Modified Nonlinear 3D Euler Bernoulli Beam Theory

Zohoor, Hassan; Khorsandijou, S. Mahdi; Abedinnasab, Mohammad H.

doi:10.1299/jsdd.2.1170

Cited by 3 publications

(1 citation statement)

References 14 publications

(31 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Shi et al [15] derived a complete second-order deformation field together with the governing equations within a graphtheoretic formulation of the beam model. An enhanced nonlinear 3D Euler-Bernoulli beam model governed by ten coupled PDEs was proposed by Zohoor and Khorsandijou [16], and then, it was extended with newly added elastic terms exhibiting tension-compression, torsion and two spatial bending dynamical effects [17].…”

Section: Introductionmentioning

confidence: 99%

On the general theory of chaotic dynamics of flexible curvilinear Euler–Bernoulli beams

et al. 2014

View full text Add to dashboard Cite

We present chaotic dynamics of flexible curvilinear shallow Euler-Bernoulli beams. The continuous problem is reduced to the Cauchy problem by the finite-difference method of the secondorder accuracy and finite element method (FEM). The Cauchy problem is solved through the fourth-and sixth-order Runge-Kutta methods with respect to time. This preserves reliability of the obtained results. qualitative theory of differential equations. Frequency power spectra using fast Fourier transform, phase and modal portraits, autocorrelation functions, spatiotemporal dynamics of the beam, 2D and 3D Morlet wavelets, and Poincaré sections are constructed. Four first Lyapunov exponents are estimated using the Wolf algorithm. Transitions from regular to chaotic dynamics are detected, illustrated and discussed. Depending on signs of four Lyapunov exponents the chaotic, hyper chaotic, hyper-hyper chaotic, and deep chaotic dynamics is reported. Curvilinear beams are treated as systems with an infinite number of degrees of freedom. Charts of vibration character, elastic-plastic deformations, and stability loss zone versus control parameters of the studied beams are reported.

show abstract

Section: Introductionmentioning

confidence: 99%