An important goal in astrophysics is to model phenomena such as the gravitational collapse of stars and accretion onto black holes. Under the assumption that the spacetime metric remains fixed on the time scales of fluid motion, the relevant physics can be modeled by the equations of relativistic hydrodynamics. These equations form a system of hyperbolic balance laws that are strongly nonlinear...

In the paper, a novel magneto-electro-elastic model of bi-directional (2D) functionally graded materials (FGMs) beams is developed for investigating nonlinear dynamics. It shown that asymmetric modes induced by 2D FGMs may significantly affect dynamic responses, which tremendously different from previous studies. Taking into account geometric nonlinearity, equation motion and associated boundar...

Dynamics, control, and stability of roll oscillations a biased ship in regular sea waves are investigated. The under oscillation is modelled as the classical Helmholtz–Duffing oscillator with strongly nonlinear asymmetric restoring moment characteristics. incremental harmonic balance method, amended pseudo-arc-length continuation approach, employed to obtain uncontrolled controlled frequency re...

Quasi-periodic responses composed of multiple base frequencies widely exist in science and engineering problems. The harmonic balance (MHB) method is one the most commonly used approaches for such However, it limited by low-order estimations due to complex symbolic operations practical uses. Many variants have been developed improve MHB method, among which time domain MHB-like methods are regar...