Vibrational model of a prismatic multilayered tapered cantilever using perturbation analysis

In this work we present a novel semi-analytical model of the vibrational dynamics of a multi-layered tapered prismatic cantilever. The derivation of the model is based on a perturbation expansion of the tapered cantilever's partial differential equations using Euler-Bernoulli beam theory as a starting point. The proposed semi-analytical solution of the model enables a 101-sample modal analysis to run more than 250 × faster when using 20 perturbation components than a computationally efficient commercial FEM solution that uses 101 shell-type finite elements along the beam length and 6 elements along the beam width. In this case, the primary mode model prediction error on resonance frequency is below 0.1% for 20 perturbation components and below 10% for 4 components.