Disperse: A General Purpose Program for Creating Dispersion Curves

Abstract

Mechanical Engineering Oepartment Exhibition Road, London SW7 2BX INTROOUCTIONThe application of guided waves in NOT can be hampered by the Iack of readily available dispersion curves for complex structures. To overcome this hindrance, we have developed a general purpose program that can create dispersion curves for a very wide range of systems and then effectively communicate the information contained within those curves. The program uses the global matrix method to handle multi-layered Cartesian and cylindrical systems. The solution routines cover both leaky and non-leaky cases and remain robust for systems which are known to be difficult, such as !arge frequency-thicknesses and thin layers embedded in much thicker layers. Elastic and visco-elastic isotropic materials are fully supported; anisotropic materials are also covered, but are currently limited to the elastic, non-leaky, Cartesian case.An extremely !arge amount of work has already been clone to describe the wave propagation in layered systems, which began in the late nineteenth century and continues today There is not enough space in this paper to describe the contributions that many excellent researchers have made to the field. Instead, this paper describes how we have combined some of this previous work and our own research to create a robust, user friendly, general purpose tool. A review of matrix techniques as they apply to modelling ultrasonic waves in multi-layered media is given in (1).When creating dispersion curves, the displacements and stresses for each type of material and geometry are described in a materiallayer matrix. By satisfying the given boundary conditions at each interface, the individuallayer matrices are assembled to describe the behaviour of the entire system. The dispersion curves then emerge as solutions to the assembled system of equations.Once the dispersion curves are generated, our program provides many easy methods to explore and use the information contained within the curves. A mode shape display continually updates the distribution of stresses, displacements, and energy as points are selected on a dispers10n curve. The phase velocity, group velocity, attenuation, real wave-number, angle of incidence, etc. can be shown and compared. In addition, an interface to our finite element program allows the interaction of gutded waves with defects to be examined.The program has been developed as a by-product of our research. It has proven to be a valuable tool for understanding wave propagatwn in complex systems and transferring that understanding to new ultrasomc testwg applications

Quantitative Evaluation of the Blocking Ratio of a Blockage inside a Pipe Utilizing Film-Type PZT Elements

“…We observed the two waveforms at almost the same time. The measured propagation velocity of both the waves was 1.75 × 10 3 m/s and corresponded to the calculated group velocity of the L(0,1) mode of a guided wave at a frequency of 100 kHz for the used pipe; the group velocity was calculated using the software DISPERSE (6) . H. Sato et al (7) reported the propagation of a guided wave both in the water inside a pipe and in the pipe wall with the same propagation velocity.…”

Local guided wavefield analysis for characterization of delaminations in composites

“…In order to determine window size, the software package DISPERSE v2.0.16i [16] was used to calculate theoretical wavenumber for a number of ply "stackups" corresponding to laminate regions above delaminations at the 4-5, 6-7, 7-8, 17-18 ply interfaces and for the pristine 26 ply plate. Material properties used to perform the calculations are obtained from the literature and are presented in Table 1 [17,18].…”

Damage Sensing in Blades

“…3.12, dispersion curves of phase velocity and group velocity are represented against the frequency for symmetric and antisymmetric modes of a 3-mm thick aluminium plate. (Pavlakovic et al 1997) The dispersion equations of Lamb waves for plate-like isotropic structures are (Rose 2014): tan .qh/ q C 4k 2 p tan .ph/ .k 2 q 2 / 2 D 0 for symmetric modes (3.5a) q tan .qh/ C k 2 q 2 2 tan .ph/ 4k 2 p D 0 for antisymmetric modes (3.5b)…”