Abstract
Guided waves have immense potential for structural health monitoring applications in numerous industries including aerospace. It is necessary to evaluate guided wave dispersion characteristics, i.e., group velocity and phase velocity profiles, for using them effectively. For complex structures, the profiles can have highly irregular shapes. In this work, a direct method for calculating the group velocity profiles for complex, composite, and periodic structures using a wave and finite element scheme is presented. The group velocity calculation technique is easy to implement, highly computationally efficient, and works with the standard finite element formulation. The major contribution is summarised in the form of a comprehensive algorithm for calculating the group velocity profiles. The method is compared with the existing analytical and numerical methods for calculation of dispersion curves. Finally, an experimental study in a multilayered composite plate is conducted and the results are found to be in good agreement. The technique is suitable to be used in all guided wave application areas such as material characterisation, non-destructive testing, and structural health monitoring.
Highlights
Structural health monitoring (SHM) in the aerospace sector has the potential to reduce costs and increase reliability [1]
The semi-analytical finite element (SAFE) method is similar to the wave and finite element (WFE) scheme, where the finite element method is used for discretising the cross-section of the waveguide [35]
This work presented a new approach for the direct calculation of group velocity curves using the WFE scheme
Summary
Structural health monitoring (SHM) in the aerospace sector has the potential to reduce costs and increase reliability [1]. For isotropic plates with constant thickness, the group and phase velocities do not have angular dependence and the 2D profile is circular This quickly becomes non-trivial in complex multilayered structures where the directions of wave propagation and energy propagation are different. The semi-analytical methods use finite element (FE) approaches to model part of the structure and impose wave solutions in the propagation directions. The most well-known is the semi-analytical finite element (SAFE) method, where FE is used to model the cross-section, and a complex exponential function is used to describe the displacement field in the direction of wave propagation [19]. The principal novelty of the work exhibited in this manuscript is the calculation of the group velocity curves for two dimensional complex periodic and/or composite structures using a wave and finite element scheme without involving any finite differentiation. Stiffness, damping, and mass matrices Dynamic stiffness matrix Angular frequency Vector of nodal degrees of freedom Vector of internal forces Transformation matrix Propagation constant Wavenumber Transfer matrix Modeshape vector Energy and power Group velocity and phase velocity Propagation direction
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