Spectrally formulated one-dimensional element for analysis of wave propagation in pretwisted anisotropic strips

A spectrally formulated one-dimensional element is developed to study the wave propagation in pretwisted anisotropic strips. The element is based on linear sectional analysis of pretwisted anisotropic strips with small pretwist. Firstly, the governing equations of the strip are obtained through dimensional reduction of laminated shell theory to a linear one dimensional (1-D) theory using the variational asymptotic method (VAM). Next, an exact dynamic stiffness matrix is derived in the frequency-wavenumber domain using spectral finite element (SFE) method. In SFE formulation the mass distribution is modeled exactly and as a result a single element is sufficient to capture the exact frequency response of a regular structure. For numerical validation of the proposed model, the natural frequencies of the strip are compared to the modal behavior of pretwisted composite strips available in literature. The model is used to predict wave responses due to modulated sinusoidal input. The different wave modes present, namely axial, flexural, and torsional modes are seen and their velocities are compared to that obtained from the dispersion plot. This proposed modeling strategy is a first step towards the development of a comprehensive model to do structural health monitoring of structures idealized as pretwisted strips.