The dynamic behavior of Bernoulli-Euler, Rayleigh and Timoshenko beam models lying on an elastic foundation is considered. A comparative analysis of their dispersion curves is given. The behaviour of the Rayleigh beam dispersion curve has been found to coincide qualitatively with the behaviour of the lower branch of the Timoshenko beam dispersion curve. Accounting for the cubic nonlinearity of the elastic foundation in these models leads to the generation of higher harmonics, which do not, however, practically interact (due to strong dispersion). The stability and instability domains of quasi-harmonic flexural waves have been found. It is shown that, in contrast to the Bernoulli-Euler model, the Rayleigh model may be used in studying low-frequency flexural waves.
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