Abstract
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.
Original language | English |
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Journal | Acta Mechanica Sinica/Lixue Xuebao |
Volume | 36 |
Issue number | 1 |
DOIs | |
Publication status | Published - Feb 1 2020 |
Keywords
- Effective mass coefficient
- Generalized stiffness coefficient
- Lumped parameter modelsPower-law Euler–Bernoulli beams
- Power-law Euler–Bernoulli beams
ASJC Scopus subject areas
- Applied Mathematics
- Materials Science (miscellaneous)
- Mechanical Engineering