Incoming Elastic Wave Research Articles

Global sensitivity analysis of frequency band gaps in one-dimensional phononic crystals

Phononic crystals have been widely employed in many engineering fields, which is because of their unique feature of frequency band gaps. For example, their capability to filter out the incoming elastic waves, which include seismic waves, will have a significant impact on the seismic safety of nuclear infrastructure. To design accurately design the desired frequency band gaps, one must pay attention to how the input parameters and the interaction of the parameters can affect the frequency band gaps. Global sensitivity analysis can decompose the dispersion relationship of the phononic crystals and screen the variance attributed to each of the parameters and the interaction between them. Prior to the application in one-dimensional (1D) phononic crystals, this paper will first review the theory of global sensitivity analysis using variance decomposition (Sobol’ sensitivity analysis). Afterwards, the sensitivity analysis is applied to study a simple mathematical model with three input variables for a better understanding of the concept. Then, the sensitivity analysis is utilized to study the characteristic of the first frequency band gap in 1D phononic crystals with respect to the input parameters. This study reveals the quantified influence of the parameters and their correlation in determining the first frequency band gap. In addition, simple straight-forward design equations based on reduced Sobol’ functions are proposed to estimate easily the first frequency band gap. Finally, the error associated with the proposed design equations is also addressed.

Theoretical and experimental study of shaped charge jet penetration into high and Ultra-high strength concrete targets

The depth of penetration (DOP) for concrete targets generated by a jet is required to achieve a certain value, under the premise of which the crater diameter must be sufficiently large in the present design of a shaped charge. A large cavity generated by the precursor shaped charge of a tandem warhead is conducive to the penetration of the follow-through projectile. Given the rapidly developing and increasingly extensive application of high and ultra-high strength concrete (H&UHSC), which has excellent resistance to penetration, impact and blasting, shaped charge jet penetration into the targets was investigated in this study. The chase between the incoming elastic wave, plastic wave and the jet/target interface as the shaped charge jet moves into H&UHSC targets were discussed. The response regions in the target were analyzed. Four penetration stages were proposed, while the corresponding modified Bernoulli equations were established. The two-stage mechanism of cavity growth was used to describe the penetration modes. Furthermore, the DOP experiments for two different structures of shaped charge penetration into H&UHSC targets with four strength grades were conducted. The predictions of depths and hole profiles from the present model correlate with the experimental data reasonably well. Results indicate that the DOP decreases exponentially as the compressive strength of H&UHSC increases at the beginning, and then the rate of the decreasing tendency slows down gradually and approximates the limit when the compressive strength approaches 200 MPa. Moreover, the cavity diameters resulted from the jet into the H&UHSC targets exhibit insensitivity to the increasing strength grade. The jet with diverse velocity and diameter structure may experience different penetration stages as it penetrates various H&UHSC targets, which affects the penetration result.

One sensor acoustic emission localization in plates

Acoustic emissions are elastic waves accompanying damage processes and are therefore used for monitoring the health state of structures. Most of the traditional acoustic emission techniques use a trilateration approach requiring at least three sensors on a 2D domain in order to localize sources of acoustic emission events. In this paper, we present a new approach which requires only a single sensor to identify and localize the source of acoustic emissions in a finite plate. The method proposed makes use of the time reversal principle and the dispersive nature of the flexural wave mode in a suitable frequency band. The signal shape of the transverse velocity response contains information about the propagated paths of the incoming elastic waves. This information is made accessible by a numerical time reversal simulation. The effect of dispersion is reversed and the original shape of the flexural wave is restored at the origin of the acoustic emission. The time reversal process is analyzed first for an infinite Mindlin plate, then by a 3D FEM simulation which in combination results in a novel acoustic emission localization process. The process is experimentally verified for different aluminum plates for artificially generated acoustic emissions (Hsu–Nielsen source). Good and reliable localization was achieved for a homogeneous quadratic aluminum plate with only one measurement.

Acoustic metamaterial plates for elastic wave absorption and structural vibration suppression

This article presents the design and modeling techniques and design guidelines, and reveals the actual working mechanism of acoustic metamaterial plates for elastic wave absorption and structural vibration suppression. Each of the studied metamaterial plates is designed by integrating two (or one) isotropic plates with distributed discrete mass-spring-damper subsystems that act as local vibration absorbers. For an infinite metamaterial plate, its stopband is obtained by dispersion analysis on an analytical unit cell. For a finite metamaterial plate with specific boundary conditions, frequency response analysis of its full-size finite-element model is performed to show its stopband behavior, and the stopband behavior is further confirmed by transient analysis based on direct numerical integration of the finite-element equations. Influences of the vibration absorbers׳ local resonant frequencies and damping ratios and the plate׳s damping, boundary conditions, and natural frequencies and mode shapes are thoroughly examined. The concepts of negative effective mass and spring and acoustic and optical wave modes are explained in detail. The working mechanism of acoustic metamaterial plates is revealed to be based on the concept of conventional vibration absorbers. An absorber׳s resonant vibration excited by the incoming elastic wave generates a concentrated inertial force to work against the plate׳s internal shear force, straighten the plate, and attenuate/stop the wave propagation. Numerical results show that the stopband׳s location is determined by the local resonant frequency of absorbers, the stopband׳s width increases with the (absorber mass)/(unit cell mass) ratio, and increase of absorbers׳ damping significantly increases the stopband׳s width and reduces low-frequency vibration amplitudes. However, too much damping may deactivate the stopband effect, and the plate׳s material damping is not as efficient as absorbers׳ damping for suppression of low-frequency vibrations.

Theory of Metamaterial Beams for Broadband Vibration Absorption

This article presents methods for modeling, analysis, and design of metamaterial beams for broadband vibration absorption/isolation. The proposed metamaterial beam consists of a uniform isotropic beam with many small spring-mass-damper subsystems integrated at separated locations along the beam to act as vibration absorbers. For a unit cell of an infinite metamaterial beam, governing equations are derived using the extended Hamilton principle. The existence of stopband is demonstrated using a model based on averaging material properties over a cell length and a model based on finite element modeling and the Bloch-Floquet theory for periodic structures. However, these two idealized models cannot be used for finite beams and/or elastic waves having short wavelengths. For finite metamaterial beams, a linear finite element method is used for detailed modeling and analysis. Both translational and rotational absorbers are considered. Because results show that rotational absorbers are not efficient, only translational absorbers are recommended for practical designs. The concepts of negative effective mass and stiffness and how the spring-mass-damper subsystems create a stopband (i.e., no elastic waves in this frequency range can propagate forward) are explained in detail. Numerical simulations reveal that the actual working mechanism of the proposed metamaterial beam is based on the concept of conventional mechanical vibration absorbers. It uses the incoming elastic wave in the beam to resonate the integrated spring-mass-damper absorbers to vibrate in their optical mode at frequencies close to but above their local resonance frequencies to create shear forces and bending moments to straighten the beam and stop the wave propagation. This concept can be easily extended to design a broadband absorber that works for elastic waves of short and long wavelengths. Numerical examples validate the concept and show that, for high-frequency waves, the structure’s boundary conditions do not have significant influence on the absorbers’ function. However, for absorption of low-frequency waves, the boundary conditions and resonant modes of the structure need to be considered in the design. With appropriate design calculations, finite discrete spring-mass-damper absorbers can be used, and hence expensive micro- or nanomanufacturing techniques are not needed for design and manufacturing of such metamaterial beams for broadband vibration absorption/isolation.

Seismic response of 3D topographical irregularities under incoming elastic waves from point sources

We study some effects that produce 3D topographical irregularities under incoming elastic waves from point sources using the indirect boundary element method. This technique is based on the representation of elastic waves in terms of single-layer boundary sources. In this way reflected and diffracted waves are constructed at the boundaries from where they are radiated by means of boundary sources. The field emited from the point source is computed with the moment tensor for a shear dislocation and analytical expressions of the elastodynamic 3D Green's functions. In this way we can construct a double couple with variable orientation. We compare the technique with that of Bouchon, who used the discrete wave number method for a shear dislocation in a halfspace with a triangular source function. We subsequently apply our method to simulate the seismic response of a mountain of ellipsoidal geometry. The source function that we have considered is a triangular pulse and we show results corresponding to the velocity registered over the surface of the irregularity and that of the halfspace. This motion is presented by means of snapshots showing the evolution of the wavefields that are present in the problem.