A Crack Size Quantification Method Using High-Resolution Lamb Waves

Traditional tone burst excitation cannot attain a high output resolution, due to the time duration. The received signal is much longer than that of excitation during the propagation, which can increase the difficulty of signal processing, and reduce the resolution. Therefore, it is of significant interest to develop a general methodology for crack quantification through the optimal design of the excitation waveform and signal-processing methods. This paper presents a new crack size quantification method based on high-resolution Lamb waves. The linear chirp (L-Chirp) signal and Golay complementary code (GCC) signal are used as Lamb wave excitation signals. After dispersion removal, these excitation waveforms, based on pulse compression, can effectively improve the inspection resolution in plate-like structures. A series of simulations of both healthy plates and plates with different crack sizes are performed by Abaqus CAE, using different excitation waveforms. The first wave package of the S0 mode after pulse compression is chosen to extract the damage features. A multivariate regression model is proposed to correlate the damage features to the crack size. The effectiveness of the proposed crack size quantification method is verified by a comparison with tone burst excitation, and the accuracy of the crack size quantification method is verified by validation experiments.

Free Particle, Wave Packet and Dynamics, Quantum Dots, Defects and Traps

This chapter continues with a study of the time independent Schrödinger equation and seeks to contrast the quantum behavior of a free particle with that of a particle localized in a potential quantum well. A free particle can exist over all space or can be localized in a wave package. The wave packet is a coherent superposition of the plane waves that make up the wave function that localizes the particle because of constructive and destructive interference. The wave packet spreads out in time because the waves leading to constructive interference get out of phase. In Chapter 2, the particle was localized by a quadratic potential energy. Here, the potentials are described as piecewise constant. The approach is based on assuming a one-dimensional space, x, which is relevant to many problems in the laboratory. The solution is easily generalized to higher dimensions (x-y or x-y-z), but the physics remains the same. The objective is to understand the shape of the eigenfunctions in space and to be able to relate this to the probability density of locating the particle, as well as understanding the relevance of these systems to today’s technology.

Atomic kernels as waves and catastrophes

The presentation of atomic kerrnels as particles requires for the physics duality principle that they get a wave description. This is due to presenting the SU (3) GellMann matrix space by octonians which are obtained by doubling the spacetime quaternions. Their multiplication table is different from the SU (3) matrices. The third presentation of this space is a complex 4-dimensional space where the real spacetime coordinates of a 4-dimensional Euclidean Hilbert space R4 are extended to C4. For getting from Deuteron Cooper pairs NP of a neutron and proton atomic kernels AK, the wave package superpositions for AK need the mass defect of neutrons where kg is changed to inner speeds or interaction energies. For kg octonians have a GF measuring base triple as Gleason operator. Using a projective geometrical norming, C4 is normed to CP³, a projective 3-dimensional space. Its cell C³ has spacetime coordinates C², extended by an Einstein energy plane z3 = (m,f), m mass, f = 1/∆t frequency where mass can be transformed into f by using mc² = hf. If C³ is presented as a real space R6, it can be real projective normed to a real projective space P5 for the field presentation of AK. As field the NP‘s have then a common group speed for AK wave packages superpositions with which AK moves in spacetime C² and also a presentation as a Ψ wave. As probability distribution where they can be energetically found in space serves Ψ* Ψ.

ON GENERATION OF A WAVE PACKAGE IN A WAVEGUIDE, FILLED ACTIVE MEDIUM

Excitation of electromagnetic waves in a waveguide with a medium, which is a two-level system, is considered. To describe the processes, both classical electrodynamics methods and quantum mechanics methods are used. The nature of the processes under study turns out to depend on the relationship between the Rabi frequency and the line width of the excited wave packet. It is shown that if the field energy density is high, then spatially inhomogeneous Rabi frequencies arise, which leads to oscillatory behavior of the wave field amplitudes. If the levels of the excited field are small, then the dynamics of the two-level quantum system becomes monotonic and the population inversion tends to zero.