composite beam. In order to ensure the accuracy of the present theory, convergence properties of the first seven natural frequencies are examined in detail. Numerical results are compared with those of the published existing theories and FEM solutions. The modal displacement and stress distributions in the depth direction are obtained and plotted in figures. The present global higher order approximate theories can predict the natural frequencies, buckling stresses and interlaminar stresses of multilayered composite beams as accurately as three-dimensional elasticity solutions.

Vibration analysis of a rotating timoshenko beam

Abstract: The governing equations for linear vibration of a rotating Timoshenko beam are derived by the d&Alembert principle and the virtual work principle. In order to capture all inertia e!ect and coupling between extensional and #exural deformation, the consistent linearization of the fully geometrically non-linear beam theory is used. The e!ect of Coriolis force on the natural frequency of the rotating beam is considered. A method based on the power series solution is proposed to solve the natural frequency of the rotating Timoshenko beam. Numerical examples are studied to verify the accuracy of the proposed method and to investigate the e!ect of Coriolis force on the natural frequency of rotating beams with di!erent angular velocity, hub radius and slenderness ratio. ( 2001 Academic Press

a Mesh-Free Method for Static and Free Vibration Analyses of Thin Plates of Complicated Shape

Abstract: A mesh-free method is presented to analyze the static deflection and the natural frequencies of thin plates of complicated shape. The present method uses moving least-squares (MLS) interpolation to construct shape functions based on a set of nodes arbitrarily distributed in the analysis domain. Discrete system equations are derived from the variational form of system equation. For static analysis, a penalty method is presented to enforce the essential boundary conditions. For frequency analysis of free vibration, the essential boundary conditions are represented through a weak form and imposed using orthogonal transformation techniques. The present EFG method together with techniques for imposing boundary conditions is coded in Fortran. Numerical examples are presented for rectangular, elliptical, polygonal and complicated plates to demonstrate the convergence and efficiency of the present method.

Hygrothermal effects on the dynamic behavior of multiple delaminated composite plates and shells

Abstract: A quadratic isoparametric finite element formulation based on the first order shear deformation theory is presented for the free vibration and transient response analysis of multiple delaminated doubly curved composite shells subjected to a hygrothermal environment. A simple multiple delamination model developed by the authors earlier is employed to take care of any number/size of delamination located anywhere in the laminate. The analysis takes into account the lamina material properties at elevated moisture concentration and temperature. Newmark's direct integration scheme is used to solve the dynamic equation of equilibrium at every timestep during the transient analysis. Several numerical examples are considered and the results are compared with those available in the literature. The results show a reduction in the fundamental frequency with an increase in the percentage of uniform moisture content as well as temperature for simply supported antisymmetric crossply and angleply laminates for any size of delamination considered. The central dynamic displacements and the stresses at the center of laminates are observed to increase due to the effect of moisture/temperature subjected to the suddenly applied uniform pulse loading

Free vibration of isotropic, orthotropic, and multilayer plates based on higher order refined theories

Abstract: Laminated composite plates are being increasingly used in the aeronautical and aerospace industry as well as in other \"elds of modern technology. To use them e!eciently a good understanding of their structural and dynamical behaviour is needed. The Classical ̧aminate Plate 1heory [1] which ignores the e!ect of transverse shear deformation becomes inadequate for the analysis of multilayer composites. The \"rst order theories (FSDTs) based on Reissner [2] and Mindlin [3] assume linear in-plane stresses and displacements, respectively, through the laminate thickness. Since FSDTs account for layerwise constant states of transverse shear stress, shear correction coe$cients are needed to rectify the unrealistic variation of the shear strain/stress through the thickness and which ultimately de\"ne the shear strain energy. In order to overcome the limitations of FSDTs, higher order shear deformation theories (HSDTs) that involve higher order terms in Taylor's expansions of the displacement in the thickness co-ordinate were developed. Hildebrand et al. [4] were the \"rst to introduce this approach to derive improved theories of plates and shells. Kant [5] was the \"rst to derive the complete set of variationally consistent governing equations for the #exure of a symmetrically laminated composite plate incorporating both distortion of transverse normals and e!ects of transverse normal stress/strain by utilizing the complete three-dimensional generalized Hooke's law and presented results for isotropic plate only. Later Mallikarjuna [6], Mallikarjuna and Kant [7] and Kant and Mallikarjuna [8, 9] presented a set of higher order re\"ned theories and presented formulations and solutions for the free vibration analysis of general laminated composite and sandwich plate problems based on \"nite element methods. In this investigation, analytical solutions for the free vibration analysis of laminated composite and sandwich plates based on two higher order re,ned theories already developed by the ,rst author for which analytical formulations and solutions were not reported earlier in the literature are presented. After establishing the accuracy of the present results with three-dimensional elasticity solutions for isotropic, orthotropic and composite plates, benchmark results and comparison of solutions using various theories are presented for multilayer sandwich plates. The displacement models under various theories considered in the present investigations are listed below [10}14]: Model*1 (Kant and Manjunatha, 1988):

Analysis of periodically varying gear mesh systems with coulomb friction using floquet theory

Abstract: This article presents a new analytical model of a gear pair with time varying mesh stiffness, viscous damping and sliding friction parameters. Unlike previous models, the excitation consists of three separate terms, namely the unloaded transmission error, time-invariant external torque and the periodically varying sliding friction force. A Coulomb friction model is considered using first a quasi-static mean transmitted load that is represented by the Meissner equation. Then, a truly dynamic force between gear teeth is described that leads to a triangular function, and after appropriate substitutions, this assumes the form of the Bessel equation of the one-third order. For the damped Meissner equation, the forced vibration response is found with the application of Floquet theory. Exact integrals are calculated for the state transition matrix in a piecewise manner, instead of using the Fourier series expansion, thus eliminating the mode truncation errors. From the state transition matrix, unstable zones are identified and the actual forced response of the system is found in terms of dynamic transmission error for these zones. With the aid of an example, the significance of sliding friction on system response and stability is examined. Finally, key advantages and the need for analytical methods are demonstrated for such systems.

Cyclostationary analysis of rolling-element bearing vibration signals

Abstract: Vibration signals resulting from rolling-element bearings present a mixture of physical information, the proper analysis of which can lead to the identification of possible faults. Traditionally, this analysis is performed by the use of signal processing methods, which assume statistically stationary signal features. The paper proposes an alternative framework for analyzing bearing vibration signals, based on cyclostationary analysis. This framework, being able to model, additionally, signals with periodically varying statistics, is better able to exhibit the underlying physical concepts of the modulation mechanism present in the vibration response of bearings. The basic concepts of the approach are demonstrated both in illustrative simulation results, as well as in experimental results and industrial measurements for two different types of bearing faults.

Acoustic impedance measurement, part i: a review

Abstract: In this review, impedance sensors are presented as linear sensors with two entries whose signals are influenced by both pressure and volume velocity. Pressure is generally measured with a microphone, therefore impedance sensors are classified according to the way the volume velocity is determined or controlled. The review touches on the multi-port characterization which is shown to be a generalization of impedance measurement. Finally the question of the calibration and error sources is discussed.