Showing papers in "Shock and Vibration in 1998"

Review: Rotor balancing

Abstract: This article reviews the literature concerning the balancing of rotors including the origins of various balancing techniques including ones that use influence coefficient, modal, unified, no phase, and no amplitude methods to balance. This survey covers the computational algorithms as well as the physical concepts involved in balancing rotating equipment.

Modeling Mitigation Effects of Watershield on Shock Waves

Abstract: The object of this analysis is to investigate mitigation effects of watershield on air blast waves. To examine the water mitigation concept, features of the free-field detonation process are studied from a series of one-dimensional simulations using a multimaterial Eulerian finite element technique. Five different shock Hugoniots for water are compared, and the most accurate data are suggested. To verify the numerical procedure, results are compared with available experimental data for UNDEX problem and analytical predictions for air shocks. For the case of contact watershield, the magnitude of peak pressure generally decreases and the shock arrival time increases with increasing thickness of watershield. The total pressure impulse is reduced significantly at near field. Non-contact watershield was also examined, and was found to provide a better design criterion based on the further decay of peak pressure.

Empirical Mode Decomposition and Hilbert Spectral Analysis

Abstract: The difficult facing data analysis is the lack of method to handle nonlinear and nonstationary time series. Traditional Fourier-based analyses simply could not be applied here. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data. This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. Examples from the numerical results of the classical nonlinear equation systems and data representing natural phenomena are given to demonstrate the power of this new method. The classical nonlinear system data are especially interesting, for they serve to illustrate the roles played by the nonlinear and nonstationary effects in the energy-frequency-time distribution.

Dynamic Response of Cantilevered Thin-Walled Beams to Blast and Sonic-Boom Loadings

Abstract: The paper deals with the dynamic response of anisotropic cantilevered thin-walled beams exposed to blast and sonic boom loadings. The structural model used in this study incorporates a number of nonclassical effects such as transverse shear and warping inhibition. Moreover, implementation of a specific ply-angle scheme in each constituent lamina results in elastic cross-couplings beneficial from the response behavior point of view. The influence of these effects is highlighted and the efficiency of the tailoring technique toward enhancing the dynamic response to various overpressure signatures is demonstrated.

Spherical solutions of an underwater explosion bubble

Abstract: The evolution of the 1D explosion bubble flow field out to the first bubble minimum is examined in detail using four different models. The most detailed is based on the Euler equations and accounts for the internal bubble fluid motion, while the simplest links a potential water solution to a stationary, Isentropic bubble model. Comparison of the different models with experimental data provides insight into the influence of compressibility and internal bubble dynamics on the behavior of the explosion bubble.

Surface ship shock modeling and simulation: two‐dimensional analysis

Abstract: The modeling and simulation of the response of a surface ship system to underwater explosion requires an understanding of many different subject areas. These include the process of underwater explosion events, shock wave propagation, explosion gas bubble behavior and bubble-pulse loading, bulk and local cavitation, free surface effect, fluid-structure interaction, and structural dynamics. This paper investigates the effects of fluid-structure interaction and cavitation on the response of a surface ship using USA-NASTRAN-CFA code. First, the one-dimensional Bleich-Sandler model is used to validate the approach, and second, the underwater shock response of a two-dimensional mid-section model of a surface ship is predicted with a surrounding fluid model using a constitutive equation of a bilinear fluid which does not allow transmission of negative pressures.

Underwater shock response analysis of a floating vessel

Abstract: The response of a surface vessel to underwater shock has been calculated using an explicit finite element analysis. The analysis model is two-dimensional and contains the floating steel structure, a large surrounding water volume and the free surface. The underwater shock is applied in the form ot a plane shock wave and cavitation is considered in the analysis. Advanced computer graphics, in particular video animations, provide a powerful and indispensable means for the presentation and evaluation of the analysis results.

Active Suspension of Truck Seat

Abstract: The driver’s seat of a heavy duty truck is usually mounted on a spring–damper assembly anchored to the cab floor. To improve riding comfort, this study investigated the effects of mounting a computer-controlled actuator in parallel with the traditional spring–damper assembly. A dynamic model of the seat is represented by a two degree-of-freedom system, including a cushion. In this paper, a control system is designed, using optimal control theory, which minimizes rms vertical acceleration at a point representing the driver’s hip point. In this system, accelerations of the hip point, the seat frame and the cab floor are picked up and integrated to obtain the state variables to be fed back and fed forward to the actuator through a digital computer. The actuator is constructed with electric servo-motor and ball-screw mechanism. The experimental study was carried out on a shaker, which simulates the vibrations of the cab floor in actual service. Results were obtained for both a dummy and a real human body. The vibration test produced rms accelerations of the seat and the hip point of about 1.0 m/s2 without the actuator, while the rms accelerations were suppressed to about 0.5 m/s2 at a rms input voltage to the servo-motor of 1.0 V.

Measuring the Acceleration of a Rigid Body

Abstract: Two methods to measure the six-degree-of-freedom acceleration of a point on a rigid body are presented. The first, referred to as the periphery scheme, makes use of three clusters of accelerometers mounted orthogonal to each other and coincident with the axes of the point. One of the clusters consists of the three accelerometers attached to a cube-shaped triaxial angular rate sensor (ARS). The second method, called the compact cube scheme, uses a single 3-accelerometer/ARS cluster that may be mounted anywhere on the rigid body. During impact tests with an instrumented rigid body, both methods produced measurements that were highly correlated near the time of peak acceleration. Whereas the compact cube scheme was more economical and easier to implement, the periphery scheme produced results that were less disrupted by instrument signal errors and noisy environments.

Wave dispersion and attenuation in viscoelastic split Hopkinson pressure bar

Abstract: A viscoelastic split Hopkinson pressure bar intended for testing soft materials with low acoustic impedance is studied. Using one-dimensional linear viscoelastic wave propagation theory, the basic equations have been established for the determination of the stress‐strain‐strain rate relationship for the tested material. A method, based on the spectral analysis of wave motion and using measured wave signals along the split Hopkinson pressure bar, is developed for the correction of the dispersion and attenuation of viscoelastic waves. Computational simulations are performed to show the feasibility of the method.

Review: Optimal Shock and Vibration Isolation

Abstract: This is a review of the investigations into the field of optimum shock and vibration isolation, including the mathematical foundations of both optimal open-loop and optimal feedback isolation systems. This survey covers the literature from the initial studies to the present.

On the vibration of a cracked rotating blade

Abstract: The dynamic behavior of a rotating blade containing a transverse crack was investigated. First, the local flexibility of the cracked blade was obtained by using the method of the released energy. An energy principle, in conjunction with a weighted residual method, was then applied to yield the discrete equations of motion. The equations of motion were further utilized to study the influences of the crack depth and location on the bending natural frequencies under various of rotation speeds. The numerical calculation showed that the crack effects the natural frequencies and the response appreciably only if it is relatively deep and locates near the root of the blade. However, the effects increase exponentially with the depth increases. In addition to the natural frequencies, the displacement responses of the blade with a crack under a constant lateral forces were discussed as well. This was done by calculating the deflections at the tip of the blade for various crack depths and locations. Similar to the rotation speed of the blade frequency, the deflection was offset by the increase of the rotation. However, the centrifugal effects increased significantly such that the crack’s effects became relatively insignificant. Nevertheless, the study showed that the changes on the natural frequency and the tip-deflection of the blade due to a crack may be used as indices for on-line detection of cracks.

Localizing Energy Sources and Sinks in Plates Using Power Flow Maps Computed From Laser Vibrometer Measurements

Abstract: This paper presents an experimental method especially adapted for the computation of structural power flow using spatially dense vibration data measured with scanning laser Doppler vibrometers. In the proposed method, the operational deflection shapes measured over the surface of the structure are curve-fitted using a two-dimensional discrete Fourier series approximation that minimizes the effects of spatial leakage. From the wavenumber-frequency domain data thus obtained, the spatial derivatives that are necessary to determine the structural power flow are easily computed. Divergence plots are then obtained from the computed intensity fields. An example consisting of a rectangular aluminum plate supported by rubber mounts and excited by a point force is used to appraise the proposed method. The proposed method is compared with more traditional finite difference methods. The proposed method was the only to allow the localization of the energy source and sinks from the experimental divergence plots.

Nonlinear response of cantilever beams to combination and subcombination resonances

Abstract: The nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinarydifferential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.

Optical measurement of cable and string vibration

Abstract: This paper describes a non contacting measurement technique for the transverse vibration of small cables and strings using an analog position sensing detector. On the one hand, the sensor is used to monitor the cable vibrations of a small scale mock-up of a cable structure in order to validate the nonlinear cable dynamics model. On the other hand, the optical sensor is used to evaluate the performance of an active tendon control algorithm with guaranteed stability properties. It is demonstrated experimentally, that a force feedback control law based on a collocated force sensor measuring the tension in the cable is feasible and provides active damping in the cable.

Fractal Two-Level Finite Element Method For Free Vibration of Cracked Beams

Abstract: The fractal two-level finite element method is extended to the free vibration behavior of cracked beams for various end boundary conditions. A cracked beam is separated into its singular and regular regions. Within the singular region, infinite number of finite elements are virturally generated by fractal geometry to model the singular behavior of the crack tip. The corresponding numerous degrees of freedom are reduced to a small set of generalized displacements by fractal transformation technique. The solution time and computer storage can be remarkably reduced without sacrifying accuracy. The resonant frequencies and mode shapes computed compared well with the results from a commercial program.

Identification of Unknown, Time-Varying Forces/Moments in Dynamics and Vibration Problems Using a New Approach To Deconvolution

Abstract: In this paper an alternative approach to the classical deconvolution idea is used to obtain a new and practical method for real-time identification of unknown, time-varying forces/moments in a general class of linear (linearized) dynamics and vibration problems with multiple-inputs and multiple-measurements This new method for force/moment identification is unique in the respect that the uncertainty in the force/moment time-variations is not characterized by random-process methods, but rather by a generalized splinemodel with totally unknown weighting coefficients and completely known basis-functions The basis-functions are custom chosen in each application to reflect, qualitatively, the known characteristics of the force/moment time-variations to be identified The method does not involve explicit identification of the unknown weighting coefficients Generalpurpose identification algorithms for both continuous-time and discrete-time measurements are developed, and a worked example including computer simulation results is presented

Magnetic Damping For Maglev

Abstract: Magnetic damping is one of the important parameters that control the response and stability of maglev systems. An experimental study to measure magnetic damping directly is presented. A plate attached to a permanent magnet levitated on a rotating drum was tested to investigate the effect of various parameters, such as conductivity, gap, excitation frequency, and oscillation amplitude, on magnetic damping. The experimental technique is capable of measuring all of the magnetic damping coefficients, some of which cannot be measured indirectly.

Investigation of subcombination internal resonances in cantilever beams

Abstract: Activation of subcombination internal resonances in transversely excited cantilever beams is investigated. The effect of geometric and inertia nonlinearities, which are cubic in the governing equation of motion, is considered. The method of time-averaged Lagrangian and virtual work is used to determine six nonlinear ordinary-differential equations governing the amplitudes and phases of the three interacting modes. Frequency- and force-response curves are generated for the case ω ≈ ω4 ≈ 1/2(ω2

Statistics of the von Mises stress response for structures subjected to random excitations

Abstract: Finite element-based random vibration analysis is increasingly used in computer aided engineering software for computing statistics (e.g., root-mean-square value) of structural responses such as displacements, stresses and strains. However, these statistics can often be computed only for Cartesian responses. For the design of metal structures, a failure criterion based on an equivalent stress response, commonly known as the von Mises stress, is more appropriate and often used. This paper presents an approach for computing the statistics of the von Mises stress response for structures subjected to random excitations. Random vibration analysis is first performed to compute covariance matrices of Cartesian stress responses. Monte Carlo simulation is then used to perform scatter and failure analyses using the von Mises stress response.

Sound Power Estimation by Laser Doppler Vibration Measurement Techniques

Abstract: The aim of this paper is to propose simple and quick methods for the determination of the sound power emitted by a vibrating surface, by using non-contact vibration measurement techniques. In order to calculate the acoustic power by vibration data processing, two different approaches are presented. The first is based on the method proposed in the Standard ISO/TR 7849, while the second is based on the superposition theorem. A laser-Doppler scanning vibrometer has been employed for vibration measurements. Laser techniques open up new possibilities in this field because of their high spatial resolution and their non-intrusivity. The technique has been applied here to estimate the acoustic power emitted by a loudspeaker diaphragm. Results have been compared with those from a commercial Boundary Element Method (BEM) software and experimentally validated by acoustic intensity measurements. Predicted and experimental results seem to be in agreement (differences lower than 1 dB) thus showing that the proposed techniques can be employed as rapid solutions for many practical and industrial applications. Uncertainty sources are addressed and their effect is discussed.

Damage occurrence under dynamic loading for anisotropic strain rate sensitive materials

Abstract: A damage model is integrated into the explicit finite element framework to predict the damage evolution which occurrs under dynamic loading in the crash or stamping process. This damage model is based on the description of the growth, nucleation and coalescence of the microvoids. The microvoid growth is related to the plastic incompressibility equation. The microvoid nucleation is controlled by either the plastic strain or stress. The microvoid coalescence is described by a specific function. This damage process leads to the progressive loss of the structure stress carrying capacity. The ductile fracture occurs once it has vanished. The model is adapted to take the material behaviour anisotropy and damage anisotropy into account. The sensitivity of the damage evolution under dynamic loadings in the case of porous strain rate sensitive material is analysed using single tensile tests. Static and dynamic tensile tests of a notched specimen are performed. Influences of the strain rate and the shape of specimen on the failure mode and loss of the structure’s stress carrying capacity are shown.

Effects of boundary conditions on the parametric resonance of cylindrical shells under axial loading

Abstract: In this paper, a formulation for the dynamic stability analysis of circular cylindrical shells under axial compression with various boundary conditions is presented. The present study uses Love’s first approximation theory for thin shells and the characteristic beam functions as approximate axial modal functions. Applying the Ritz procedure to the Lagrangian energy expression yields a system of Mathieu‐Hill equations the stability of which is analyzed using Bolotin’s method. The present study examines the effects of different boundary conditions on the parametric response of homogeneous isotropic cylindrical shells for various transverse modes and length parameters.

Random amplitude fatigue life of electroformed nickel micro-channel heat exchanger coupons

Abstract: The use of micro-channel heat exchangers (MCHEX) with coolant flow passage diameters less than 1 mm has been proposed for heat flux, weight, or volume limited environments. This paper presents room temperature, random amplitude, e − N (strain versus number of cycles to failure) curves for MCHEX coupons formed by electroplating nickel on a suitable form. These coupons are unique in two aspects; the microstructure formed by electroplating and the presence of holes as an integral part of the structure. The hole diameters range from approximately 10% to 50% to the specimen thickness. The fatigue life of electroformed nickel can be estimated from constant amplitude data using the formulation presented. The heat exchangers with channels parallel to the coupon direction have a lower fatigue life than the solid material.

Quasi-resonance effects observed in the 1994 Northridge earthquake, and others

Abstract: Sine-beat phenomena have been found in the 1994 Northridge earthquake records, and they are capable of producing time-history responses and damaging quasi-resonance effects in structures. Linear, single DOF (degree of freedom) oscillators, in lieu of nonlinear, multiple DOF systems, have been found adequate to discuss the failures of tall circuit breakers during the 1971 San Fernando and the 1989 Loma Prieta quakes in California. The use of sine-beat excitation for seismic-shaking-table tests of equipment continues to be a conservative simulation of earthquakes.

Fixed points of two-degree of freedom systems

Abstract: The presence of fixed points in a frequency response of vibrating systems can greatly complicate the vibration reduction if these points are not recognized. In this paper, the fixed points of two-degree of freedom systems are studied. The frequencies at which fixed points occur and their amplitudes are determined analytically.

Evaluation of Accelerometer Mechanical Filters on Submerged Cylinders Near an Underwater Explosion

Abstract: An accelerometer, mounted to a structure near an explosion to measure elasto-plastic deformation, can be excited at its resonant frequency by impulsive stresses transmitted within the structure. This results in spurious high peak acceleration levels that can be much higher than acceleration levels from the explosion itself. The spurious signals also have higher frequencies than the underlying signal from the explosion and can be removed by a low pass filter. This report assesses the performance of four accelerometer and filter assemblies. The assessment involves measurements of the response of a mild steel cylinder to an underwater explosion, in which each assembly is mounted onto the interior surface of the cylinder. Three assemblies utilise a piezoresistive accelerometer in which isolation is provided mechanically. In the fourth assembly, a piezoelectric accelerometer, with a built-in filter, incorporates both mechanical and electronic filtering. This assembly is found to be more suitable because of its secure mounting arrangement, ease of use, robustness and noise free results.

Collisions of constrained rigid body systems with friction

Abstract: A new approach is developed for the general collision problem of two rigid body systems with constraints (e.g., articulated systems, such as massy linkages) in which the relative tangential velocity at the point of contact and the associated friction force can change direction during the collision. This is beyond the framework of conventional methods, which can give significant and very obvious errors for this problem, and both extends and consolidates recent work. A new parameterization and theory characterize if, when and how the relative tangential velocity changes direction during contact. Elastic and dissipative phenomena and different values for static and kinetic friction coefficients are included. The method is based on the explicitly physical analysis of events at the point of contact. Using this method, Example 1 resolves (and corrects) a paradox (in the literature) of the collision of a double pendulum with the ground. The method fundamentally subsumes other recent models and the collision of rigid bodies; it yields the same results as conventional methods when they would apply (Example 2). The new method reformulates and extends recent approaches in a completely physical context.