Wavelet spectral finite element for modeling guided wave propagation and damage detection in stiffened composite panels

Abstract

Ultrasonic-guided wave propagation in stiffened composite panels is modeled using the wavelet spectral finite element method. The model is capable of analyzing transient response resulting from loads with short time duration, such as impacts. The model can also be used to predict the response for known excitations commonly used in ultrasonic wave–based structural health monitoring/nondestructive inspection systems. Wavelet spectral finite element is an efficient and accurate technique for wave propagation modeling in structures. Governing equations of laminated plate elements used in the model are based on the first-order shear deformation theory, which yields accurate solutions up to wavelengths close to plate thickness. Daubechies compactly supported scaling functions are used to approximate the partial differential equations in time and one spatial dimension. Resulting ordinary differential equations are rearranged and solved for wavenumbers by assuming a harmonic solution in the transformed frequency-wavenumber domain. The global dynamic stiffness matrix of the spectral plate element is formed relating transformed nodal forces and displacements. Stiffened panel is then assembled following a procedure similar to conventional finite element method, and the resulting matrix equation is solved in the frequency-wavenumber domain. Wavelet spectral finite element results are validated with conventional finite element simulations performed in Abaqus^®. In addition to transient response prediction, the usefulness of wavelet spectral finite element–based skin–stiffener model is shown in structural health monitoring for detecting skin–stiffener debond and transverse surface crack.

Keywords

Stiffened composite panels guided wave propagation structural health monitoring wavelet spectral finite element damage detection

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