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Abstract The main objective of this work is to use the time variational method (TVM), a semi-analytical approach to evaluate steady-state responses in the time-domain for absolute nodal coordinate formulation (ANCF) modeled systems. The gradient-deficient ANCF beam element's performance is demonstrated for a highly flexible cantilever beam under gravity and impulse loading, with comparisons to experiments. The damping behavior is compared for the Rayleigh proportional and the Navier–Stokes (NS) damping model for a gradient-deficient ANCF beam element. Classical finite element method (FEM) beam formulation's shortcomings in predicting large deflections of thin, flexible cantilever beams are highlighted. Unlike the harmonic balance method (HBM), TVM reduces the computational time for harmonic response evaluation compared to numerical integration techniques and handles nonlinear forces in the time-domain. The harmonic response is evaluated by exciting the cantilever beam in the linear region for both experiments and TVM computations.
Renjith et al. (Wed,) studied this question.