Wave Propagation Response Research Articles

Wave propagation in anisotropic media with non-local elasticity

In an effort to understand and quantify the effect of non-local elasticity on the wave propagation response of laminated composite layered media, a frequency-wavenumber domain based finite element method is employed. The developed elements are based on the exact solution in the transformed domain and thus exactly represent the dynamics of a layer. This feature enables to model a layer of any thickness by a single element and drastically reduces the cost of computation. The effect of non-locality on the dispersion relation and in turn on the wave response is compared with local (classical) elasticity solutions. A procedure and sample example is outlined to estimate the magnitude of the non-locality parameter by comparing the dispersion relation with lattice dynamics. The effect of non-locality, in terms of the mode-shift and appearance of dispersion on the modes of Lamb waves is further demonstrated.

Analysis of dynamic mechanical behavior in reverse Taylor anvil-on-rod impact tests

A one-dimensional analytical model has been developed for the reverse Taylor anvil-on-rod impact experiment to provide a method of extracting quantitative information from transient deformation states obtained from high-speed camera data. An indication of the plastic wave velocity and dynamic flow stress at varying locations and time are presented for two Cu OFE specimens impacted at 83 ± 1 and 205 ± 3 m / s . The results provide supporting evidence of previously reported “non-linear” and “quasi-steady” plastic wave propagation response, as well as a region of perfectly plastic behavior, which is independent of strain rate in the higher impact velocity experiment. Additionally, the results show good agreement with the average value of dynamic yield stress calculated using Wilkins’ analysis, based on a perfectly plastic material response. Furthermore, this work demonstrates the importance of careful design of Taylor impact experiments for minimizing measurement error and capitalizing on perfectly plastic response, for investigating the dynamic mechanical behavior of materials.

Impact identification on a sandwich plate from wave propagation responses

This study investigates the use of an impact detection algorithm to locate a potentially damaging impact on an orthotropic plate by detecting the stress waves generated by such an event. The proposed algorithm was tested experimentally on a sandwich plate by using ultrasonic signals. The arrival times of stress waves at different frequencies at the sensor locations were determined by analyzing the recorded signals using the wavelet transforms. The stress wave propagation phenomenon was characterized by measuring the propagation speeds along different directions. This data along with the sensor co-ordinates were input into the impact detection algorithm, which uses the difference in time of flight to the sensors and trigonometric identities to locate impact source locations. The accuracy of the method was demonstrated by the close agreement observed between the estimated locations for the three impact locations studied with the actual locations of the impact loads applied. In particular, maximum error in the estimation of the co-ordinates of the impact location was less than 9% for all different types of loading considered.

Dynamic Force–Penetration Curves in Rock by Matching Theoretical to Experimental Wave Propagation Response

Dynamic Force–Penetration Curves in Rock by Matching Theoretical to Experimental Wave Propagation Response

Dynamic force-penetration curves in rock by matching theoretical to experimental wave propagation response

A methodology to obtain the dynamic force-penetration curve of a rock specimen is presented. For this, a simple portable experimental setup is used. On one end, a hand-held hammer strikes a slender chisel. On the other end the chisel is in contact with the rock specimen into which the generated stress wave propagates. Strain gages installed at a selected section of the chisel are recorded throughout the impact duration. The theoretical signal at the same section is simulated using a numerical method based on the impulsemomentum principle previously developed by the author. Essentially the shape of the simulated theoretical response at the strain gage section depends on the impact velocity of the hammer and the slope of the assumed force-penetration curve. These two parameters are adjusted until the shape of the theoretical signal at the strain gage closely matches the experimental signal. Due to its simplicity, the proposed methodology has the potential of becoming a standard dynamic test for obtaining the force-penetration curvs in rocks.

Wave Propagation and Site Response in the Santa Clara Valley

Forty-two portable digital instruments were deployed across the Santa Clara Valley from June until early November 1998; this array recorded 14 small and moderate local events and 7 large teleseismic events. We analyze the ground motion from these events to determine station delays and relative site amplification within the Valley. P waves from an event at the southern edge of the valley are early (Δ t > -0.35 sec) at stations over an axial ridge in the basement interface in the middle of the valley, but late (Δ t < 0.20 sec) for stations over the Cupertino and Evergreen basins to either side. The S -wave delays are approximately twice as large. Teleseismic P -waves from an M = 7.0 event beneath the Bonin Islands show a similar pattern in travel-time delays. The P waves are amplified by factors of 1.5-3 for frequencies below 2 Hz at stations within either basin, compared with stations on the axial ridge. The P -wave coda appear enhanced at 2-3 sec, but coda Q estimates at frequencies from 0.2 to 1.1 Hz are not markedly different at stations over the basin compared with stations on the ridge with the possible exceptions of consistently high values over the northern end of the Evergreen Basin. We invert the S -wave spectra for site-specific attenuation and amplification from the 14 local events by assuming a common source spectra for each event, 1/ r geometrical spreading, and constraining the inversion using the 30-m velocity profile at four stations in the array. The largest amplifications occurred in the 1- to 6-Hz band at stations near the northwest edge of the Evergreen basin. While the highest amplifications occur at stations with the lowest S -wave velocities, the scatter obscures the correlation between velocity and amplification. The stations in the basins are characterized by higher attenuation than the stations on the basement ridge. Manuscript received 2 July 2001.

Acontinuous sensor for damage detection in bars

The concept of a continuous sensor for detectingvibration and stress waves in bars is investigated in thispaper. This type of sensor is a long tape with a number ofsensing nodes that are electrically connected together to forma single sensor with one channel of data output. The spacing ofthe sensor nodes can be designed such that the sensor iscapable of detecting acoustic emissions (AEs) occurring at any pointalong the length of the sensor. An active fiber compositematerial or piezoceramic wafers can be used as the activeelement of the sensor. The characteristics of this new type ofsensor were investigated by a simplified simulation and throughexperiments. The scope of the simulation is primarily todetermine the characteristics of the new type of sensor that isproposed and the simulation is not intended to model thecomplex dispersion characteristics of guided waves in bars. The sensor was modeled as being integrated within a uniformcantilever bar to measure longitudinal stress wave propagation.Damping was included in the model to attenuate the wave as ittravels. The sensor was connected to an electrical tuningcircuit to examine the capability to filter out undesirablenoise due to ambient vibration that would occur in practice. Theelastic response of the bar was computed in closed form, and thecoupled piezoelectric constitutive equations and electriccircuit equations were solved using the Newmark-Beta numericalintegration method. Strain, vibration, and wave propagationresponses were simulated and results indicate that damage tothe bar can be detected by recognizable changes in the sensoroutput as the wave propagates along the bar and passes over eachsensor node. Experiments were performed to verify the concept ofthe continuous sensor on a composite bar. The testing showedthe continuous sensor can replace four or more individualsensors to detect AEs and thus may be apractical method for structural health monitoring.

Finite element analysis of free vibration and wave propagation in asymmetric composite beams with structural discontinuities

A new refined locking free first-order shear deformable finite element is presented, and its utility in solving free vibration and wave propagation problems in laminated composite beam structures with symmetric as well as asymmetric ply stacking is demonstrated. The paper also illustrates the application of the element to handle different types of structural discontinuities such as ply-drops, multiply connected beams with rigid joints, lap joints and the beams with delaminations. The developed finite element has a static stiffness matrix that is obtained by exactly solving the axial–flexural–shear coupled governing homogeneous differential equations. Results from the analysis show that the formulated element predicts response that compares very well with the available results reported in the literature. A novel way of modeling structural discontinuities such as delamination is given which significantly reduces the modeling effort to determine static, dynamic and wave propagation responses quickly and accurately.

A Continuous Sensor to Measure Acoustic Waves in Plates

An active fiber composite tape with segmented electrodes was modeled for use as a continuous sensor for structural health monitoring of plate structures. The material has unidirectional piezoceramic fibers with interdigital electrodes on the top and bottom surfaces and is poled in the fiber direction. The elastic response of a plate with the modeled sensor was computed in closed form at small time steps, and the coupled piezoceramic constitutive equations were solved. Wave propagation responses and the corresponding sensor voltages were computed in the simulations. The simulations indicate that the continuous sensor can detect damage to the plate based upon high frequency wave propagation characteristics. A continuous sensor comprised of monolithic piezoceramic patches was built and tested to measure simulated acoustic emissions on panel structures. The monolithic patches were used to simplify fabrication of the sensor. The sensor detected simulated acoustic emissions in a fiberglass panel using only one channel of data acquisition. The continuous sensor can potentially reduce the cost, complexity, number of channels of data acquisition, and the weight of monitoring instrumentation to a level where it becomes practical to perform health monitoring on large structures.

Analytical solutions of impact problems of rod structures with springs

In this paper, the analytical solutions of rigid (without the contact deformation) impact problems of two typical rod structures with elastic-supports are given. The effects of boundary conditions upon wave propagation and impact responses are thoroughly analyzed by illustrative examples, and there are no difference between results obtained here and those of wave theory. The nonlinear impact problem of a particle on a rod is also studied, and the validity of the adopted solving technique is verified by the comparison with known method.

Stream-Aquifer Interaction Model with Diffusive Wave Routing

A practical approach to modeling the hydraulic interaction of a stream and aquifer via streambed leakage is based on the established U.S. Geological Survey (USGS) model, MODFLOW. To represent flood-wave propagation and the associated bank storage, MODFLOW’s STREAM module is replaced by the Muskingum-Cunge diffusive-wave-routing scheme. The diffusive wave model closely approximates a dynamic model of a flood wave’s speed, shape, and streambed leakage. Because the stream responds more rapidly to disturbances than the aquifer, streambed leakage is calculated at the flood routing time scale in order to properly represent the stream-aquifer coupling. However, both the relative magnitude and timing of aquifer response to a flood wave depend on the strength of this coupling. We find discrepancies in both the flood wave and the streambed leakage when the wave and ground-water motions are evaluated at different time scales. These discrepancies are significant in the case of a strong stream-aquifer coupling, for which equal aquifer and flood-routing time steps may be required. Wave diffusion and bank storage are shown to be comparable in magnitude and should, therefore, be included in stream-aquifer interaction models. Diffusive wave routing more accurately represents wave propagation, bed leakage, and aquifer response if short aquifer time steps are taken, and is preferable to the STREAM module for simulating short time transients. However, the STREAM module is useful for simulating large time frames if accurate modeling of the flood-wave propagation is not required.

Dynamics of Disordered Periodic Structures

For functional or aesthetic reasons, many a structural system is designed to be spatially periodic; namely, it is composed of identical sub-units which are connected to form a spatially periodic pattern. The main construction of the hull of a ship, the fuselage of an aircraft, and a space antenna are examples. Such a structure possesses interesting dynamic properties. However, due to material, geometric and manufacturing variabilities, an ideally periodic structure does not exist. The departure from the ideal designed configuration is known as disorder, which can cause drastic change in the dynamic behavior. The present paper gives a review of some recent works on wave propagation and frequency response of disordered periodic structures, of interest to researchers on vibration and noise control.

Impact force identification from wave propagation responses

The inverse problem of solving for the impact force history using experimentally measured structural responses tends to be ill-conditioned. This paper uses a frequency domain deconvolution method to help clarify some of the fundamental difficulties and issues involved in this problem. Force reconstructions obtained using experimentally measured acceleration responses from four example structures are used to illustrate the points.

Ray Solutions on Surfaces of Revolution

Our concern is the development of techniques for the analysis of wave propagation and general transient response of thin shells to local loading. In general, ray methods are useful for such problems. In the present work, the ray solutions are obtained for a shell of revolution with high prestress, for which the bending stiffness of the shell wall can be neglected. The equation is that for an inhomogeneous, anisotropic medium with a non-Euclidean metric. Of special interest in the present shell problem is the global connectivity of ray paths. For an example the conical shell is considered. The rays for uniform pressure are shown to deviate substantially from geodesics. A ray emitted from a point on the cone may make several spirals around the small end of the cone before moving toward the large end in an almost straight line. The implication is that high focusing of energy can occur from a mild impact on the side of a conical shell.

A Penalty Function Type of Virtual Work Principle for Impact Contact Problems of Two Bodies

This paper shows how an impact contact force can be expressed as a product series of penalty functions and subsidiary contact conditions having relative movement components between two bodies on a contact surface. A penalty function type of virtual work principle for various contact and separate states of two bodies is formulated by using the expression of the impact force. This principle is most effective for solving a general impact response of the alternation between contact and separation, and a stress wave propagation response of cracked structures with open and/or closed states on a cracked surface, because of both the use of the relative components and the relaxation of all the subsidiary conditions in this principle. A finite element method (FEM) based on this principle is applied to a two-dimensional analysis for longitudinal impact of two uniform rods. The mean value of impact force by FEM results coincides well with the value from the theory of one-dimensional elastic stress wave propagation.

A penalty function type of virtual work principle for impact contact problems of two bodies.

This paper presents that an impact contact force can be expressed as the product series of penalty functions and subsidiary contact conditions having relative movement components between two bodies on a contact surface. A penalty function type of virtual work principle for various contact and separate states of two bodies is formulated by using the expression of the impact force. This principle is most effective for solving a general impact response of the alternation between contact and separation, and a stress wave propagation response of cracked structures with open and/or closed states on a cracked surface. This is because of both the use of the relative components and the relaxation of all the subsidiary conditions in this principle. A finite element method (FEM) based on this principle is applied to a two- dimensional analysis for longitudinal impact of two uniform rods. The mean value of impact forced by FEM results coincides well with the value from the theory of one-dimensional elastic stress wave propagation.

Use of Ritz vectors in wave propagation and foundation response : Bayo, E P; Wilson, E L Earthq Engng Struct DynamV12, N4, July–Aug 1984, P499–505

Use of Ritz vectors in wave propagation and foundation response : Bayo, E P; Wilson, E L Earthq Engng Struct DynamV12, N4, July–Aug 1984, P499–505

Use of ritz vectors in wave propagation and foundation response

AbstractThe accuracy of a numerical method is demonstrated for the dynamic analysis of large complex finite element systems in which the spatial distribution of the loading is constant. The method is based on the use of a special class of Ritz vectors which were previously proposed and can be generated with minimum numerical effort. The purpose of this paper is to extend the use of these vectors to the solution of wave propagation and foundation response problems.The method is applied to one‐, twoand three‐dimensional problems in order to illustrate the efficiency and accuracy of the technique. Unless it is necessary to evaluate the very high‐frequency behaviour of a structural system, it is shown that a small number of Ritz vectors will produce excellent results. Therefore, they can be very effective in the solution of three‐dimensional soil‐structure systems subjected to earthquake loading.

Wave propagation and vibration response of a periodically supported pipe conveying fluid

Propagation of free harmonic waves, in a periodically supported infinite pipe, has been studied. The presence of the Coriolis term in the equation of motion renders the phase velocity different for the positive and the negative going waves. Hence no classical normal modes (in the sense of standing modes) exist. Natural frequencies of a periodically supported finite pipe have been obtained by using the wave approach. The response of the infinite pipe to a convected harmonic pressure field has also been obtained. Owing to the difference in the phase velocities of the positive and the negative going free waves, the coincidence frequency depends on the direction of the convected loading. The static buckling or the divergence instability of such pipes has also been considered from the wave approach.