Incident Compression Wave Research Articles

Bond-associated non-ordinary state-based peridynamic model for multiple spalling simulation of concrete

The non-ordinary state-based peridynamic (NOSB PD) model has the capability of incorporating existing constitutive relationships in the classical continuum mechanics. In the present work, we first develop an NOSB PD model corresponding to the Johnson–Holmquist II (JH-2) constitutive damage model, which can describe the severe damage of concrete under intense impact compression. Besides, the numerical oscillation problem of the NOSB PD caused by zero-energy mode is analyzed and hence a bond-associated non-ordinary state-based peridynamic (BA-NOSB PD) model is adopted to remove the oscillation. Then, the elastic deformation of a three-dimensional bar is analyzed to verify the capability of BA-NOSB PD in eliminating the numerical oscillation. Furthermore, concrete spalling caused by the interaction of incident compression wave and reflected tension wave is simulated. The dynamic tensile fracture process of concrete multiple spalling is accurately reproduced for several examples according to the spalling number and spalling thickness analysis, illustrating the approach can well simulate and analyze the concrete spalling discontinuities.

A blast-tolerant sandwich plate design with a polyurea interlayer

This paper presents a study of both conventional and modified sandwich plate designs subjected to blast loads. The conventional sandwich Design (1) consists of thin outer (loaded side) and inner facesheets made of fibrous laminates, separated by a layer of structural foam core. In the modified Design (2), a thin polyurea interlayer is inserted between the outer facesheet and the foam core. Comparisons of the two designs are made during a long time period of 5.0 ms, initiated by a pressure impulse lasting 0.05 ms applied to a single span of a continuous plate. In the initial response period the overall deflections are limited and significant foam core crushing is caused in the conventional design by the incident compression wave. This type of damage is much reduced in the modified design, by stiffening of the polyurea interlayer under shock compression, which provides support to the outer facesheet and alters propagation of stress waves into the foam core. This benefits the long term, bending response and leads to significant reductions in facesheet strains and overall deflection. The total kinetic energy of the modified sandwich plate is much lower than that of a conventionally designed plate, and so is the stored and dissipated strain energy. Similar reductions are found when the conventional and the enhanced sandwich plates have equal overall thickness or equal total mass.

Reflection and transmission of a compression wave at a tunnel portal

Analyses are made of the interaction of the nonlinearly steepened, compression wavefront generated by a high-speed train in a tunnel with the tunnel portal ahead of the train. The ‘micro-pressure’ pulse emitted from the portal can rattle structures in nearby buildings, and the expansion wave reflected back towards the train can cause discomfort to passengers. It is concluded that the usual simplified approximation of one-dimensional propagation within the tunnel provides an adequate representation of interactions of the wave with the portal, and also with ‘windows’ in the tunnel wall near the portal. It is shown how a discrete distribution of windows can be used to produce a reflected expansion wave that varies linearly across the wavefront, and how the thickness of that wavefront can be made many times larger than the thickness of the incident compression wave profile. A detailed analysis of the wave radiated from the portal reveals that cumulative nonlinear effects of propagation over long distances make little or no contribution to the free-space radiation of the micro-pressure wave.

An experimental method for dynamic tensile testing of concrete by spalling

A new application of the spalling phenomenon in long specimens is reported in this paper. The new experimental technique is based on an experimental setup which consists of an air launcher of cylindrical projectiles with a Hopkinson bar as a measuring tool and a relatively long concrete specimen in contact with the bar. The incident compression wave transmitted by the Hopkinson bar into the specimen is reflected as a tensile wave causing spalling. Although such configurations have been reported in the past, the main advantage of the present approach lies in the application of the detailed analysis, based on the wave mechanics with dispersion, to extract the specimen behaviour. Such an approach leads to an exact estimation of the local failure stress in tension at high strain rates, even above 100 s −1. This paper demonstrates, using two series of tests on concrete, that this experimental setup can cover one decimal order of strain rates, from ∼10 to ∼120 s −1. The tests performed at high strain rates on wet and dry concrete have indicated that the tensile strength is substantially influenced by the loading rate or strain rate. The absolute value of the failure stress for wet and dry concrete is almost the same for a particular strain rate, which does not occur when subject to low strain rates in tension or compression. A brief discussion is offered on a high rate sensitivity of concrete strength in tension at high strain rates.

Experimental study on compression wave propagating in a sudden reduction duct

Compression waves propagating in a high-speed railway tunnel develops large pressure fluctuations on the train body or tunnel structures. The pressure fluctuations would cause an ear discomfort for the passengers and increase the aerodynamic resistance of trains. As a fundamental research to resolve the pressure wave phenomenon in the tunnel, experiments were carried out by using a shock tube with an open end. A blockage to model trains inside the tunnel was installed on the lower wall of shock tube, thus forming a sudden cross-sectional area reduction. The compression waves were obtained by the fast opening gate valve instead of a conventional diaphragm of shock tube and measured by the flush mounted pressure transducers with a high sensitivity. The experimental results were compared with the previous theoretical analyses. The results show that the ratio of the reflected to the incident compression wave at the sudden cross-sectional area reduction increases but the ratio of the passing to the incident compression wave decreases, as the incident compression wave becomes stronger. This experimental results are in good agreements with the previous theoretical ones. The maximum pressure gradient of the compression wave abruptly increases but the width of the wave front does not vary, as it passes over the sudden cross-sectional area reduction.

Theoretical study on compression wave propagating in a sudden reduction duct

Compression waves propagating in a high speed railway tunnel impose large pressure fluctuations on the train body or tunnel structures. The pressure fluctuations can cause ear discomfort for the passengers and increase the aerodynamic resistance of trains. As a fundamental research to resolve the pressure wave phenomenon in the tunnel, a steady theory of Chester-Chisnell- Whitham was applied to a simple shock tube with a sudden cross-sectional area reduction to model trains inside the tunnel. The results of the present theoretical analysis were compared with the experiments of the shock tube. The results show that the reflected compression wave from the model becomes stronger as the strength of incident compression wave and the blockage ratio increase. However, the compression wave passing through the model is not strongly dependent on the blockage ratio. The theoretical results are in good agreement with the experiments.

Emission of a Propagating Compression Wave from an Open End of a Tube. 2nd Report. Relation between Incident Compression Wave and Impulsive Wave.

When a compression wave propagates along a constant-area straight tube and reaches its open end, an impulsive wave is emitted outward from the exit toward the surrounding area. Assuming a compression waveform as an arctangent curve, the magnitude of an impulsive wave is obtained explicitly in terms of the pressure rise and length of the compression wave. The variation of pressure with time at the exit and the magnitude of an impulsive wave obtained from the present method agree well with the numerical results solved by the TVD scheme.

Calculations of the reflection and transmission of ultrasound by cracks in steel filled with solid sodium

The reflection and transmission coefficients are calculated for 2.25 MHz compression and shear waves incident on idealized cracks (ie, a slot with smooth, flat, parallel faces) in steel filled with solid sodium. The coefficients are calculated as a function of crack width and angle of incidence. Both polarizations (SV and SH) of shear wave are considered, as well as compression wave incidence. It is concluded that a crack of width 0.01 mm or greater, full of solid sodium, will return at least 10% of the incident compression wave amplitude. With a suitable choice of inspection angle, 40% reflection of the incident amplitude can be achieved for either compression or shear (SV) waves. The use of shear waves with the uncommon SH polarization also looks promising.

Calculations of the reflection and transmission of ultrasound by cracks in steel filled with liquid sodium

The ultrasonic reflection and transmission amplitudes of idealized cracks in steel filled with liquid sodium are calculated as a function of the angle of incidence and crack width for an incident compression wave of frequency 2.25 MHz. It is concluded that it should be no more difficult to detect a liquid-sodium filled crack than an air filled crack for widths greater than 0.01 mm, which is typical of fatigue crack widths.

Reflection of nonlinear shock waves in a lattice

An analysis is made of the longitudinal shock response of a finite one-dimensional elastic lattice with a step jump in velocity applied at one end and the remaining end free. For linearly elastic interactions between nearest-neighbor particles, an exact solution is obtained using transform theory. For nonlinear elastic interactions, an asymptotic solution is obtained for the head of the pulse response near the free end, in terms of incident compression wave and reflected tension wave contributions. Nonlinear solutions for particle velocity and strain response near the free end are presented and discussed when the incident shock wave that has evolved in a lattice is of oscillatory form or is a sequence of solitary waves. On reflection of an incident shock wave at a free end, the strain response of a lattice behind the reflected wave rapidly alternates between compression and tension rather than behaving as an elastic continuum with a strain-free response. The cumulative effect of nonlinear elastic interaction is to accentuate these changes near the free end and noticeably increase the difference between lattice and continuum responses.

Diffraction of Elastic Waves

An integral solution to the differential equations of elastodynamics is given. The solution for the displacement at any point in an isotropic homogeneous, elastic medium is obtained in terms of the initial distribution of body forces within a given volume and the initial distribution of displacements and stresses over the bounding surface of the volume. These quantities appear in the solutions as retarded displacements, stresses, and body forces, with two types of retardation depending upon the velocities of longitudinal and transverse waves. From the integral solution the diffraction of elastic waves through large apertures bounded by opaque walls in solid materials is formulated. The incident wave motions may be either of longitudinal or transverse polarizations. The expected shear-compression interaction is obtained in the course of the computation. By analogy with optical procedure, Fraunhofer diffraction of elastic waves may be investigated as a special case. In the example of diffraction by a slit, an incident compression wave is diffracted into (1) a compression wave with the “ordinary” spatial distribution similar to that obtained in the corresponding optical problem and (2) a weaker shear wave with an “extraordinary” distribution. In the case of incident shear waves, there is obtained a diffracted shear wave with an ordinary distribution, and a possible weak compression wave with the extraordinary distribution. The presence of the diffracted compression wave depends upon the polarization of the incident shear wave. Opacity in the Kirchhoff sense is a property of materials which are perfectly rigid.