The dynamics of the pendulum suspended on the forced Duffing oscillator

We investigate the dynamics of the pendulum suspended on the forced Duffing oscillator. The detailed bifurcation analysis in two parameter space (amplitude and frequency of excitation) which presents both oscillating and rotating periodic solutions of the pendulum has been performed. We identify the areas with low number of coexisting attractors in the parameter space as the coexistence of different attractors has a significant impact on the practical usage of the proposed system as a tuned mass absorber.Comment: Accepte

Forced large amplitude periodic vibrations of non-linear Mathieu resonators for microgyroscope applications

International audienceThis paper describes a comprehensive non-linear multiphysics model based on the Euler-Bernoulli beam equation that remains valid up to large displacements in the case of electrostatically actuated Mathieu resonators. This purely analytical model takes into account the fringing field effects and is used to track the periodic motions of the sensing parts in resonant microgyroscopes. Several parametric analyses are presented in order to investigate the effect of the proof mass frequency on the bifurcation topology. The model shows that the optimal sensitivity is reached for resonant microgyroscopes designed with sensing frequency four times faster than the actuation one

Performance, robustness and sensitivity analysis of the nonlinear tuned vibration absorber

The nonlinear tuned vibration absorber (NLTVA) is a recently-developed nonlinear absorber which generalizes Den Hartog's equal peak method to nonlinear systems. If the purposeful introduction of nonlinearity can enhance system performance, it can also give rise to adverse dynamical phenomena, including detached resonance curves and quasiperiodic regimes of motion. Through the combination of numerical continuation of periodic solutions, bifurcation detection and tracking, and global analysis, the present study identifies boundaries in the NLTVA parameter space delimiting safe, unsafe and unacceptable operations. The sensitivity of these boundaries to uncertainty in the NLTVA parameters is also investigated.Comment: Journal pape

Review of nonlinear vibration energy harvesting: Duffing, bistability, parametric, stochastic and others

Vibration energy harvesting typically involves a mechanical oscillatory mechanism to accumulate ambient kinetic energy, prior to the conversion to electrical energy through a transducer. The convention is to use a simple linear mass-spring-damper oscillator with its resonant frequency tuned towards that of the vibration source. In the past decade, there has been a rapid expansion in research of vibration energy harvesting into various nonlinear vibration principles such as Duffing nonlinearity, bistability, parametric oscillators, stochastic oscillators and other nonlinear mechanisms. The intended objectives for using nonlinearity include broadening of frequency bandwidth, enhancement of power amplitude and improvement in responsiveness to non-sinusoidal noisy excitations. However, nonlinear vibration energy harvesting also comes with its own challenges and some of the research pursuits have been less than fruitful. Previous reviews in the literature have either focussed on bandwidth enhancement strategies or converged on select few nonlinear mechanisms. This article reviews eight major types of nonlinear vibration energy harvesting reported over the past decade, covering underlying principles, advantages and disadvantages, and application-specific guidance for researchers and designers

A preliminary investigation into the effects of nonlinear response modification within coupled oscillators

This thesis provides an account of an investigation into possible dynamic interactions between two coupled nonlinear sub-systems, each possessing opposing nonlinear overhang characteristics in the frequency domain in terms of positive and negative cubic stiffnesses. This system is a two degree-of-freedom Duffing oscillator coupled in series in which certain nonlinear effects can be advantageously neutralised under specific conditions. This theoretical vehicle has been used as a preliminary methodology for understanding the interactive behaviour within typical industrial ultrasonic cutting components. Ultrasonic energy is generated within a piezoelectric exciter, which is inherently nonlinear, and which is coupled to a bar-horn or block-horn to one, or more, material cutting blades, for example. The horn/blade configurations are also nonlinear, and within the whole system there are response features which are strongly reminiscent of positive and negative cubic stiffness effects. The two degree-of-freedom model is analysed and it is shown that a practically useful mitigating effect on the overall nonlinear response of the system can be created under certain conditions when one of the cubic stiffnesses is varied. It has also bfeen shown experimentally that coupling of ultrasonic components with different nonlinear characteristics can strongly influence the performance of the system and that the general behaviour of the hypothetical theoretical model is indeed borne out in practice

Some Interesting Effects of High-Frequency Non-Resonant Harmonic Excitations on the Slow Response of Duffing Oscillators

This dissertation investigates the response of Duffing oscillators to bi-harmonic ex-citations consisting of a soft resonant component and a hard high-frequency non-resonant component. To this end, the dissertation uses approximate analytical solutions, numerical simulations, and an especially-designed experimental module to detail the influence of non-resonant excitation on the resonant response for oscillators with symmetric/asymmetric, mono and bi-stable potential energy functions. For mono-stable Duffing oscillators, we demonstrate that the high-frequency excitation has a substantial influence on the shape of the potential energy function associated with the slow dynamics. In specific, we show that the hard excitation stiffens the slow response for oscillators with a symmetric potential energy function. For asymmetric potential energy functions, we clearly illustrate that the high-frequency excitation tends to symmetrize the potential function, therewith reducing the softening nonlinear behaviour of the system. In such case, we also demonstrate that the high-frequency excitation can be the effectively utilized to change the effective nonlinearity of the slow dynamics from the softening to the hardening type. Therefore, by choosing the proper parameters, the hard excitation can be used to locally linearize the resonant dynamics of an asymmetric mono-stable Duffing oscillator. We also demonstrate that by reducing the depth of the potential wells and bringing them closer together, a high-frequency hard excitation can influence the effective properties of the slow dynamics of a bi-stable Duffing oscillator. This has the effect of amplifying the intra-well response. The reduction of the depth of the potential wells also causes the wells to become more asymmetric which increases the softening nonlinearity of the slow dynamics. Furthermore, once the magnitude of the non-resonant excitation exceeds a certain threshold, the potential function loses its bi-stable properties and becomes mono-stable. In summary, this dissertation highlights many interesting effects of the hard excitation on the qualitative properties of the slow resonant response. Such effects can be utilized as an effective open-loop tool to alter the resonant behaviour of the system, which, in turn, can be useful in various application problems including, but limited to, vibration mitigation, sensor sensitivity enhancement, and system identification. Here, we present one illustration where we exploit the hard excitation for parametric system identification of a nonlinear mono-stable oscillator. We present the proposed methodology and apply it successfully to identify the nonlinear parameters of several experimental systems

Vibrational energy transfer in coupled mechanical systems with nonlinear joints

Acknowledgement This work was supported by National Natural Science Foundation of China under Grant number 12172185, by Zhejiang Provincial Natural Science Foundation of China under Grant number LY22A020006, and by Ningbo Municipal Natural Science Foundation under Grant number 2022J174.Peer reviewedPostprin

Delayed Feedback Control on a Class of Generalized Gyroscope Systems under Parametric Excitation

AbstractThe nonlinear dynamics of the parametrically excited vibrations of a class of generalized gyroscope systems under delayed feedback control is investigated by the averaging method and simulations in this paper. The influence of feedback control on the stability of the trivial solution and the amplitude of the periodic vibrations is presented based on Routh-Hurwitz criterion and the Levenberg-Marquardt method respectively. It is shown that the stability of the trivial solution can be varied when feedback control and time delay are employed. The amplitudes of periodic solutions can also be modulated greatly by feedback gain and time delay. However, the influence of time delay on amplitudes is periodic. The simulations obtained by numerically integrating the original system are in good agreement with the analytical results