Chapter 6: Euler–Bernoulli Beams

This chapter is devoted to studying chaotic dynamics of the Euler–Bernoulli beams. At first, numerical approaches being further applied including both Benettin and Wolf algorithms, neural networks and classical and modified Gramm–Schmidt orthonormalization procedures are described and validated using the standard maps. Then the planar beams are investigated in a standard way, i.e. the governing PDEs are reduced to nonlinear ODEs, and the latter are analyzed using time histories, Fourier frequency spectra, phase curves, 3D beam deflections, as well as the first four Lyapunov exponents (LES) and Morlet wavelets. Numerous novel examples of beam chaotic and hyperchaotic dynamics are illustrated and discussed…