Analysis on global and chaotic dynamics of nonlinear wave equations for truss core sandwich plate

Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation

“…e first and second measurements are then applied to explore the homoclinic chaos and the chaotic threshold for the wave equation. Afterward, numerical examples are also carried out using the differential quadrature method [27][28][29]. e simulating results confirm the validity of the theoretical prediction and illustrate larger damping coefficient resulting in the more complicated dynamical behaviors of the GBE.…”

“…According to [27][28][29][30], the second measurement, called as the geometric analysis (Figure 3(b)), is described as…”

“…e persistent homoclinic orbits of nonlinear Schrödinger (NLS) and sine-Gordon (SG) equations were constructed by using invariant manifolds, foliations, and Melnikov analysis. Furthermore, Zhang et al [27], Wu and Qi [28,29], and Li et al [30] improved the analytic theory for infinite-dimensional systems [23][24][25][26] to obtain the chaotic threshold of mechanical systems such as truss core sandwich plates, pipes conveying fluid, axial moving beams, and carbon nanotubes. e aforementioned literature focused on solid structure systems; however, analysis on global dynamics for fluid systems, e.g., GBE, remains lacking.…”

“…e objective of this study is to derive the analytical chaotic threshold of the GBE and indicate how the damping coefficient can clearly affect the dynamical responses of the GBE. e reductive perturbation method (RPM) [27,30] is employed to transform the complicated PDE of the GBE into a topologically equivalent wave equation.…”

Modeling and Analysis of Chaos and Bifurcations for the Attitude System of a Quadrotor Unmanned Aerial Vehicle

“…Faramin and Ataei [20] analyzed the chaos of the satellite attitude via the Lyapunov exponents (LEs), designed a nonlinear robust control to suppress chaos, and confirmed its suppression using Melnikov's analysis. Generally, the Melnikov method affords the necessary conditions for the existence of chaotic motion [31][32][33][34]. In dynamic research, a typical rigid body is the gyrostat.…”