Spectral super-elements for wave propagation in structures with local non-uniformities

Ultrasonic guided waves are very useful for structural health monitoring. They have the potential to interrogate and detect damage in a structure over a large area with few transducers. Guided plate modes (Lamb waves) are used and proposed for damage detection at a distance in semi-monococque structures such as airplane fuselages and spacecraft structures. The interaction of guided plate waves with stiffening members such as ribs, stringers, or the integral stiffeners used in spacecraft structures limits the distance over which structural health monitoring non-destructive evaluation systems can detect damage. This paper develops a simple explanatory model for the scattering of low-order ultrasonic Lamb waves crossing a stiffening device. The model illuminates the underlying mechanics of waves crossing a stiffener. The model shows that stop-bands for transmission of S0 (longitudinal pressure) waves across a stiffener line up with flexural resonances of the stiffener. It also demonstrates why transmission o...

Reflection and transmission of guided ultrasonic plate waves by vertical stiffeners

A formulation of the dynamics of a collection of connected simple 1-dimensional Cosserat continua and rigid bodies is presented in terms of sections of an SO(3) fibration over a 1-dimensional net. A large class of junction conditions is considered in a unified framework. All the equations of motion and junction conditions are derived as extrema of a constrained variational principle on the net and are analysed perturbatively for structures with Kirchhoff constitutive properties. The whole discussion is based on the notion of a Cosserat net and its contractions obtained by taking certain limits that transform Cosserat elements to rigid structures. Generalisations are briefly discussed within this framework.

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The dynamics of Cosserat nets

This investigation comprises an experimental and numerical study of elastic wave propagation in angled beams. Axial impact by two strikers of different lengths was applied to three steel beams, each bent to incorporate a “V” section of different angle in the middle. Finite element simulation using ABAQUS was employed to examine details of the elastic waves generated in the impact tests. The numerical results correlated well with experimental data, and computational simulation was utilized to analyse the propagation of energy associated with the elastic waves. This demonstrated that after several reflections from and transmission across the bends energy is progressively smeared throughout the entire beam and does not concentrate at any particular segment; the bulk of the energy is conveyed via flexural waves. Numerical simulation of wave propagation in a beam with a single angle was also undertaken to study the energy associated with waves reflected from and transmitted across the bend, and how these are affected by the bend angle. The effects of input pulse duration, beam thickness and beam material properties on energy reflection and transmission at a bend are also discussed; this leads to the conclusion that when a longitudinal pulse of a particular frequency impinges on a bend, the ratio between its wavelength and the beam thickness governs the energy reflected from and transmitted across the bend. Moreover, the bend junction geometry (curvature) is found to have a significant influence on the energy reflected and transmitted, especially for obtuse bend angles.

Elastic wave and energy propagation in angled beams

Stress respectively force oscillation in mechanical testing is a phenomenon that can be monitored independent of material, stress state and test setup. This study looks at the phenomenon of force oscillation in tensile impact testing on viscoelastic materials and its dependency on longitudinal stress wave propagation. In addition to the extensive research on stress wave propagation and the force oscillation phenomenon, published within the last decades, the Society of Automotive Engineering (SAE) also gives valuable recommendations regarding tensile impact testing on polymer materials. Existing limitations to tensile impact testing reported earlier can be overcome using the approach outlined in this paper. Furthermore, we give an analysis to stress wave propagation in tensile impact testing and its correlation to force oscillations: We find that (1) longitudinal stress wave propagation in tensile specimens cannot be considered to be the origin of the force oscillation phenomenon - even more so it can be neglected, (2) specimens in tensile impact testing are exposed to a nearly oscillation free loading which is presented for haul-off velocities of up to 10 m/s and (3) it is not possible to achieve force equilibrium in the load train conducting tensile impact tests. In addition, we present an approach to measure a nearly oscillation free force signal in tensile impact testing on polymer materials up to 10 m/s. For this purpose a modification of a standard dumbbell specimen is introduced. Measurements presented in this paper are conducted using state of the art 3D high-speed deformation measurement technology based on Digital Image Correlation (DIC).

K.J. Atkins

Papers

Generation of elastic stress waves at a T-junction of square rods