Dynamics of a linear beam with an attached local nonlinear energy sink

We provide numerical evidence of passive and broadband targeted energy transfer from a linear flexible beam under shock excitation to a local essentially nonlinear lightweight attachment that acts, in essence, as nonlinear energy sink—NES. It is shown that the NES absorbs shock energy in a one-way, irreversible fashion and dissipates this energy locally, without 'spreading' it back to the linear beam. Moreover, we show numerically that an appropriately designed and placed NES can passively absorb and locally dissipate a major portion of the shock energy of the beam, up to an optimal value of 87%. The implementation of the NES concept to the shock isolation of practical engineering structures and to other applications is discussed

Tailoring strongly nonlinear negative stiffness

Negative, nonlinear stiffness elements have been recently designed as configurations of pairs or groups of linear springs. We propose a new design of such a system by using a single linear spring with its moving end rolling on a path described by an equation of varying complexity. We examine the effect that the selection of the path has on the size of the deflection regime where negative stiffness is achieved. The stability properties of the equilibrium positions of the system are also investigated, highlighting the influence that the complexity of the path equation brings. The latter naturally affects the characteristics of the forcing functions around these positions. It is demonstrated that the properties of the system can be tailored according to the nature of the equation used and we show how essentially nonlinear negative stiffness elements, (i.e., with no linear parts) can be designed. These results provide a useful standpoint for designers of such systems, who wish to achieve the desired properties in reduced space, which is a common requirement in modern applications

Analytical characterization of damping in gear teeth dynamics under hydrodynamic conditions

Using an analytical method, we characterize damping and stiffness in lightly loaded, lubricated gear pairs at different operating speeds and lubricant temperatures. This is accomplished by employing a trace method to approximate and model the hysteresis loop of the lubricant reaction, thus recording the energy transformation mechanism during the gear teeth oscillatory motion. The method can be expanded for use in a variety of problems where hydrodynamic vibro-impacts lead to energy dissipation

Targeted energy transfer in automotive powertrains

Torsional oscillations generated by the internal combustion engine induce various NVH phenomena in the drivetrain system, one being transmission rattle. Palliatives devices such as the clutch predampers or dual mass flywheel have been used to mitigate these NVH phenomena. However, usually these devices are effective over a limited range of frequencies, and not so for broadband transient phenomenon, such as any impulsive actions. This paper considers the Targeted Energy Transfer (TET) method to mitigate torsional vibrations in automotive powertrains. TET is a concept which attempts to direct the mechanical (vibration) energy (in a nearly irreversible manner) from a source (primary system) to a strongly nonlinear attachment (Nonlinear Energy Sink – NES), where it is absorbed, redistributed and/or dissipated. In contrast to the classical powertrain palliative methods, NES should be capable of operating over a broader band of frequencies (with the additional aim of being lightweight and compact). Although the TET concept has been extensively studied for translational systems, there is a dearth of studies for rotational (torsional) ones. In the present work, preliminary parametric studies are performed on a reduced automotive powertrain model, incorporating a NES attachment. The NES parameters, including nonlinear stiffness, viscous linear damping and inertia are varied in order to determine NES effects on engine order (EO) vibration

On the effect of multiple parallel nonlinear absorbers in palliation of torsional response of automotive drivetrain

Torsional vibrations transmitted from the engine to the drivetrain system induce a plethora of noise, vibration and harshness (NVH) concerns, such a transmission gear rattle and clutch in-cycle vibration, to name but a few. The main elements of these oscillations are variations in the inertial imbalance and the constituents of combustion power torque, collectively referred to as engine order vibration. To attenuate the effect of these transmitted vibrations and their oscillatory effects in the drive train system, a host of palliative measures are employed in practice, such as clutch pre-dampers, slipping discs, dual mass flywheel and others, all of which operate effectively over a narrow band of frequencies and have various unintended repercussions. These include increased powertrain inertia, installation package space and cost. This paper presents a numerical study of the use of multiple Nonlinear Energy Sinks (NES) as a means of attenuating the torsional oscillations for an extended frequency range and under transient vehicle manoeuvres. Frequency–Energy Plots (FEP) are used to obtain the nonlinear absorber parameters for multiple NES coupled in parallel to the clutch disc of a typical drivetrain configuration. The results obtained show significant reduction in the oscillations of the transmission input shaft, effective over a broad range of response frequencies. It is also noted that the targeted reduction of the acceleration amplitude of the input shaft requires significantly lower NES inertia, compared with the existing palliative measures

A study on torsional vibration attenuation in automotive drivetrains using absorbers with smooth and non-smooth nonlinearities

The automotive industry is predominantly driven by legislations on stringent emissions. This has led to the introduction of downsized engines, incorporating turbocharging to maintain output power. As downsized engines have higher combustion pressures, the resulting torsional oscillations (engine order vibrations) are of broadband nature with an increasing severity, which affect noise and vibration response of drive train system. Palliative devices, such as clutch pre-dampers and dual mass flywheel have been used to mitigate the effect of transmitted engine torsional oscillations. Nevertheless, the effectiveness of these palliative measures is confined to a narrow band of response frequencies. Studying nonlinear targeted energy transfers is a promising approach to study vibration mitigation within a broader range of frequencies, using nonlinear vibration absorbers (or nonlinear energy sinks – NESs). These devices would either redistribute vibration energy within the modal space of the primary structure thus dissipating the vibrational energy more efficiently through structural damping, or passively absorb and locally dissipate a part of this energy (in a nearly irreversible manner) from the primary structure . The absence of a linear resonance frequency of an NES, enables its broadband operation (in contrast to the narrowband operation of current linear tuned mass dampers). Parametric studies are reported to determine the effectiveness of various smooth or non-smooth nonlinear stiffness characteristics of such absorbers. A reduced drivetrain model, incorporating single and multiple absorber attachments is used and comparison of the predictions to numerical integrations proves its efficacy