Showing papers in "Shock and Vibration in 1996"
141 citations
TL;DR: In this paper, an experimental procedure for obtaining angular and translational vibration in one measurement, using a continuously scanning laser Doppler vibrometer, was described, where the frequency response sidebands were obtained by using multiplied excitation force and mirror-drive signals.
Abstract: An experimental procedure for obtaining angular and translational vibration in one measurement, using a continuously scanning laser Doppler vibrometer, is described. Sinusoidal scanning, in a straight line, enables one angular vibration component to be measured, but by circular scanning, two principal angular vibrations and their directions can be derived directly from the frequency response sidebands. Examples of measurements on a rigid cube are given. Processes of narrow-band random excitation and modal analysis are illustrated with reference to measurements on a freely suspended beam. Sideband frequency response references are obtained by using multiplied excitation force and mirror-drive signals.
38 citations
TL;DR: In this article, different arrangements for double-pulsed holographic and speckle interferometry for vibration analysis are described, and the phases of the two reconstructed wave fields are calculated from the complex amplitudes.
Abstract: Different arrangements for double-pulsed holographic and speckle interferometry for vibration analysis will be described. Experimental results obtained with films (classical holographic interferometry) and CCD cameras (digital holographic interferometry) as storage materials are presented. In digital holography, two separate holograms of an object under test are recorded within a few microseconds using a CCD camera and are stored in a frame grabber. The phases of the two reconstructed wave fields are calculated from the complex amplitudes. The deformation is obtained from the phase difference. In the case of electronic speckle pattern interferometry (or image plane hologram), the phase can be calculated by using the sinusoid-fitting method. In the case of digital holographic interferometry, the phase is obtained by digital reconstruction of the complex amplitudes of the wave fronts. Using three directions of illumination and one direction of observation, all the information necessary for the reconstruction of the 3-dimensional deformation vector can be recorded at the same time. Applications of the method for measuring rotating objects are discussed where a derotator needs to be used.
29 citations
TL;DR: In this article, a space-frequency regressive approach was proposed to deal with the problem when spatially dense mobility shapes are measured with scanning laser Doppler vibrometers, which is often impractical to use phase-separation modal parameter estima- tion methods due to the excessive number of highly coupled modes and to the prohibi- tive computational cost of processing huge amounts of data.
Abstract: When spatially dense mobility shapes are measured with scanning laser Doppler vibrometers, it is often impractical to lise phase-separation modal parameter estima tion methods due to the excessive number of highly coupled modes and to the prohibi tive computational cost of processing huge amounts of data. To deal with this problem, a data compression method llsing Chebychev polynomial approximation in the fre quency domain and two-dimensional discrete Fourier series approximation in the spatial domain, is proposed in this article. The proposed space-frequency regressive approach was implemented and verified using a numerical simulation of a free-free free-free sllspended rectangular aluminum plate. To make the simulation more realis tic, the mobility shapes were synthesized by modal superposition using mode shapes obtained experimentally with a scanning laser Doppler vibrometer. A reduced and smoothed model, which takes advantage of the sinusoidal spatial pattern of structural mobility shapes and the polynomial frequency-domain pattern of the mobility shapes, is obtained. From the reduced model, smoothed curves with any desired frequency and spatial resolution can he produced whenever necessary. The procedure can he used either to generate nonmodal models or to compress the measured data prior to modal parameter extraction. © /996 John Wiley & Sons, inc.
19 citations
TL;DR: In this article, the authors applied the receptance method to the analytical study of the free vibrations of a simply supported circular cylindrical shell that is either empty or filled with an in viscid, incompressible fluid and with lumped masses attached at arbitrary positions.
Abstract: The receptance method is applied to the analytical study of the free vibrations of a simply supported circular cylindrical shell that is either empty or filled with an in viscid, incompressible fluid and with lumped masses attached at arbitrary positions. The receptance of the fluid-filled shell is obtained using the added virtual mass approach to model the fluid–structure interaction. The starting data for the computations is the modal properties of the cylinder that can be obtained using any theory of shells. Numerical results are obtained as roots of the frequency equation and also by considering the trivial solution. They are compared to data obtained by experimental modal analysis performed on a stainless steel tank, empty, or filled with water, with a lead mass attached.
17 citations
TL;DR: In this paper, a theoretical approach, using artificial spring systems to characterize the mechanical coupling between substructures, is extended to include fluid loading, and a structure consisting of a plate-ended cylindrical shell and its enclosed acoustic cavity is analyzed.
Abstract: This article deals with the modeling of vibrating structures immersed in both light and heavy fluids, and possible applications to noise control problems and industrial vessels containing fluids. A theoretical approach, using artificial spring systems to characterize the mechanical coupling between substructures, is extended to include fluid loading. A structure consisting of a plate-ended cylindrical shell and its enclosed acoustic cavity is analyzed. After a brief description of the proposed technique, a number of numerical results are presented. The analysis addresses the following specific issues: the coupling between the plate and the shell; the coupling between the structure and the enclosure; the possibilities and difficulties regarding internal soundproofing through modifications of the joint connections; and the effects of fluid loading on the vibration of the structure.
17 citations
TL;DR: In this paper, the Gaussian enveloped oscillating wavelet is used to extract different sizes of features from the signal and the time-frequency and time-scale distributions generated by the wavelet transform are shown to be effective in identifying mechanical faults.
Abstract: The wavelet transform is introduced to indicate short-time fault effects in associated vibration signals. The time-frequency and time-scale representations are unified in a general form of a three-dimensional wavelet transform, from which two-dimensional transforms with different advantages are treated as special cases derived by fixing either the scale or frequency variable. The Gaussian enveloped oscillating wavelet is recommended to extract different sizes of features from the signal. It is shown that the time-frequency and time-scale distributions generated by the wavelet transform are effective in identifying mechanical faults.
17 citations
15 citations
TL;DR: In this paper, a modified Lindstedt-Poincare method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities.
Abstract: A modified Lindstedt-Poincare method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are intro duced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good. © 1996 John Wiley & Sons, Inc.
15 citations
TL;DR: In this article, a detailed solution to the transient interaction of plane acoustic waves with a spherical elastic shell was obtained more than a quarter of a century ago based on the classical separation of variables, series expansion, and Laplace transform techniques.
Abstract: A detailed solution to the transient interaction of plane acoustic waves with a spherical elastic shell was obtained more than a quarter of a century ago based on the classical separation of variables, series expansion, and Laplace transform techniques. An eight term summation of the time history series was sufficient for the convergence of the shell deflection and strain, and to a lesser degree, the shell velocity. Since then, the results have been used routinely for validation of solution techniques and computer methods for the evaluation of underwater explosion response of submerged structures. By utilizing modern algorithms and exploiting recent advances of computer capacities and floating point mathematics, sufficient terms of the inverse Laplace transform series solution can now be accurately computed. Together with the application of the Cesaro summation using up to 70 terms of the series, two primary deficiencies of the previous solution are now remedied: meaningful time histories of higher time derivative data such as acceleration and pressure are now generated using a sufficient number of terms in the series; and uniform convergence around the discontinuous step wave front is now obtained, completely eradicating spurious oscillations due to the Gibbs' phenomenon. New results of time histories of response items of interest are pre sented. © 1996 John Wiley & Sons, Inc.
TL;DR: In this paper, the authors present a methodology for the optimization of structures under impact loading, where the structural behavior is nonlinear dynamic and the optimization problem is to minimize the structural mass with constraints on the transient dynamic response of the structure.
Abstract: In the design process structural optimization is a useful tool to reach design decisions. The impact behavior of structures is important for many designs, such as for automobiles. This article reviews methodology for the optimization of structures under impact loading. The optimization problem is to minimize the structural mass with constraints on the transient dynamic response of the structure. The structural behavior is nonlinear dynamic. Optimization is performed using the approximation concept. Design sensitivity analysis for transient response is treated.
TL;DR: In this paper, a theoretical approach was developed for predicting the plastic deformation of a cylindrical shell subject to asymmetric dynamic loads by solving for the transverse deflections of a rigid-plastic beam/string-on-foundation.
Abstract: A theoretical approach was developed for predicting the plastic deformation of a cylindrical shell subject to asymmetric dynamic loads. The plastic deformation of the leading generator of the shell is found by solving for the transverse deflections of a rigid-plastic beam/string-on-foundation. The axial bending moment and tensile force in the beam/string are equivalent to the longitudinal bending moments and membrane forces of the shell, while the plastic foundation force is equivalent to the shell circumferential bending moment and membrane resistances. Closed-form solutions for the transient and final deformation profile of an impulsive loaded shell when it is in a “string” state were derived using the eigenfunction expansion method. These results were compared to DYNA 3D predictions. The analytical predictions of the transient shell and final centerline deflections were within 25% of the DYNA 3D results.
TL;DR: In this article, a simplified governing equations and corresponding boundary conditions of vibration of viscoelastically damped unsymmetrical sandwich shells are given, and the asymptotic solution to the equations is discussed.
Abstract: The simplified governing equations and corresponding boundary conditions of vibration of viscoelastically damped unsymmetrical sandwich shells are given. The asymptotic solution to the equations is then discussed. If only the first terms of the asymptotic solution of all variables are taken as an approximate solution, the result is identical with that obtained from the modal strain energy method. By taking more terms of the asymptotic solution with successive calculations and use of the Pade approximants method, accuracy of natural frequencies and modal loss factors of sandwich shells can be improved. The lowest three or four natural frequencies and modal loss factors of simply supported cylindrical sandwich shells are calculated.
TL;DR: In this article, the in-plane membrane control forces and counteracting control moments induced by the distributed actuator in a laminated cylindrical shell and a piezoelectric shell are evaluated.
Abstract: Distributed actuators offer spatially distributed actuations and they are usually effective to multiple modes of a continuum. Spatially filtered distributed vibration controls of a laminated cylindrical shell and a piezoelectric shell are investigated, and their control effectivenesses are evaluated in this study. In general, there are two control actions, the in-plane membrane control forces and the counteracting control moments, induced by the distributed actuator in the laminated shell. There is only an in-plane circumferential control force in the piezoelectric shell. Analyses suggest that in either case the control actions are effective in odd natural modes and ineffective in even modes. Spatially filtered control effectiveness and active damping of both shells are studied.
TL;DR: In this article, a simple I-dimensional model is presented to investigate elastic stress waves in composite laminates excited by underwater explosion shocks, where the focus is on the elastic dynamic stress fields in the composite laminate immediately after the action of the shock wave.
Abstract: A simple I-dimensional model is presented to investigate elastic stress waves in com posite laminates excited by underwater explosion shocks. The focus is on the elastic dynamic stress fields in the composite laminate immediately after the action of the shock wave. In this model, the interaction between the laminate and the water is taken into account, and the effects of the laminate-water interaction on the stress wave fields in the laminate are investigated. In the formulation of the model, wave fields in the laminate and the water are the first obtained in the frequency domain and then transferred into the time domain using the Fourier transform techniques. A quadrature technique is used to deal with the Fourier transform integrals in which the integrands have very sharp peaks on the integral axis. Numerical examples for stress waves in a steel plate and a glass reinforced plastic sandwich laminate are presented. The technique and the results presented in this article may be used in the design of ship hull structures subjected to underwater explosions. © 1996 John Wiley & Sons, Inc.
TL;DR: In this paper, the power spectra computed from vibration signals measured during the lift-off of a large launch vehicle at 12 locations in a structural region where equipment will be mounted are compared and the merits and liabilities of the various procedures are discussed.
Abstract: It is common to establish shock and vibration design and/or test criteria for equipment mounted on a structure by computing a conservative upper bound for the spectrum of the dynamic load induced response of the structure based upon predicted or measured spectra at various points. This task is usually accomplished by one of five procedures, namely, the computation from the available spectra of a simple envelope, a normal tolerance limit, a distribution-free tolerance limit, an empirical tolerance limit, or a normal prediction limit. These five procedures are reviewed and illustrated using the power spectra computed from vibration signals measured during the lift-off of a large launch vehicle at 12 locations in a structural region where equipment will be mounted. The results are compared and the merits and liabilities of the various procedures are discussed.
TL;DR: In this paper, the SLDV velocity data of a partial surface area of an aircraft fuselage were mapped to truly spatial evenly spaced coordinates by using the spatial DFT-IDFT technique with minimum distortion.
Abstract: The scanning laser Doppler vibrometry (SLDV) technique provides velocities of a structure at 2-dimensional (2-D) angularly evenly spaced (in the laser scanning sense) data points. This causes an unevenly spaced data point distribution on the surface of the test structure. In many cases evenly spaced data point distribution with square or rectangular grids is highly desirable. In this study the SLDV velocity data of a partial surface area of an aircraft fuselage were mapped to truly spatial evenly spaced coordinates by using the spatial DFT-IDFT technique with minimum distortion. This 2-D data mapping technique certainly is not limited to the fuselage, hut can he very useful for many other 3-D structures.
TL;DR: In this article, a numerical study was conducted to obtain a better understanding of localization of perfectly periodic structures, and it was found that any mode, even the first mode, can localize due to the presence of small imperfections.
Abstract: Extensive work has been done on the vibration characteristics of perfectly periodic structures. Disorder in the periodic pattern has been found to lead to localization in one-dimensional periodic structures. It is important to understand localization be cause it causes energy to be concentrated near the disorder and may cause an overes timation of structural damping. A numerical study is conducted to obtain a better understanding of localization. It is found that any mode, even the first, can localize due to the presence of small imperfections. © 1996 John Wiley & Sons, Inc.
TL;DR: In this article, the second part of a two part review of shock and vibration isolation is presented, covering three distinct categories of shock excitation: pulselike, velocity and complex.
Abstract: This is the second part of a two part review of shock and vibration isolation. It covers three distinct categories of shock excitation—pulselike shock, velocity shock, and complex shock—and discusses the means that are available in each case to measure the effectiveness of shock mitigation by the imposition of flexible connections between the isolated system and its base.
TL;DR: In this paper, it was shown that the usual method for estimating the coherence functions (ordinary, partial, and multiple) for a general multiple-input! multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross-spectral density matrix of the input and output records.
Abstract: It is shown that the usual method for estimating the coherence functions (ordinary, partial, and multiple) for a general multiple-input! multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross-spectral density matrix of the input and output records. The results can be equivalently obtained using singular value decomposition (SVD) of the cross-spectral density matrix. Using SVD suggests a new form of fractional coherence. The formulation as a SVD problem also suggests a way to order the inputs when a natural physical order of the inputs is absent.
TL;DR: In this paper, a procedure of dynamic force identification for beam-like structures is developed based on an improved dynamic stiffness method, where the entire structure is first divided into substructures according to the excitation locations and the measured response sites.
Abstract: In this study a procedure of dynamic force identification for beamlike structures is developed based on an improved dynamic stiffness method. In this procedure, the entire structure is first divided into substructures according to the excitation locations and the measured response sites. Each substructure is then represented by an equivalent element. The resulting model only retains the degree of freedom (DOF) associated with the excitations and the measured responses and the DOF corresponding to the boundaries of the structures. Because the technique partly bypasses the processes of modal parameter extraction, global matrix inversion, and model reduction, it can eliminate many of the approximations and errors that may be introduced during these processes. The principle of the method is described in detail and its efficiency is demonstrated via numerical simulations of three different structures. The sensitivity of the estimated force to random noise is discussed and the limitation of the technique is pointed out.
TL;DR: In this paper, the detrimental consequences that resulted when mechanical impedance effects were not considered in relating vibration test requirements with field measurements were explored, and comparison of three impedance methods was accomplished based on a cumulative damage criterion.
Abstract: The work presented here explored the detrimental consequences that resulted when mechanical impedance effects were not considered in relating vibration test requirements with field measurements. The ways in which these effects can be considered were evaluated, and comparison of three impedance methods was accomplished based on a cumulative damage criterion. A test structure was used to simulate an equipment and support foundation system. Detailed finite element analysis was performed to aid in computation of cumulative damage totals. The results indicate that mechanical impedance methods can be effectively used to reproduce the field vibration environment in a laboratory test. The establishment of validated computer models, coupled with laboratory impedance measurements, can eliminate the overtesting problems inherent with constant motion, infinite impedance testing strategies.
TL;DR: In this article, the authors investigated the dissipation of hysteretic energy in the isolator of the base isolated structure under seismic excitation, where the authors derived a nonlinear differential equation to model the hystèretic force-deformation characteristics of a base isolator.
Abstract: Dissipation of hysteretic energy in the isolator of the base isolated structure under seismic excitation is investigated. The hysteretic force-deformation characteristics of the base isolator is specified by a nonlinear differential equation. The parameters of the equation can be adjusted to obtain various types of hysteretic models of the isolator including the elastoplastic type. The variation of hysteretic energy dissipated in the isolators is obtained for both harmonic and El-Centro 1940 earthquake ground motion for a set of important parameters. They include time period of superstructure, ratio of superstructure mass to base mass, level of yield strength of the isolator, post- to preyielding stiffness ratio, and the ratio of harmonic excitation frequency to base isolation frequency. It is shown that the dissipation of hysteretic energy in the isolator is significantly influenced by the above parameters.
TL;DR: In this article, nonlinear equations of motion and their transformation are formulated in detail and a convenient way of selection of the generalized basis vector and its limitations are described, within its limitations, may be applied to dynamic problems where the response is global in nature with finite amplitude.
Abstract: The large number of unknown variables in a finite element idealization for dynamic structural analysis is represented by a very small number of generalized variables, each associating with a generalized Ritz vector known as a basis vector. The large system of equations of motion is thereby reduced to a very small set by this transformation and computational cost of the analysis can be greatly reduced. In this article nonlinear equations of motion and their transformation are formulated in detail. A convenient way of selection of the generalized basis vector and its limitations are described. Some illustrative examples are given to demonstrate the speed and validity of the method. The method, within its limitations, may be applied to dynamic problems where the response is global in nature with finite amplitude.
TL;DR: In this paper, the authors deal with the interaction between wave effects in mounts and resonances of foundations inflexible vibration isolation systems and propose a new model that is represented as a rigid mass supported by two linear unidirectional isolators on a flexible foundation beam, whose closed-form solutions for transmissibility and response ratio are then obtained.
Abstract: This article deals with the interaction between wave effects in mounts and resonances of foundations inflexible vibration isolation systems. A new model is proposed that is represented as a rigid mass supported by two linear unidirectional isolators on a flexible foundation beam, whose closed-form solutions for transmissibility and response ratio are then obtained, with which the influence of wave effects coupled with the flexibility of the foundation on the effectiveness of isolation is discussed. The wave effects on flexible isolation systems are analyzed under various parametric conditions and compared with those in rigid systems. In addition, several special cases are presented to show the transition between various limiting cases. Some approaches to control wave effects are also proposed.
TL;DR: In this article, the constrained eigenstructure assignment method (CEAM) is extended to finite element model updating, and the existing formulation is modified to accommodate larger systems by developing a quadratic linear optimization procedure.
Abstract: This article deals with an extended application of the constrained eigenstructure assignment method (CEAM) to finite element model updating. The existing formulation is modified to accommodate larger systems by developing a quadratic linear optimization procedure that is unconditionally stable. Further refinements include the updating of the mass matrix, a hysteretic damping model, and the introduction of elemental correction factors. Six numerical test cases, dealing with effects of damping and measurement noise, mode shape incompleteness, and discretization differences, were conducted in the case of a 3-D frame model with 114 coordinates. The performance of the CEAM was evaluated systematically for both the purpose of error location and the global correction of the initial model. The same cases were also studied using another model updating approach, namely the response function method (RFM). It was found that the CEAM had a number of distinct advantages, such as yielding a noniterative direct solution, requiring much less computing power, and providing acceptable results for cases, that could not he handled using the RFM.