This study proposes the use of a novel nonlinear tuned mass damper inerter device in vibration suppression of the ship propulsion shafting system and evaluates its performance. The device consists of an axial inerter and a pair of lateral inerters to create geometric nonlinearity. The system response subjected to propeller forces is determined by using the harmonic balance method with alternating-frequency-time technique and a numerical time-marching method. The force transmissibility and energy flow variables are employed to assess the performance of the device. The results show that the proposed device can reduce the peak force and energy transmission to the foundation while increase the energy dissipation within the device. Its use can lead to an improved vibration attenuation effect than the traditional mass-spring-damper device for low-frequency vibration. The configurations of the nonlinear inerter-based device can be adjusted to obtain an anti-peak at a resonance frequency of the original system, providing superior vibration suppression performance.

By using 1~2 degrees of freedom (DOF) examples, linear/nonlinear and quasi-periodical systems (QPS) are investigated based on the energy-flow theory (EFT), which reveals the following new findings on chaotic motions. (a) A 1-DOF linear non-damped-forced motion is chaotic if there is no least common multiple (LCM) for the periods of natural and force frequencies. (b) For a 1-DOF nonlinear non-damping-forced system with nonlinear stiffness of $\gamma x^2,\left(\gamma >0\right),$ both the free vibration by initial conditions and the composed motion with forced one excited by a force of given frequency are chaotic; while, when damping is added, the free vibration is damped to zero, but the forced vibration consists of different frequency components showing chaotic characteristics. (c) For a 1-DOF system of natural frequency 1 with nonlinear damping $2\epsilon \left(\dot{x}\right)=-2+\dot{x}+{\dot{x}}^2,$ $\epsilon \left(\dot{x}\right)<0$, ${\epsilon \left(\dot{x}\right)}^2<1,$ the free vibration by the initial conditions ($x_0=1,p_0=0$) is along a non-repeating orbit towards a zero energy-flow limit circle of $\dot{E}=0, p=-1$. The tackled 1-DOF systems of no LCMs belong to a type of QPS, which implies that the orbit of a QPS in the phase space is also a non-closed curve, and based on the EFT, its motion is chaotic. The chaotic orbits of above 1-DOF cases in the phase space, as well as a 2-DOF free vibration case, are numerically examined to confirm the theoretical prediction. The findings may suggest that the LCMs could be an important factor in identifying chaotic motions. It is demonstrated that the generalised potential energy (GPE) and the energy-flow characteristic factors (EFCF), respectively, play a Lyapunov function and exponents to tackle the stabilities and chaotic motions of dynamic systems.

The conventional synchronous generator (SG) can regulate the active and reactive power for frequency and voltage stability, when the system fluctuates. In renewable energy generation system (RES), the stability problem of RES can be solved by adding virtual inertia and damping in the control strategy of the grid-connected inverter. The grid-connected inverter and renewable energy system with this kind of control strategy, called as virtual synchronous generator (VSG), acts as a synchronous generator. In this paper, the topology of grid-connected PV array and energy storage system is proposed. The VSG used in grid-connected inverter, is modelled as stator and rotor model by stator voltage equation and rotor motion equation, respectively. Meanwhile, the VSG control mechanism, based on droop control and model of VSG, can be divided as active power-frequency and reactive power-voltage control. Besides, the system stability is analyzed based on small signal model, for the design of inertia and damping. The simulation model is designed by MATLAB/Simulink for the implementation of VSG. In simulation, it is compared that the dynamic regulation performance of VSG with different control coefficient, such as virtual inertia, virtual damping, droop coefficient and integral coefficient. The optimization for regulation performance in simulation provides an appropriate selection method of the control coefficient for VSG.

This study presents an optimization methodology for nonlinear energy sinks (NES) aimed at attenuating longitudinal vibration in marine propulsion systems. A cubic-stiffness NES model integrated with propulsion dynamics was validated through the harmonic balance and Runge-Kutta methods. An enhanced Harris Hawks Optimization (HHO) algorithm simultaneously minimizes force transmission and maximizes energy dissipation. The optimized NES effectively reduces vibrations across multiple resonances. Sensitivity analysis identifies the mass ratio as the dominant parameter, while nonlinear stiffness plays a key role in balancing the two objectives. These findings establish practical design guidelines for NES in marine propulsion, demonstrating that effective vibration suppression can be achieved with minimal added mass.