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Abstract Aeolian vibration is a significant factor contributing to the fatigue failure of power transmission lines. The mitigation of such vibrations in power lines has traditionally been achieved using Stockbridge dampers along the line spans, which are modeled as fixed vibration absorbers. They largely depend on their resonant frequencies and placement on the cable. Therefore, given the stochastic nature of the wind, recent studies have explored the concept of dynamic/moving absorbers. Although the effectiveness of the moving absorber has been demonstrated in the literature to be superior to that of the fixed absorber, analyses have primarily been limited to linear cases and have not accounted for nonlinearity introduced by the moving absorber or the wind inflow on the powerline. Aiming to fill this gap, this work combines the nonlinearities from the fluctuating lift force modeled as a van der Pol oscillator, with a nonlinear moving absorber into a single model to investigate the effect of a nonlinear mobile damper relative to its linear counterpart. We observe that the system with a nonlinear moving absorber exhibits smaller amplitude oscillations when compared to its linear counterpart. This finding underscores the superior mitigation characteristics of nonlinear vibration absorbers and suggests the potential for designing an optimal nonlinear moving vibration absorber. 

Abstract The impact of the vibration absorber on the synchronization region during vortex-induced vibration of turbine blades is investigated. This work is based on a 3DOF model, including a coupled plunge-pitch airfoil motion and a van der Pol oscillator to the fluid-structure interaction caused by the vortex shedding of the incoming flow. The aeroelastic system is increased by a degree of freedom, namely, the vibration absorber. Linear and nonlinear vibration absorbers are used in this investigation to analyze the effectiveness of the vibration absorber. To demonstrate the effect of the resonator on the lock-in, the coupled natural frequencies, numerical frequency responses, and time histories are plotted. The study reveals the promising capability of the absorber to reduce the lock-in region and mitigate the VIV amplitudes within these regions. For the current application, however, the nonlinear absorber response was indifferent compared to its linear counterpart for the given values of coupling coefficients. This observation indicates that a linear absorber efficiently shrinks the lock-in regions and mitigates the VIV in turbomachinery. 

Abstract The application of servocontrolled mechanical-bearing-based precision motion stages (MBMS) is well-established in advanced manufacturing, semiconductor industries, and metrological applications. Nevertheless, the performance of the motion stage is plagued by self-excited friction-induced vibrations. Recently, a passive mechanical friction isolator (FI) has been introduced to reduce the adverse impact of friction in MBMS, and accordingly, the dynamics of MBMS with FI were analyzed in the previous works. However, in the previous works, the nonlinear dynamics components of FI were not considered for the dynamical analysis of MBMS. This work presents a comprehensive, thorough analysis of an MBMS with a nonlinear FI. A servocontrolled MBMS with a nonlinear FI is modeled as a two DOF spring-mass-damper lumped parameter system. The linear stability analysis in the parametric space of reference velocity signal and differential gain reveals that including nonlinearity in FI significantly increases the local stability of the system's fixed-points. This further allows the implementation of larger differential gains in the servocontrolled motion stage. Furthermore, we perform a nonlinear analysis of the system and observe the existence of sub and supercritical Hopf bifurcation with or without any nonlinearity in the friction isolator. However, the region of sub and supercritical Hopf bifurcation on stability curves depends on the nonlinearity in FI. These observations are further verified by a detailed numerical bifurcation, which reveals the existence of nonlinear attractors in the system. 

Abstract Recent studies in passively-isolated systems have shown that mode coupling is desirable for best vibration suppression, thus refuting the long-standing rule of mode decoupling. However, these studies have ignored the non-linearities in the isolators. In this work, we consider stiffness nonlinearity from pneumatic isolators and study the nonlinear free undamped vibrations of a passively-isolated ultra-precision manufacturing (UPM) machine. Experimental analysis is conducted to guide the mathematical formulation. The system comprises linearly and nonlinearly coupled in-plane horizontal and rotational motion of the UPM machine with quadratic nonlinear stiffness from the isolators. We present closed-form expressions using the method of multiple scales for two cases viz. the non-resonant case and the bounded internal resonance case. We validate our theoretical findings through direct numerical simulations. For the non-resonant case, we show that the system behaves similar to a linear system. However, for the nearly internal resonance case, we demonstrate strong energy exchange between the modes stemming from nonlinear mode coupling. We further study the effect of nonlinear mode coupling on the vibration isolation performance and demonstrate that mode coupling is not always desirable.