Abstract
The paper deals with analytically predicting the
effects of weak nonlinearity on the dispersion relation
and frequency band-gaps of a periodic Bernoulli–
Euler beam performing bending oscillations. Two
cases are considered: (i) large transverse deflections,
where nonlinear (true) curvature, nonlinear material
and nonlinear inertia owing to longitudinal motions
of the beam are taken into account, and (ii) midplane
stretching nonlinearity. A novel approach is
employed, the method of varying amplitudes. As a
result, the isolated as well as combined effects of
the considered sources of nonlinearities are revealed.
It is shown that nonlinear inertia has the most
substantial impact on the dispersion relation of a nonuniform
beam by removing all frequency band-gaps.
Explanations of the revealed effects are suggested, and
validated by experiments and numerical simulation.
| Original language | English |
|---|---|
| Article number | 20150751 |
| Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 472 |
| Issue number | 2186 |
| Number of pages | 22 |
| ISSN | 1364-5021 |
| DOIs | |
| Publication status | Published - 2016 |
Keywords
- Elastic wave propagation
- Dispersion relation
- Frequency band-gaps
- Weak nonlinearity
- Periodic Bernoulli–Euler beam
- Method of varying amplitudes