Showing papers in "Journal of Sound and Vibration in 2000"
TL;DR: In this paper, a denoising method based on wavelet analysis is applied to feature extraction for mechanical vibration signals, which is an advanced version of the famous soft thresholding denoizing method proposed by Donoho and Johnstone.
Abstract: The vibration signals of a machine always carry the dynamic information of the machine. These signals are very useful for the feature extraction and fault diagnosis. However, in many cases, because these signals have very low signal-to-noise ratio (SNR), to extract feature components becomes difficult and the applicability of information drops down. Wavelet analysis in an effective tool for signal processing and feature extraction. In this paper, a denoising method based on wavelet analysis is applied to feature extraction for mechanical vibration signals. This method is an advanced version of the famous “soft-thresholding denoising method” proposed by Donoho and Johnstone. Based on the Morlet wavelet, the time-frequency resolution can be adapted to different signals of interest. In this paper, this denoising method is introduced in detail. The results of the application in rolling bearing diagnosis and gear-box diagnosis are satisfactory.
823 citations
TL;DR: In this paper, a model-dependent method with piezoelectric sensor and actuator incorporated into composite structures is proposed for on-line damage detection and health-monitoring on composite structures.
Abstract: There are strong needs and requirements for on-line damage (delamination) detection and health-monitoring techniques on composite structures. Vibration-based model-dependent methods with piezoelectric sensor and actuator incorporated into composite structures offer a promising option to fulfil such requirements and needs. These methods utilize finite element analysis techniques, together with experimental results, to detect damage. They locate and estimate damage events by comparing dynamic responses between damaged and undamaged structures. According to the dynamic response parameters analyzed, these methods can be subdivided into modal analysis, frequency domain, time domain and impedance domain. Model-dependent methods are able to provide global and local damage information. They are cost-effective and are relatively easy to operate. However, there are still many challenges and obstacles before these methods can be implemented in practice.
753 citations
TL;DR: The concept of discordancy from the statistical discipline of outlier analysis is used to signal deviance from the norm in a statistical method for damage detection.
Abstract: This paper constitutes a study of a statistical method for damage detection. The lowest level of fault detection is considered so that the methods are simply required to signal deviations from normal condition; i.e., the problem is one of novelty detection. In this paper, the concept of discordancy from the statistical discipline of outlier analysis is used to signal deviance from the norm. The method is demonstrated on four case studies of engineering interest: one simulation, two pseudo-experimental and one experimental.
561 citations
TL;DR: In this paper, it is shown that large dynamic amplifications appear in the dynamic response of the rail/embankment/ground system as the train speed approaches an apparently critical value.
Abstract: Results from instrumented test runs with a high-speed train on a soft soil site in Sweden are presented. It is shown that large dynamic amplifications appear in the dynamic response of the rail/embankment/ground system as the train speed approaches an apparently critical value. The measured dynamic response is analyzed in detail, and it is shown that the critical speed is controlled by the minimum phase velocity of the first Rayleigh mode of the soil and embankment profile at the site. Moreover, it is shown that the critical speed and the amount of dynamic amplification also depend on a coincidence between characteristic wavelengths for the site and the distances between bogies and axles in the train. The displacement response is found to consist of a speed-independent portion in quasi-static equilibrium with the train loads and a dynamic portion representing freely propagating Rayleigh waves. An efficient computer code for the prediction of ground response to high-speed trains has been developed and its ability to reproduce the observed behaviour is demonstrated.
377 citations
TL;DR: In this paper, the dynamic response of a spur gear pair is investigated using a finite element/contact mechanics model, which offers significant advantages for dynamic gear analyses and can be used to reveal complex non-linear phenomena.
Abstract: The dynamic response of a spur gear pair is investigated using a finite element/contact mechanics model that offers significant advantages for dynamic gear analyses. The gear pair is analyzed across a wide range of operating speeds and torques. Comparisons are made to other researchers' published experiments that reveal complex non-linear phenomena. The non-linearity source is contact loss of the meshing teeth, which, in contrast to the prevailing understanding, occurs even for large torques despite the use of high-precision gears. A primary feature of the modelling is that dynamic mesh forces are calculated using a detailed contact analysis at each time step as the gears roll through the mesh; there is no need to externally specify the excitation in the form of time-varying mesh stiffness, static transmission error input, or the like. A semi-analytical model near the tooth surface is matched to a finite element solution away from the tooth surface, and the computational efficiency that results permits dynamic analysis. Two-single-degree-of-freedom models are also studied. While one gives encouragingly good results, the other, which appears to have better mesh stiffness modelling, gives poor comparisons with experiments. The results indicate the sensitivity of such models to the Fourier spectrum of the changing mesh stiffness.
376 citations
TL;DR: In this article, the dynamics of a gear-pair system involving backlash and time-dependent mesh stiffness are investigated, where the system is under the action of external excitation, caused by torsional moments and gear geometry errors.
Abstract: The present work investigates dynamics of a gear-pair system involving backlash and time-dependent mesh stiffness. In addition, the system is under the action of external excitation, caused by torsional moments and gear geometry errors. First, the equation of motion is established in a strongly non-linear form. Then, the emphasis is laid on a specific forcing frequency range, corresponding to conditions of simultaneous fundamental parametric resonance and principal external resonance. For these conditions, several types of periodic steady state response are identified and determined by employing suitable methodologies, including techniques applicable to piecewise linear systems and to oscillators with time-periodic coefficients. Moreover, these methodologies are complemented by appropriate procedures revealing the stability properties of the located periodic solutions. In the second part of the work, numerical results are presented. These results verify the validity and effectiveness of the new analytical methodology and provide information on the gear-pair dynamics. First, series of typical response diagrams are obtained, illustrating the effect of the mesh stiffness variation, the damping and the forcing parameters on the gear-pair periodic response. These response diagrams are accompanied by results obtained with direct integration of the equation of motion. In this way, it is demonstrated that for some parameter combinations, the dynamical system examined can exhibit more complicated and irregular response, including crises and intermittent chaos.
300 citations
TL;DR: In this paper, a simple and unified approach for the vibration analysis of a generally supported beam is presented, where the flexural displacement of the beam is sought as the linear combination of a Fourier series and an auxiliary polynomial function.
Abstract: A simple and unified approach is presented for the vibration analysis of a generally supported beam. The flexural displacement of the beam is sought as the linear combination of a Fourier series and an auxiliary polynomial function. The polynomial function is introduced to take all the relevant discontinuities with the original displacement and its derivatives at the boundaries and the Fourier series now simply represents a residual or conditioned displacement that has at least three continuous derivatives. As a result, not only is it always possible to expand the displacement in a Fourier series for beams with any boundary conditions, but also the solution converges at a much faster speed. The reliability and robustness of the proposed technique are demonstrated through numerical examples.
295 citations
TL;DR: In this article, the authors developed simple and accurate elastic force models that can be used in the absolute nodal co-ordinate formulation for the analysis of two-dimensional beams, which can account for the coupling between bending and axial deformations.
Abstract: The objective of this study is to develop simple and accurate elastic force models that can be used in the absolute nodal co-ordinate formulation for the analysis of two-dimensional beams. These force models which account for the coupling between bending and axial deformations are derived using a continuum mechanics approach, without the need for introducing a local element co-ordinate system. Four new different force models that include different degrees of complexity are presented. It is shown that the vector of the elastic forces can be significantly simplified as compared to the elastic force model developed for the absolute nodal co-ordinate formulation using a local element frame [1]. Despite the simplicity of the new models, they account for elastic non-linearity in the strain–displacement relationship. Therefore, they lead to more accurate results as compared to the more complex models developed using the local frame method which does not account for the non-linearities in the strain–displacement relationships. Numerical results are presented in order to demonstrate the use of the new models and test their performances in the analysis of large deformations of flexible multibody systems.
277 citations
TL;DR: In this article, a tunable solid-state piezoelectric vibration absorber and an active tuning method were developed and demonstrated, where the effective stiffnesses of these elements were adjusted electrically, using a passive capacitive shunt circuit, to tune the resonance frequency of the device.
Abstract: A tunable solid-state piezoelectric vibration absorber and an active tuning method were developed and demonstrated. A passive vibration absorber generally acts to minimize structural vibration at a specific frequency associated with either a tonal disturbance or a lightly damped structural vibration mode. Because this frequency is rarely stationary in real applications, damping is usually added to ensure some level of effectiveness over a range of frequencies. Maximum response reductions, however, are achieved only if the absorber is lightly damped and accurately tuned to the frequency of concern. Thus, an actively tuned vibration absorber should perform better than a passive one and, furthermore, could be made lighter. In its simplest form, a vibration absorber consists of a spring–mass combination. A key feature of the tunable vibration absorber described herein is the use of piezoelectric ceramic elements as part of the device stiffness. The effective stiffnesses of these elements were adjusted electrically, using a passive capacitive shunt circuit, to tune the resonance frequency of the device. The tuning range of the absorber is thus bounded by its short- and open-circuit resonance frequencies. An alternative tuning approach might employ resistive shunting, but this would introduce undesirable damping. Another feature of the device is the ability to use the piezoelectric elements as sensors. A control scheme was developed to estimate the desired tuning frequency from the sensor signals, to determine the appropriate shunt capacitance, and then to provide it. The shunt circuit itself was implemented in 10 discrete steps over the tuning range, using a relay-driven parallel capacitor ladder circuit. Experimental results showed a 20 dB maximum, and a 10 dB average improvement in vibration reduction across the tuning range, as compared to a pure passive absorber tuned to the center frequency, with additional benefit extending beyond the tuning range.
257 citations
TL;DR: In this paper, the authors considered the discrete inverse problem in acoustics, where a number of acoustic sources are located at known spatial positions and the acoustic pressure is measured at a many of spatial positions in the radiated field.
Abstract: This paper deals with the discrete inverse problem in acoustics. It is assumed that a number of acoustic sources are located at known spatial positions and that the acoustic pressure is measured at a number of spatial positions in the radiated field. The transfer functions relating the strengths of the acoustic sources to the radiated pressures are also assumed known. In principle, the strengths of the acoustic sources can be deduced from the measured acoustic pressures by inversion of this matrix of transfer functions. The accuracy of source strength reconstruction (in the presence of noise which contaminates the measured pressures) is crucially dependent on the conditioning of the matrix to be inverted. This paper examines the conditioning of this inverse problem, particularly with regard to the geometry and number of sources and measurement positions and the non-dimensional frequency. A preliminary investigation is also presented of methods such as Tikhonov regularization and singular value discarding which can improve the accuracy of source strength reconstruction in poorly conditioned cases. Results are also presented which enable the solution of the inverse problem when the time histories of the acoustic sources are time-stationary random processes and the spectra and cross-spectra are measured at a number of positions in the radiated field. The paper illustrates the possibilities and limitations of the use of inverse methods in the deduction of acoustic source strength from radiated field measurements.
237 citations
TL;DR: Particle impact damping (PID) is a means for achieving high structural damping by the use of a particle-filled enclosure attached to the structure in a region of high displacements.
Abstract: Particle impact damping (PID) is a means for achieving high structural damping by the use of a particle-filled enclosure attached to the structure in a region of high displacements. The particles absorb kinetic energy of the structure and convert it into heat through inelastic collisions between the particles and the enclosure, and amongst the particles. In this work, PID is measured for a cantilevered aluminium beam with the damping enclosure attached to its free end; lead particles are used in this study. The effect of acceleration amplitude and clearance inside the enclosure on PID is studied. PID is found to be highly non-linear. Perhaps the most useful observation is that for a very small weight penalty (about 6%), the maximum specific damping capacity (SDC) is about 50%, which is more than one order of magnitude higher than the intrinsic material damping of a majority of structural metals (O(1%)). Driven by the experimental observations, an elementary analytical model of PID is constructed. A satisfactory comparison between the theory and the experiment is observed. An encouraging result is that in spite of its simplicity, the model captures the essential physics of PID.
TL;DR: A review of theoretical models that have been developed to predict these phenomena is given in this article, where the authors consider three main categories of wheel/rail noise: rolling noise, impact noise, and squeal noise.
Abstract: Mechanisms associated with the interaction of the wheel and the rail dominate the noise production of railway operations at conventional speeds and remain significant even for high-speed trains. This wheel/rail noise may be divided into three main categories. Rolling noise occurs on straight track and is predominantly caused by undulations of the wheel and rail surfaces which induce a vertical relative vibration. Impact noise can be considered as an extreme form of rolling noise occurring at discontinuities of the wheel or rail surface. The excitation is again vertical, but non-linearities play a greater role. Squeal noise, occurring on sharp radius curves, is usually induced by a lateral excitation mechanism. A review of theoretical models that have been developed to predict these phenomena is given.
TL;DR: In this article, the effect of radial internal clearance of the ball bearing on the dynamic response of the rotor is studied and the system equations have been numerically integrated, the results have been validated with harmonic balance alternating frequency time domain method.
Abstract: The response of a balanced horizontal rigid motor rotor supported by a deep groove ball bearing is theoretically simulated. The effect of radial internal clearance of the ball bearing on the dynamic response of the rotor is studied. The system equations have been numerically integrated, the results of which have been validated with harmonic balance alternating frequency time domain method. Variation of radial internal clearance shifts the peak response as the speed is changed over a range. The results of a parametric study done by taking radial internal clearance have resulted in the observation of a third region of instability which has not been reported in literature. The appearance of regions of periodic, subharmonic and chaotic behavior is seen to be strongly dependent on the radial internal clearance. The system response is analyzed for stability and nature with the help of Floquets method for stability analysis and generation of higher order Poincare maps. The bearing stiffness is estimated experimentally and the effect of variation in radial internal clearance on the bearing stiffness is studied.
TL;DR: In this article, a two-dimensional formulation of the Ffowcs Williams and Hawkings equation in the frequency domain is presented, which is capable of predicting the farfield noise from non-linear nearfield flow quantities.
Abstract: This paper describes a two-dimensional formulation of the Ffowcs Williams and Hawkings equation in the frequency domain. By assuming subsonic rectilinear motion of all acoustic sources, an efficient and easily implemented form of the equation is developed. This method is capable of predicting the farfield noise from non-linear nearfield flow quantities. The ability to use non-linear input data is a clear advantage over Kirchhoff methods, that are only valid in regions where the linear wave equation accurately describes the flow. Several example problems are used to demonstrate that the new method performs well for problems with a mean flow, tonal and broadband noise signatures, and non-linear near fields. In most practical acoustic problems, three-dimensionality is important and should not be neglected. For these real-world applications, two-dimensional solutions can be used to guide and augment full three-dimensional calculations, but not replace them.
TL;DR: In this article, the authors used Reddy's third order plate theory to study buckling and steady state vibrations of a simply supported functionally gradient isotropic polygonal plate resting on a Winkler-Pasternak elastic foundation and subjected to uniform inplane hydrostatic loads.
Abstract: We use Reddy's third order plate theory to study buckling and steady state vibrations of a simply supported functionally gradient isotropic polygonal plate resting on a Winkler–Pasternak elastic foundation and subjected to uniform in-plane hydrostatic loads. Young's modulus and the Poisson ratio for the material of the plate are assumed to vary only in the thickness direction. Effects of rotary inertia are considered. The problem of determining the critical buckling load or the vibration frequency of the plate is found to be analogous to that of ascertaining the frequency of a membrane clamped at the edges and whose shape coincides with that of the plate. The critical buckling load and the vibration frequency are shown to be positive. Some available results for plates symmetric about the mid-plane can be retrieved from the present analysis.
TL;DR: A survey of simple, flexible structural elements subjected to non-conservative follower loads, such as those caused by the thrust of rocket and jet engines, and by dry friction in automotive disk-and drum-brake systems, is presented in this paper.
Abstract: This paper offers a survey of simple, flexible structural elements subjected to non-conservative follower loads, such as those caused by the thrust of rocket- and jet engines, and by dry friction in automotive disk- and drum-brake systems. Emphasis is on the “canonical problems”, Beck's, Reut's, Leipholz's, and Hauger's columns. Beck's and Reut's columns have been realized experimentally, and very good agreement between theory and experiments has been found. Leipholz's column is basically realized in an automobile brake system, where noise due to dynamic or parametric instability (brake squeal) is a well-known environmental problem. It is attempted to give a broad overview, with emphasis on experimental works and the associated theoretical problems. Structural optimization is also included in the review, as many studies in that area have served an important purpose in the development of optimization techniques for practical, large-scale optimization problems with non-conservative forces, such as in aeroelasticity.
TL;DR: In this paper, a first order sandwich plate theory is applied to obtain the fundamental frequencies of sandwich laminates in cylindrical bending and for the simply supported case, and the results suggest that the dynamic performance of a sandwich structure could be significantly improved with a proper design of the unit cell shape of the honeycomb.
Abstract: This paper is concerned with re-entrant cell honeycombs which show in-plane negative Poisson's ratio values, in which their anisotropic mechanical properties are described using the cellular material theory. Out-of-plane shear moduli are affected by the unit cell geometric parameters and, for some ranges of the latter, it is possible to obtain higher values of the shear moduli compared to those of a regular hexagonal honeycomb, in particular for cell geometries with a negative Poisson's ratio. A first order sandwich plate theory is applied in order to obtain the fundamental frequencies of sandwich laminates in cylindrical bending and for the simply supported case. Sensitivities of the frequencies per unit mass versus the geometric cell parameters are also calculated. The results suggest that the dynamic performance of a sandwich structure could be significantly improved with a proper design of the unit cell shape of the honeycomb. In particular, re-entrant cell cores offer improvements in bending stiffness capabilities for particular cell parameter ranges.
TL;DR: In this article, the dynamic stiffness matrix of a uniform rotating Bernoulli-Euler beam is derived using the Frobenius method of solution in power series, which includes the presence of an axial force at the outboard end of the beam in addition to the usual centrifugal force arising from the rotational motion.
Abstract: Starting from the governing differential equations of motion in free vibration, the dynamic stiffness matrix of a uniform rotating Bernoulli–Euler beam is derived using the Frobenius method of solution in power series. The derivation includes the presence of an axial force at the outboard end of the beam in addition to the existence of the usual centrifugal force arising from the rotational motion. This makes the general assembly of dynamic stiffness matrices of several elements possible so that a non-uniform (or tapered) rotating beam can be analyzed for its free-vibration characteristics by idealizing it as an assemblage of many uniform rotating beams. The application of the derived dynamic stiffness matrix is demonstrated by investigating the free-vibration characteristics of uniform and non-uniform (tapered) rotating beams with particular reference to the Wittrick–Williams algorithm. The results from the present theory are compared with published results. It is shown that the proposed dynamic stiffness method offers an accurate and effective method of free-vibration analysis of rotating beams.
TL;DR: In this article, the effect of planet phasing to suppress planetary gear vibration in certain harmonics of the mesh frequency is examined based on the physical forces acting at the sun-planet and ring-planet meshes.
Abstract: The effectiveness of planet phasing to suppress planetary gear vibration in certain harmonics of the mesh frequency is examined based on the physical forces acting at the sun–planet and ring–planet meshes. The analysis does not rely on assumptions of the nature of the dynamic excitation (e.g., static transmission error or time-varying mesh stiffness) or on an underlying dynamic model. Instead, the inherent system symmetries imply distinct relationships between the forces at the multiple meshes. These relationships lead naturally to simple rules for when a particular harmonic of mesh frequency is suppressed in the dynamic response. An important implication is that certain expected resonances when a mesh frequency harmonic and a natural frequency coincide are suppressed. Systems with equal planet spacing and those with unequally spaced, diametrically opposed planets are considered. In both cases, a substantial number of mesh frequency harmonics are suppressed naturally without optimization of the phasing. The phenomena are demonstrated with a dynamic finite element/contact mechanics simulation.
TL;DR: In this article, the free vibration analysis of two simply supported beams continuously joined by a Winkler elastic layer is presented, where the motion of the system is described by a homogeneous set of two partial differential equations, which is solved by using the classical Bernoulli-Fourier method.
Abstract: In this paper, the free vibration analysis of two parallel simply supported beams continuously joined by a Winkler elastic layer is presented. The motion of the system is described by a homogeneous set of two partial differential equations, which is solved by using the classical Bernoulli–Fourier method. The natural frequencies of the system are determined. The initial-value problem is considered to find the final form of the free vibrations. The free vibrations of an elastically connected double-beam complex system are realized by synchronous and asynchronous deflections. The presented theoretical analysis is illustrated by a numerical example, in which the effect of physical parameters characterizing the vibrating system on the natural frequencies is investigated.
TL;DR: In this article, a novel procedure is developed for the identification of linear discrete models of dynamical systems from noisy data based on a representation of the governing differential equations with respect to a wavelet basis, and the formulation of an inverse algebraic problem in the associated subspace.
Abstract: A novel procedure is developed for the identification of linear discrete models of dynamical systems from noisy data. Of particular interest is the application of the methodology to time-varying systems. The procedure is based on a representation of the governing differential equations with respect to a wavelet basis, and the formulation of an inverse algebraic problem in the associated subspace. The effect of noisy data is considered and numerical simulations demonstrating the applicability of the method to single- and multi-degree-of-freedom dynamical systems are presented.
TL;DR: In this article, a non-linear dynamic analysis of a horizontal rigid rotor having unbalance and supported on ball bearings has been done and the results show the appearance of instability and chaos in the dynamic response as the speed of the rotor-bearing system is changed.
Abstract: The non-linear dynamic analysis of a horizontal rigid rotor having unbalance and supported on ball bearings has been done. The non-linearity is both due to Hertzian contact and the radial internal clearance. The system is excited by the varying compliance frequency and the rotational frequency. For finding out the fixed point and stability of the system the concept of higher order Poincare map and interpolation technique has been applied. The results show the appearance of instability and chaos in the dynamic response as the speed of the rotor-bearing system is changed. Period doubling and mechanism of intermittency have been observed as the routes to chaos. The experimental investigations for a horizontal rotor-bearing system have shown the effect of varying compliance and increase in non-linearity due to radial internal clearance of the ball bearing. The orbit plots, cascade plots and frequency plots bring out the effect of radial internal clearance on the rotor response.
TL;DR: In this paper, the vibrational response to harmonic force of a cantilever beam with cracks of different size and location is analyzed using this "harmonic balance" approach and the results are compared with those obtained through numerical integration.
Abstract: The aim of this article is to present a technique capable of evaluating the dynamic response of a beam with several breathing cracks perpendicular to its axis and subjected to harmonic excitation. The method described is based on the assumption of periodic response and that cracks open and close continuously. In this way, a non-linear system of algebraic equations can be defined and solved iteratively, with the advantage over direct numerical integration of the equation of motion of being easier and therefore faster to compute. In this article, the vibrational response to harmonic force of a cantilever beam with cracks of different size and location is analyzed using this “harmonic balance” approach and the results are compared with those obtained through numerical integration.
TL;DR: In this paper, two regularization methods, Tikhonov regularization and singular value discarding, are used to improve the accuracy of reconstruction of acoustic source strength by inverse techniques.
Abstract: Two regularization methods, Tikhonov regularization and singular value discarding, are used to improve the accuracy of reconstruction of acoustic source strength by inverse techniques. In this paper, some methods are investigated for choosing the Tikhonov regularization parameter and the singular values to be discarded. Of these, we concentrate on the use of ordinary cross-validation and generalized cross-validation. These methods can provide an appropriate regularization parameter without prior knowledge of either the acoustic source strength or the contaminating measurement noise. Some experimental results obtained using a randomly vibrating simply supported plate mounted in a baffle are presented to illustrate the performance of the methods for choosing the regularization parameters.
TL;DR: In this paper, an exact method for solving the vibration of a double-beam system subject to harmonic excitation is presented, which involves a simple change of variables and modal analysis to decouple and to solve the governing differential equations respectively.
Abstract: An exact method is presented for solving the vibration of a double-beam system subject to harmonic excitation. The system consists of a main beam with an applied force, and an auxiliary beam, with a distributed spring k and dashpot c in parallel between the two beams. The viscous damping and the applied forcing function can be completely arbitrary. The damping is assumed to be neither small nor proportional, and the forcing function can be either concentrated at any point or distributed. The Euler–Bernoulli model is used for the transverse vibrations of beams, and the spring–dashpot represents a simplified model of viscoelastic material. The method involves a simple change of variables and modal analysis to decouple and to solve the governing differential equations respectively. A case study is solved in detail to demonstrate the methodology, and the frequency responses are shown in dimensionless parameters for low and high values of stiffness (k/k0) and damping (c/c0). The plots show that each natural mode consists of two submodes: (1) the in-phase submode whose natural frequencies and resonant peaks are independent of stiffness and damping, and (2) the out-of-phase submode whose natural frequencies are increased with increasing stiffness and resonant peaks are decreased with increasing damping. The closed-form solution and the plots, especially the three-dimensional ones, not only illustrate the principles of the vibration problem but also shed light on practical applications.
TL;DR: In this article, the results of a finite element analysis of a system may be post-processed to form energy flow models, yielding time and, perhaps, frequency average subsystem energies as well as input and dissipated powers.
Abstract: Computationally efficient methods are described by which the results of a finite element analysis of a system may be post-processed to form energy flow models, yielding time and, perhaps, frequency average subsystem energies as well as input and dissipated powers. The methods are particularly efficient for excitation which is spatially distributed or broadband (e.g., rain-on-the-roof) or if the frequency average response is required. First a method based on a global finite element analysis is presented. This involves a global modal decomposition and a reordering of the subsequent numerical calculations. The properties of the distribution of the excitation and the system's mass and stiffness lead to subsystem force distribution, mass distribution and stiffness distribution matrices. The response is given by a sum of terms involving the interaction of a pair of global modes, the contribution of each pair depending on the appropriate elements of the distribution matrices. Frequency averaging is performed by separating the resulting frequency-dependent terms and integrating. In most practical cases this integration can be done analytically. Next an alternative method involving component mode synthesis is described. In this, individual finite element analyses are performed for each subsystem using, here, the fixed interface method. These are then assembled to perform a global modal analysis, with the order of the model being much reduced. The consequent results are then post-processed in the same way. Finally, a system comprising three coupled plates is presented as a numerical example.
TL;DR: In this article, the Euler-Bernoulli model is used to analyze the surface vibration of a 2D elastic layer generated by a point load moving uniformly along a beam, which is located inside the layer.
Abstract: Vibration of a surface of a two-dimensional (2D) elastic layer generated by a point load moving uniformly along a beam, which is located inside the layer is investigated theoretically. It is supposed that the layer possesses a small viscosity, is fixed along the bottom, and has a traction-free surface. The beam is described by the Euler–Bernoulli model and located parallel both to the surface and the bottom of the layer. The surface vibration is analysed under three types of the load, namely constant, harmonically varying and a stationary random load. For the deterministic loads, the vector displacement of an observation point on the layer surface is analyzed along with the amplitude spectrum of vibration in this point. For the random load main attention is paid to the variance of vibration at the observation point. Qualitative features of obtained results are discussed via kinematic analyses of the wave propagation in the structure.
TL;DR: In this paper, a generalization of geometrically linear shear deformation theory for multilayered anisotropic shells of general shape is presented, which includes the effects of shear deformations and rotary inertia as well as initial curvature.
Abstract: The present work deals with a generalization of geometrically linear shear deformation theory for multilayered anisotropic shells of general shape. No assumptions are made other than to neglect the transverse normal strain. The results, which include the effects of shear deformations and rotary inertia as well as initial curvature (included in the stress resultants and assumed transverse shear stresses) are deduced by application of the virtual work principle, with displacements and transverse shear as independent variables. These equations are applied to different shell geometries, such as revolution, cylindrical, spherical and conical shells as well as rectangular and circular plates.
TL;DR: In this paper, the dynamic behavior of a multi-span continuous beam traversed by a moving mass at a constant velocity is investigated, in which it is assumed that each span of the continuous beam obeys uniform Euler-Bernoulli beam theory.
Abstract: The dynamic behavior of the multi-span continuous beam traversed by a moving mass at a constant velocity is investigated, in which it is assumed that each span of the continuous beam obeys uniform Euler–Bernoulli beam theory. The solution to this system is simply obtained by using both eigenfunction expansion or the modal analysis method and the direct integration method in combination. The effects of the inertia and the moving velocity of the load on the dynamic response of the continuous beam are evaluated for three kinds of continuous beams having uniform span length.