Generalized stiffness and effective mass coefficients for power-law Euler–Bernoulli beams

We extend the well-known concept and results for lumped parameters used in the spring-like models for linear materials to Hollomon’s power-law materials. We provide the generalized stiffness and effective mass coefficients for the power-law Euler–Bernoulli beams under standard geometric and load conditions. In particular, our mass-spring lumped parameter models reduce to the classical models when Hollomon’s law reduces to Hooke’s law. Since there are no known solutions to the dynamic power-law beam equations, solutions to our mass lumped models are compared to the low-order Galerkin approximations in the case of cantilever beams with circular and rectangular cross-sections.