Showing papers on "Vibration published in 1988"
TL;DR: In this article, the effects of disorder on the modes of vibration of nearly periodic structures are investigated, and perturbation methods for the eigenvalue problem are applied to predict the occurrence of strong localization and eigen value loci veering.
388 citations
TL;DR: In this paper, the finite element equations for a variationally consistent higher-order beam theory are presented for the static and dynamic behavior of rectangular beams, which correctly accounts for the stress-free conditions on the upper and lower surfaces of the beam while retaining the parabolic shear strain distribution.
364 citations
TL;DR: In this paper, the complementary energy method is applied to the free vibration analysis of various structural components, including prismatic and tapered bars, prismatic beams, and axisymmetric motion of circular membranes.
Abstract: Two approximate methods, which have not previously been used for structural dynamics problems, are applied to the free vibration analysis of various structural components. The first method is a new version of the complementary energy method. It is shown to be considerably more accurate than the conventional Rayleigh and Rayleigh-Schmidt methods when applied to spatially one-dimensional free vibration problems: prismatic and tapered bars, prismatic beams, and axisymmetric motion of circular membranes. The second method is the differential quadrature method introduced by Bellman and his associates. It is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates.
307 citations
TL;DR: In this paper, the effect of delamination on the natural vibration characteristics of laminated beam type structures is studied and an analytical model is presented for beams with through-width delaminations parallel to the beam surface located arbitrarily in both the spanwise and thicknesswise directions.
267 citations
TL;DR: In this article, a finite element for the cracked prismatic beam is developed to evaluate the dynamic response of a cracked cantilever beam to harmonic point force excitation, which can be used in any appropriate matrix analysis of structures program.
228 citations
TL;DR: In this paper, a non-linear model is used for the dynamic analysis of a gear pair and a computer program is developed for calculating the dynamic mesh and tooth forces, dynamic factors based on stresses, and dynamic transmission error from measured or calculated loaded static transmission errors.
223 citations
TL;DR: In this article, the influence of a constant axial compressive load on natural frequencies and mode shapes of a uniform single-span beam with ten different combinations of end conditions is presented, and it is observed that Galef's formula, previously assumed to be valid for beams with all types of end constraints, is valid only for a few.
219 citations
TL;DR: In this article, a simple but exact computer model of the subharmonic vibration was developed based on the numerical integration of a finite difference formulation. But the model is not suitable for systems with low damping and extreme nonlinearity.
Abstract: Subharmonic vibration refers to the response of a dynamic system to excitation at a whole-number multiple (n) of its natural frequency by vibrating asynchronously at its natural frequency, that is, at (1/n) of the excitation. The phenomenon is generally associated with asymmetry in the stiffness vs. deflection characteristic of the system. It may be characterized as the “bouncing” of the rotor on the surface of the stiff support, energized by every nth unbalance impulse prior to contact. Second, third and fourth order subharmonic vibration responses have previously been observed in high speed rotating machinery with such an asymmetry in the bearing supports. An incident is reported where 8th and 9th order subharmonic vibration responses have been observed in a high speed rotor. A simple but exact computer model of the phenomenon has been evolved based on the numerical integration of a finite difference formulation. Response curves and wave forms of rotor deflection at individual speeds are computed. It is shown that the response is a series of pseudo-critical peaks at whole-number multiples of the rotational speed. Very high orders of subharmonic vibration are found to be possible for systems with low damping and extreme nonlinearity.
212 citations
TL;DR: A thermally compensated tube scanner scanning tunneling microscope utilizes two concentric piezoelectric tubes, one for scanning and one for coarse translation as well as fine adjustment of sample position while in tunneling range as mentioned in this paper.
Abstract: A thermally compensated tube scanner scanning tunneling microscope utilizes two concentric piezoelectric tubes, one for scanning and one for coarse translation as well as fine adjustment of sample position while in tunneling range. There are no mechanical components such as springs, levers, gears, or stepper motors which are known to result in considerable vibration sensitivity and thermal drift. Consequently, the standard mode of atomic resolution operation for the device is without vibration isolation and with a thermal drift of less than 1 angstrom per hour.
184 citations
TL;DR: In this article, the Rayleigh-Ritz technique was used to model the vibrations of rectangular orthotropic plates and the characteristic functions of vibrating beams were used as the assumed functions for plates with boundary conditions consisting of clamped and free edges.
164 citations
01 Sep 1988
TL;DR: Theoretical expressions relating amplitude and wavelength of surface imperfections in thrust loaded ball bearings to vibration forces and frequencies produced under constant-speed operating conditions were derived in this article, where they were derived under constant speed operating conditions.
Abstract: Theoretical expressions are derived relating amplitude and wavelength of surface imperfections in thrust loaded ball bearings to vibration forces and frequencies produced under constant-speed operating conditions.
TL;DR: A degrading, hysteretic restoring force model for structures subjected to extreme dynamic loads has been developed by Wen and Baber as mentioned in this paper, and a method for identifying the parameters of the model, given observed structural response, is then developed.
Abstract: A degrading, hysteretic restoring force model for structures subjected to extreme dynamic loads has been developed by Wen (1976; 1980) and Baber and Wen (1981). A need has arisen for systematically identifying the parameters of this model. A brief discussion of the model is first presented here along with an extension developed to model displacement-dependent degrading behavior of reinforced concrete structures. A method for identifying the parameters of the model, given observed structural response, is then developed. The method is based on a classic, time domain-least squares procedure where the system parameters are obtained by solving a system of simultaneous linear equations. The parameter identification method should prove useful in developing models of complex structures for nonlinear, random vibration analysis. Based on applications of the parameter identification method, using actual structural restoring force experimental results, simple rules for determining the model parameters are suggested and presented at the conclusion.
TL;DR: In this article, the authors proposed a means for computing the distance between the input pen and the vibration detection means from the time determined by the control means, where the time of arrival of the vibration is defined as the zero-cross point of the signal.
Abstract: A coordinates input apparatus such as a digitizer has: vibration propagation medium such as a transparent glass plate for allowing a vibration to propagate therethrough; an input pen for applying vibration (50) to the vibration propagation means; vibration detecting means for detecting vibration (51) applied by the input pen; envelope output means for producing an envelope signal (52) representing the envelope of the vibration detected by the vibration detecting means; differentiation means for conducing a differentiation (53) of the envelope signal produced by the envelope output means so as to determine the peak (at time Tg); control means adapted for determining, as the time of arrival of the vibration, a zero-cross point of the vibration (51) detected by the vibration detecting means located in the vicinity of a zero-cross point of the signal (53) from the differentiation means; and computing means for computing the distance between the input pen and the vibration detection means from the time determined by the control means.
TL;DR: In this paper, the in-plane and out-of-plane free vibrations of a rotating Timoshenko beam are analyzed by means of a finite element technique, where the beam is discretized into a number of simple elements with four degrees of freedom each.
TL;DR: In this article, the effect of the coupling terms upon the vibration waveforms were investigated by using both a linearized analysis and numerical solution of the differential equations, and it was found that for small values of the ratio of the flexible beam and rigid shaft inertia uncoupled equations can lead to substantially incorrect results, particularly with regard to frequencies.
TL;DR: In this article, it is shown that the rotor self-excited vibrations (known as oil whirl and oil whip) due to fluid dynamic forces generated in the oil-lubricated bearing, can exhibit multiple regimes.
TL;DR: In this article, a 6 × 6 compliance matrix describing the local flexibility in a short shaft element which includes the crack is presented and a method for the determination of the intervals of instability of the first and of second kind is developed.
Abstract: A transverse surface crack is known to add to a shaft a local flexibility due to the stress-strain singularity in the vicinity of the crack tip. This flexibility can be represented, in the general case by way of a 6 × 6 compliance matrix describing the local flexibility in a short shaft element which includes the crack. This matrix has off-diagonal terms which cause coupling along the directions which are indicated by the off-diagonal terms. In addition, when the shaft rotates the crack opens and closes. Then the differential equations of motion have periodically varying stiffness coefficients and the solution can be expressed as a sum of harmonic functions of time. A method for the determination of the intervals of instability of the first and of second kind is developed. The results have been presented in stability charts in the frequency vs. depth of the crack domain. The coupling effect due to the crack leads to very interesting results such as new frequencies and vibration modes.
TL;DR: In this paper, a ship, towing a heavier-than-water cable with a neutrally buoyant slender cylinder attached to the downstream end of the cable, is considered, and the effect of cable properties on transmission along the cable is investigated.
Abstract: A ship, towing a heavier-than-water cable with a neutrally buoyant slender cylinder attached to the downstream end of the cable, is considered. The neutrally buoyant element contains a sonar array. Linear changes in the ship's velocity cause perturbations of both the cable and cylinder. The form of transverse vibrations of the neutrally buoyant cylinder was determined in Part 1. The propagation of disturbances along the cable is investigated in this paper. In particular, the effectiveness of the cable at isolating the sonar array from forcing due to unsteady ship motion is examined.The cable and cylinder are found to be stable under constant towing conditions. It is therefore appropriate to investigate their response to forcing. Meanderings in the ship's track produce transverse displacements of both the cable and the cylinder. These transverse oscillations entirely decouple from any in-plane motion. The propagation of disturbances of frequency ω along the cable depends strongly on the value of the non-dimensional frequency ωlC/U, where lC is the cable length and U is the towing speed, and only weakly on the other cable parameters. The cable acts as an effective low-pass filter to transverse oscillations, the amplitude of disturbances with non-dimensional frequency greater than 10 being reduced by at least 90% as they propagate along the cable.Unsteadiness in the ship's speed can result in in-plane deflections of the cable, and vertical oscillations of the cylinder containing the sonar array. In contrast to the transverse oscillations a significant proportion of the in-plane disturbances at the ship travels to the sonar array at all values of the frequency. Low- and high-frequency analytical forms are derived to explain why this occurs. Perturbations in the ship's position are most effectively transformed into vertical oscillations of the array at a frequency of 2.8U/lC. The effect of cable properties on transmission along the cable is investigated. The transmission again depends on the value of the non-dimensional frequency ωlC/U. Parameter changes, which increase the cable critical angle, increase the proportion of the disturbance at the towing point that is transformed into vertical array motion, for a fixed value of ωlC/U. This is explained by reference to the low- and high-frequency analytical solutions.
TL;DR: In this paper, the effects of soil-structure interaction during forced vibration tests were analyzed for the nine-storey reinforced concrete Millikan Library Building and it was shown that the deformation of the superstructure at the fundamental frequencies of the system is almost entirely due to the inertial forces generated by translation and rocking of the base.
Abstract: SUMMARY Forced vibration tests designed to isolate the effects of soil-structure interaction are described and the results obtained for the nine-storey reinforced concrete Millikan Library Building are analysed. It is shown that it is possible to determine experimentally the fixed-base natural frequencies and modal damping ratios of the superstructure. These values may be significantly different from the resonant frequencies and damping ratios of the complete structure-foundation-soil system. It is also shown that forced vibration tests can be used to obtain estimates of the foundation impedance functions. In the case of the Millikan Library it is found that during forced vibration tests the rigid-body motion associated with translation and rocking of the base accounts for more than 30 per cent of the total response on the roof and that the deformation of the superstructure at the fundamental frequencies of the system is almost entirely due to the inertial forces generated by translation and rocking of the base. Full-scale forced vibration tests are commonly used to determine the natural frequencies, modal damping values and mode shapes of structures. The frequent practice in interpreting the results of forced vibration tests is to neglect the effects of the interaction between the structure and the soil. Such a simplifying assumption may lead to serious errors in that resonant frequencies, energy dissipation and other dynamic characteristics of the complete structure-foundation-soil system are ascribed to the superstructure. The typical result is that the fixed-base natural frequencies of the structure are underestimated while the energy dissipation in the structure is overestimated. The principal objective of this study is to analyse in detail the effects of soil-structure interaction during forced vibration tests. In particular, an attempt is made at extracting structural characteristics, such as fixed- base natural frequencies and energy dissipation mechanism, as well as foundation-soil characteristics, such as foundation impedance functions, from forced vibration test results which involve the complete structure-foundation-soil system. Although a large number of theoretical studies of the interaction between structures and the supporting soil have been made and a variety of sophisticated analytical models have been proposed, the experimental study of the interaction phenomenon has been very limited. The second objective of this study is associated with the need of illustrating the interaction effects under controlled experimental conditions. For the purpose of this study the nine-storey reinforced concrete Millikan Library Building was selected as the experimental site. The Millikan Library has been the subject of a large number of forced vibration tests (Kuroiwa,12 Jennings and Kuroiwa,9 Trifunac,19 Foutch et al.,' Luco et al.,'3) and ambient vibration tests (Blandford et al.,' Trifunac,19 McLamore," Udwadia and Trifunac20). Accelerograms for the 1968 Borrego Mountain, 1970 Lytle Creek and 1971 San Fernando earthquakes have been recorded in the Library and a
TL;DR: In this article, a study of the dynamic impedances for radially inhomogeneous, infinite viscoelastic layers with a circular hole, and for piles embedded in a medium represented by such layers is made.
Abstract: A study of the dynamic impedances for radially inhomogeneous, infinite viscoelastic layers with a circular hole, and for piles embedded in a medium represented by such layers is made. Systems in vertical and torsional modes of vibration are examined considering both a discontinuous variation in shear modulus and an exponentially increasing, continuous variation. The results are evaluated over wide ranges of the parameters involved and compared with those obtained for a homogeneous layer. In addition, the harmonic response of strip foundations supported at the surface of a vertically inhomogeneous viscoelastic half‐space is examined, and it is shown that within the framework of a previously proposed approximation, the impedances of such foundations for both horizontal and vertical modes of vibration may be deduced from those obtained for the vertically excited, radially inhomogeneous layer.
TL;DR: In this paper, two methods for damping analysis of a partially covered sandwich beam were developed based on simplified methods and one based on an exact method, respectively, for the Euler beam theory for the uncovered portion of the beam, and for the covered portion, with continuity conditions at the common sections, have been used.
TL;DR: In this paper, the equations of motion for the study of the fiexural dynamic behaviour of a general rotating system, based on the finite element method and on the use of complex co-ordinates, are described.
TL;DR: In this paper, the coupling of bending and longitudinal vibration of a stationary cracked shaft with an open crack is modeled by way of a 2×2 local flexibility matrix with coupling terms.
Abstract: This paper describes the coupling of bending and longitudinal vibration of a stationary cracked shaft with an open crack. The crack is modeled by way of a 2×2 local flexibility matrix with coupling terms. The elements of this matrix are obtained analytically. One of the elements compares well with experimental data of other investigators. The free vibration of the shaft, and the influence of the crack on the vibrational behavior of the shaft is studied. The relation of the eigenvalues of the system and the crack depth as functions of the slenderness ratio are presented. The forced vibration of the shaft is also studied and the coupling of the vibration modes is verified analytically and experimentally. The applicability of the method as a crack identification tool is demonstrated.
TL;DR: In this article, the forced steady response of a single degree of freedom system involving a large nonlinearity, represented by unsymmetric piecewise linear stiffness, is determined by a harmonic balance Newton-Raphson method with the application of the fast Fourier transformation (FFT) algorithm.
Book•
20 Oct 1988
TL;DR: Vibration of Structures as discussed by the authors provides the basic principles of vibration theory so that civil engineers can assess the dynamic performance of different types of structure at the design stage, including mass and spring systems.
Abstract: Vibration of Structures aims to provide civil engineers with the basic principles of vibration theory so that they can assess the dynamic performance of different types of structure at the design stage. The emphasis throughout is on physical behaviour and the mathematical treatment is kept as simple as possible. The book begins with simple mass and spring systems and then carefully develops the theory for systems with many degrees of freedom, including the propagation of vibration and waves through the ground. An important feature of the book is a chapter on finite element modelling of vibration problems. This is included because excellent finite element programs now exist that run on low-cost desk top computers making dynamic analysis of complex structures not only feasible but also economical. Six chapters are devoted to important civil engineering applications: earthquake engineering, wind induced oscillations, vibrations of machine foundations, traffic loading, crowd loading, blasting and pile driving. Finally there are two chapters on design criteria, dealing with human response to vibration and fatigue of structures. The text is generously illustrated and numerous fully worked examples are included.
TL;DR: In this paper, the Coriolis effect on the balanced driven mode of vibration was used to couple energy into the pickup mode of the pickup system in order to measure angular rotation rate.
Abstract: An inertial sensing system includes a geometric structure having several independent mechanically resonant modes of vibration such that when the structure is subjected to outside inertial motions that are to be sensed, a driven mode of vibration will couple energy in a specific manner into a pickup mode. The driven mode serves as a reference motion. The system measures angular rotation rate by sensing the vibrations in the pickup mode caused by the action of the Coriolis effect on the balanced driven mode which couples energy into the pickup mode. The system includes a portion of the geometric structure that is subject to strain caused by linear acceleration in one direction. The strain introduces an imbalance in the driven mode which causes energy to be coupled to the pickup mode of vibration in a nominally linear manner. A sensing circuit is provided to sense the amount of energy coupled into the pickup system as a measure of applied angular rotation and applied acceleration. The coupling of energy into the pickup caused by linear acceleration is orthogonal to the coupling of energy caused by angular rotation rate, and the effects of the two sources of coupled energy can be separated by the system circuitry such that independent determination of the two types of input motion is realized. The sensing system is preferably made of a material such as crystalline quartz that is mechanically stable and is also piezoelectric so that the driving and sensing can be accomplished by piezoelectric techniques.
Patent•
11 Mar 1988
TL;DR: In this paper, an accelerometer is mounted in the bottom hole assembly to generate data in the form of electrical signals corresponding to the acceleration experienced by the assembly and an alarm signal is sent to the surface so corrective measures can be taken to prevent damage to downhole equipment.
Abstract: Apparatus for monitoring vibration of a bottom hole assembly used to drill a well includes at least one accelerometer mounted in the bottom hole assembly to generate data in the form of electrical signals corresponding to the acceleration experienced by the assembly. The computer in the assembly is programmed to collect data from the accelerometer and compute magnitude of the assembly acceleration. Means are provided for selecting from the collected data a value which exceeds a preset level. In one form, when the collected data has a value above a preset level, an alarm signal is sent to the surface so corrective measures can be taken to prevent damage to downhole equipment.
TL;DR: In this paper, it was shown that the flow properties of fresh concrete are no longer represented by the simple linear Bingham model but approximate to those of a power law pseudoplastic with zero yield value.
Abstract: Synopsis Using a set-up in which the bowl of a two-point workability test apparatus was mounted on an electro-magnetic vibrating table, measurements were made on unvibrated fresh concrete and on the same samples under vibration. It was shown that when vibration is applied the flow properties of fresh concrete are no longer represented by the simple linear Bingham model but approximate to those of a power law pseudoplastic with zero yield value. At very low shear rates behaviour approximates to that of a Newtonian fluid and, subject to the exceeding of a small threshold condition, fluidity decreases as a simple exponential function of the maximum velocity of vibration.
TL;DR: In this paper, a vibration control system for damping vibration of a body to be isolated against vibration, where the body is supported on a movable base through the medium of vibration damping supporting structure, is presented.
Abstract: A vibration control system for damping vibration of a body to be isolated against vibration, wherein the body (1) is supported on a movable base (3) through the medium of vibration damping supporting structure (2). The control system comprises a vibration sensor (4) for detecting vibration of the movable base (3), an inverse vibration signal generating circuit (20) including a digital sensor and supplied with a detection signal outputted from the vibration sensor (4) for generating a vibration signal of such a waveform to cancel out the vibration of the body through interference therewith, and an actuator (12) connected operatively to the movable base and the inverse vibration signal generating circuit for converting the vibration signal derived from the latter into a mechanical vibration to be applied to the body for thereby decreasing the vibration thereof.
TL;DR: In this article, a higher-order shear-deformable beam model is proposed, which is based on a higher order displacement model and incorporates linear and quadratic variation of transverse normal strain and transverse shearing strain through the beam thickness.