Elastodynamic Behaviour of Laminate Structures with Soft Thin Interlayers: Theory and Experiment

Laminate structures composed of stiff plates and thin soft interlayers are widely used in aerospace, automotive and civil engineering encouraging the development of reliable non-destructive strategies for their condition assessment. In the paper, elastodynamic behaviour of such laminate structures is investigated with emphasis on its application in ultrasonic based NDT and SHM for the identification of interlayer mechanical and interfacial contact properties. A particular attention is given to the practically important frequency range, in which the wavelength considerably exceeds the thickness of the film. Three layer model with spring-type boundary conditions employed for imperfect contact simulation is used for numerical investigation. Novel effective boundary conditions are derived via asymptotic expansion technique and used for analysis of the peculiar properties of elastic guided waves in considered laminates. It is revealed that the thin and soft film influences the behaviour of the laminate mainly via the effective stiffnesses being a combination of the elastic moduli of the film, its thickness and interface stiffnesses. To evaluate each of these parameters separately (or to figure out that the available experimental data are insufficient), a step-wise procedure employing the effective boundary conditions is proposed and tested versus the laser Doppler vibrometry data for Lamb waves in Aluminium/Polymer film/Alumunium structure. The possibility of using film-related thickness resonance frequencies to estimate the film properties and contact quality is also demonstrated. Additionally, the rich family of edge waves is also investigated, and the splitting of fundamental edge waves into pairs is revealed.

Asymptotics of sloshing eigenvalues for a triangular prism

We consider the three-dimensional sloshing problem on a triangular prism whose angles with the sloshing surface are of the form ${\pi}/{2q}$ , where q is an integer. We are interested in finding a two-term asymptotic expansion of the eigenvalue counting function. When both angles are ${\pi}/{4}$ , we compute the exact value of the second term. As for the general case, we conjecture an asymptotic expansion by constructing quasimodes for the problem and computing the counting function of the related quasi-eigenvalues. These quasimodes come from solutions of the sloping beach problem and correspond to two kinds of waves, edge waves and surface waves. We show that the quasi-eigenvalues are exponentially close to real eigenvalues of the sloshing problem. The asymptotic expansion of their counting function is closely related to a lattice counting problem inside a perturbed ellipse where the perturbation is in a sense random. The contribution of the angles can then be detected through that perturbation.

Characteristics of maximal energy component of waves in Terpeniya Bay (Sakhalin Island)

Analysis of natural sea surface oscillations was performed in order to determine maximal spectral energy components in sea waves in the area of Terpeniya Bay. It has been found out that maximal components appear at periods of 5 and 8 seconds and reach energy of 3 · 106 cm2·s during storms. During calm weather maximums can be observed in the range of swell waves, herewith maximums exist at periods of 12 and 15 seconds. Energy of these maximums doesn’t go upper then 8 · 105 cm2·s and 3 · 105 cm2·s accordingly. Maximum components in the infragravity band of energy spectrum were estimated as well. Two steady energy peaks were determined at periods of 75 and 135 seconds, which are most probably relate to edge waves in considered water area.

The Detection of Impact Damage to the Edges of CFRP Plates Using Extensional Ultrasonic Edge Waves

Extensional edge waves propagate along the edges of plates, with low attenuation in the propagation direction and amplitude decreasing rapidly (within one or two wavelengths) in the direction perpendicular to the plate edge. This makes them an ideal candidate for inspecting the edges of plate-like structures. Here, finite-element models and experiments are used to investigate the propagation and scattering of extensional edge waves in composite plates and application to damage detection is demonstrated. Piezoceramic transducers attached to the edge of a 4-mm-thick carbon-fibre-reinforced polymer (CFRP) plate were used to excite 140-kHz edge waves and damage detection demonstrated using two experimental configurations: pitch-catch and two-transducer pulse-echo. Damage due to edge-on impacts of 5 J and 10 J were detected in both configurations. A mass-addition damage model was used to investigate the effect of damage location. Detection was specific to damage within 33 mm (1.5 wavelengths) of the plate edge with propagation unaffected by features beyond that distance. The time of arrival of reflected signals in pulse-echo mode was accurately predicted using the edge-wave group velocity indicating that this configuration can be used for locating damage on edges. The localisation of edge waves means that they can specifically detect damage at the edges of structures, and attenuation measurements indicate that their useful propagation distance is large (5.5 m).

The tsunami energy radiation directivity on the example of the 1994, 2006 and 2007 events

<p>Determining the tsunami source danger is currently one of the most urgent tasks. The vast majority of recorded tsunamis are of seismic origin. Part of the energy released during an earthquake passes into the energy of the initial tsunami source. The tsunami excitation efficiency depends on a number of factors: the depth of the sea above the source and its location relative to the coast and continental slope; the shape and area of residual post-seismic bottom displacements, as well as the bottom relief directly in the zone of the seismic source; inhomogeneities of the ocean floor relief along the path of tsunami propagation (for estimating wave heights in the zone farthest from the source); time inhomogeneities of tsunami wave radiation from the source zone; non-isotropy of the tsunami radiation spectrum.</p><p>To study the tsunami source efficiency, we considered three tsunamis in the Kuril ridge region: the Shikotan tsunami of 1994, and two Simushir tsunamis of 2006 and 2007. The choice of events was largely determined by the close geographical location – all of them belong to the Kuril-Kamchatka subduction zone. Also, these events are well studied, and there is quite a large amount of data on tsunami measurements onshore and in the deep ocean. At the same time, all three sources differ in the mechanisms of the seismic focus and location relative to the coast and the continental slope.</p><p>We analyzed the tsunami wave field for three events near the Russian Pacific coast. Tsunami energy flow calculations show that frontal energy flow is mainly directed to the southeast. The flux magnitude decreases with distance from the source as a result of geometric divergence and scattering. At longer distances, the effect of refraction becomes more significant – the flow is divided into separate rays due to the focusing on the irregular bottom relief.</p><p>The radiation patterns of each source that also were created show the part of wave energy that penetrated the Sea of Okhotsk through the Kuril Straits. It is easy to indicate the effect of the capture of tsunami waves by the shelf and the formation of edge waves that carry the wave energy away from the source area along the Kuril Ridge shelf. For 2006 and 2007 events a relatively small part of the wave energy went into the captured waves, but for 1994 the initial sea surface displacement area was in the shelf zone and a significant part of the energy was transferred to the captured edge waves, radiated mainly in the northeast direction.</p>

An investigation into edge-wave generation by wind

<p>Edge waves (EW) are surface gravity waves topographically trapped near the highly reflective ocean shorelines. Over mildily sloping beaches, the high-reflectivity condition is only satisfied for infragravity waves (IGW, periods of a few minutes). Initially believed to drive alongshore-periodic shoreline features, EW have been shown to be important also for a variety of coastal ocean processes such as nonlinear shoaling of wind waves, coastal flooding, ice-shelf break up in polar oceans, and others.  As IGW, on mildly sloping beaches EW are outside the wind-wave frequency range, which seems to exclude direct wind forcing as generating mechanism. It is generally agreed that IGW ove mildly sloping beaches are generated by nonlinear swell interaction.</p><p>Wave-wave interactions can excite both alongshore progressive and standing EW, but EW directional symmetry should match swell directionalty. This simple rule is confirmed also by observations. Exceptions to thius rule are intriguing: if directionally-asymmetric edge waves fields that do not match the swell direction, occur, the implication is that wave-wave interactions are not the dominant IGW/EW generation mechanism. Direct wind forcing would then be the only conceivable candidate. The high correlation of swell and IG wave directionality, however, suggests that such occurrences must be rare, possibly associated with peculiar coastal weather conditions. </p><p>We investigate data produced by the most comprehensive effort to date to study EW - the nearshore array deployed by Elgar, Herbers, O'Reilly and Guza during the SandyDuck'97 experiment - which recorded pressure and velocity continuously at 2 Hz from August to December 1997, at sensors distributed on six alongshore lines between approximately the 1-m and 6-m isobaths near the Duck NC pier. Estimates directional IGW/EW match well swell directionality. However, a few events exhibit strong IG/EW directional asymmetry matching wind direction, with nearly shorenormal offshore swells. In most of these cases, IGW propagate against the nearshore current. These events are consistent with a mechanism for direct generation of IGW/EW by wind. It is not clear whether their scarcity is due to intrinsic properties of the wind generation mechanism, or to the rather low-energy conditions of the SandyDuck'97 experiment. In general, both nonlinear wave-wave interactions and wind generation should be taken into account, and we expect the wind generation mechanism to play an increasingly important role in storms, for example, for modeling wave surges. An investigation into modeling EW generation by wind will be reported elsewhere. </p><p> </p>