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Ocean waves are abundant in energy; however, they also cause ships to sway and can disrupt the operation of precision equipment. Harvesting energy from ocean waves and isolating vibrations in marine precision equipment have long posed significant challenges due to the inherently low-frequency nature of ocean waves. This study proposes a dynamic-constrained nonlinear (DCN) stiffness method for low-frequency energy harvesting and vibration isolation. A generalized mathematical model of the DCN stiffness system is established, and its semi-analytical solution is derived using the harmonic balance method and the arc-length extension method. Finally, various application scenarios for energy harvesting and vibration isolation using the nonlinear stiffness method are explored. The results demonstrate that the DCN stiffness method can significantly enhance the performance of low-frequency wave energy, capture and provide excellent low-frequency vibration isolation. Notably, this method exhibits a strong adaptive capability to excitation compared to traditional nonlinear stiffness methods.

Vibration suppression and stability control are classic issues in the field of vibration and control. The nonlinear energy sink (NES) is an effective approach for vibration reduction proposed in recent years. It has the advantages of wide frequency vibration isolation properties and without inputting excessive energy. This paper focuses on the stability and passive vibration control of a plate in subsonic airflow by applying the NES. Two kinds of NESs with linear stiffness and with cubic stiffness are proposed and their vibration control performances are compared. The kinetic equations of the plate with NES are established by using the extended Hamilton principle and analyzed by the incremental harmonic balance (IHB) method. The advantages of the hybrid stiffness NES are demonstrated by comparing with the cubic nonlinear stiffness NES. From the results, the vibration suppression effect of the hybrid stiffness NES is more significant than the purely cubic one. However, the effective vibration reduction range of the cubic stiffness NES is wider than the hybrid one. The optimal design parameters of the NES and the effect of the installation position are also discussed.

The main aim of this paper is to focus on analysis of the dynamic properties of the electromechanical system with an impact element. This model is constructed with three degrees of freedom in the mechanical oscillating part, two translational and one rotational, and is completed with an electric circuit. The mathematical model of the system is represented by three mutually coupled second-order ordinary differential equations. Here, the most important nonlinearities are: stiffness of the support spring elements and internal impacts. Several important results were obtained by means of computational simulations. The impacts considerably increase the number of resonance peaks of the frequency response characteristic. Character of the system motion strongly depends on the width of clearances between the impact body and the rotor frame and changes from simple periodic to close to chaotic or to periodic with a large number of ultraharmonic components. For a suitably chosen system parameters, a significant damping effect of the impact element was observed.

The main aim of this paper is focused on vibration attenuation of the electromechanical system flexibly coupled with a baseplate and damped by an impact element. The model is constructed with three degrees of freedom in the mechanical oscillating part, two translational and one rotational. The system movement is described by three mutually coupled second-order ordinary differential equations, derived by the force balance method. Here, the most important nonlinearities are: stiffness of the support spring elements and internal impacts. The main results show the impact damping device attenuates vibrations of the rotor frame in a wide range of the excitation frequencies, that is wider then in the case when the impact element works only as an inertia damper without occurrence of any impacts.

Traditionally, nonlinear stiffness is achieved using mechanical components designed for a specific structure under certain loading conditions. In the present paper, the desired stiffness nonlinearity with various controlled stiffness values is obtained using smart materials. A prototype nonlinear spring is designed by a cantilever beam with bonded macro-fiber composite (MFC). The novel active prototype is modeled, simulated and experimentally validated to realize the artificial nonlinear spring (ANS) approach. To characterize the dynamic behavior of the proposed MFC-beam system, a dynamic linearized model is identified using a fourth order transfer function. Proportional integral (PI) controller is implemented to achieve the required spring stiffness function. According to the applied load estimation technique, three models are used to control the nonlinear stiffness. The results show precise nonlinear responses to measurable static and quasi-static external loads. Unmeasurable loads are real-time estimated and adequately responded. Both softening and hardening springs with a wide range of nonlinear stiffness values are obtained and tuned according to the demands. The proposed approach widens the application range of nonlinear springs and improves their performance.