The nondestructive assessment of the damage that occurs in components during service plays a key role for condition monitoring and residual life estimation of in-service components/structures. Ultrasound has been widely utilized for this; however most of these conventional methods using ultrasonic characteristics in the linear elastic region are only sensitive to gross defects but much less sensitive to micro-damage. Recently, the nonlinear ultrasonic technique, which uses nonlinear ultrasonic behavior such as higher-harmonic generation, subharmonic generation, nonlinear resonance, or mixed frequency response, has been studied as a positive method for overcoming this limitation. In this paper, overall progress in this technique is reviewed with the brief introduction of basic principle in the application of each nonlinear ultrasonic phenomenon.

Nonlinear ultrasonic techniques for nondestructive assessment of micro damage in material: A review

Solitons, Introduction to.

Transformations for a generalized variable-coefficient Korteweg de Vries model from blood vessels, Bose Einstein condensates, rods and positons with symbolic computation

We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.

/pdf/nonlinear-layered-lattice-model-and-generalized-solitary-1yhmv9v9sz.pdf

Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures

In literature, nonlinear waves in elastic rods have been studied by many authors. Usually, the Navier-Bernoulli hypothesis (the assumption that plane cross-sections remain planar and normal to the rod axis) is used. Intuitively, one would expect that this would be a good approximation when one is mainly interested in longitudinal waves. However, there are no rigorous theoretical justifications available. Also, a defect of this assumption is that comparing with the exact three-dimensional theory the boundary conditions on the lateral surface can never be satisfied. Recently, three papers have been published to overcome this defect, but they contain some algebraic errors (which implies that the approach adopted there cannot be used to overcome this defect). So, this problem remains open. In this paper, we present our recent research results for this problem, and we have managed to establish asymptotically valid one-dimensional rod equations which are consistent with the lateral boundary conditions. Further, their dispersion relation can match with that of the exact three-dimensional field equations to any asymptotic order in the long-wave limit. For solitary waves in the far field, we derive to the leading order the KdV equation. Comparing its solitary-wave solution with that of the KdV equation obtained through the Navier-Bernoulli hypothesis, we find that the difference is very small. This provides some evidence to the validity of the assumption that plane cross sections remain planar and normal to the rod axis.

Asymptotically approximate model equations for nonlinear dispersive waves in incompressible elastic rods

The evolution of a longitudinal-strain solitary wave (a soliton) is studied theoretically and in experiments in a nonlinearly elastic tapered rod. Amplification (focusing) of the soliton is predicted and observed in the rod with decreasing cross section. An asymmetric soliton deformation when focused is observed. An approach is developed to obtain analytical relationships between longitudinal and shear nonlinear strains, and an asymptotic solution to the problem is found, accurately satisfying the boundary conditions on the lateral rod's surface. The explicit relationship is obtained for the soliton amplitude dependence upon the cross section radius' variations of the nonlinearly elastic rod. An allowed interval of soliton velocities is shown to exist that is dependent on elasticity. It was proved in experiments that the elastic strain soliton is not absorbed even at distances much greater than the typical linear dissipation length for linear waves in polystyrene.

Longitudinal-strain soliton focusing in a narrowing nonlinearly elastic rod

We report first experimental registration of the splitting induced generation of a soliton train from a single incident strain soliton in two- and three-layered elastic waveguides. The origin is in the nonlinear response of the wave to an abrupt change of physical properties of the waveguide. We show a good agreement between our experimental results and theoretical estimates, based on a weakly nonlinear solution for the doubly dispersive (Boussinesq type) equation with piecewise constant coefficients for the waveguide made of a piecewise isotropic nonlinearly elastic material.

Splitting induced generation of soliton trains in layered waveguides

We report the registration of delamination induced variations in the dynamics of bulk strain solitary waves in layered polymeric bars with the glassy and rubber-like adhesives, for the layers made of the same material. The key phenomenon in a layered structure with the glassy bonding is the delamination caused fission of a single incident soliton into a wave train of solitons, with the detectable increase in the amplitude of the leading solitary wave. The significant feature of bulk strain solitons in structures bonded with the rubber-like adhesive is the generation of radiating solitary waves, whilst co-propagating ripples disappear in the delaminated area. The observed variations may be used for the detection of delamination in lengthy layered structures.

Bulk strain solitary waves in bonded layered polymeric bars with delamination

We study the effect of two types of adhesive bonding on the propagation of a localized longitudinal strain wave in two- and three-layered elastic bars. The detectable variation in the decay rate of the wave at relatively long distances of propagation is observed. It is proposed that such variation can be used as an indicator of the type of an interface.

Comparison of the effect of cyanoacrylate-and polyurethane-based adhesives on a longitudinal strain solitary wave in layered polymethylmethacrylate waveguides

Reflection of a solitary longitudinal strain wave (soliton) from the end face of a nonlinearly elastic rod is investigated theoretically and experimentally. It is shown that the wave reflected from the free end of the rod has a reversed amplitude sign, which results in dispersion of the wave. If the end of the rod is fixed, the reflected wave retains its polarity and properties of the incident solitary wave and propagates back to the input end.

Galina V. Dreiden

Papers

Longitudinal-strain soliton focusing in a narrowing nonlinearly elastic rod

Splitting induced generation of soliton trains in layered waveguides

Bulk strain solitary waves in bonded layered polymeric bars with delamination

Comparison of the effect of cyanoacrylate-and polyurethane-based adhesives on a longitudinal strain solitary wave in layered polymethylmethacrylate waveguides

Reflection of a Longitudinal Strain Soliton from the End Face of a Nonlinearly Elastic Rod