KDamping: A Stiffness Based Vibration Absorption Concept

© 2016, © The Author(s) 2016. The KDamper is a novel passive vibration isolation and damping concept, based essentially on the optimal combination of appropriate stiffness elements, which include a negative stiffness element. The KDamper concept does not require any reduction in the overall structural stiffness, thus overcoming the corresponding inherent disadvantage of the “Quazi Zero Stiffness” (QZS) isolators, which require a drastic reduction of the structure load bearing capacity. Compared to the traditional Tuned Mass damper (TMD), the KDamper can achieve better isolation characteristics, without the need of additional heavy masses, as in the case of the T Tuned Mass damper. Contrary to the TMD and its variants, the KDamper substitutes the necessary high inertial forces of the added mass by the stiffness force of the negative stiffness element. Among others, this can provide comparative advantages in the very low frequency range. The paper proceeds to a systematic analytical approach for the optimal design and selection of the parameters of the KDamper, following exactly the classical approach used for the design of the Tuned Mass damper. It is thus theoretically proven that the KDamper can inherently offer far better isolation and damping properties than the Tuned Mass damper. Moreover, since the isolation and damping properties of the KDamper essentially result from the stiffness elements of the system, further technological advantages can emerge, in terms of weight, complexity and reliability. A simple vertical vibration isolation example is provided, implemented by a set of optimally combined conventional linear springs. The system is designed so that the system presents an adequate static load bearing capacity, whereas the Transfer Function of the system is below unity in the entire frequency range. Further insight is provided to the physical behavior of the system, indicating a proper phase difference between the positive and the negative stiffness elastic forces. This fact ensures that an adequate level of elastic forces exists throughout the entire frequency range, able to counteract the inertial and the external excitation forces, whereas the damping forces and the inertia forces of the additional mass remain minimal in the entire frequency range, including the natural frequencies. It should be mentioned that the approach presented does not simply refer to discrete vibration absorption device, but it consists a general vibration absorption concept, applicable also for the design of advanced materials or complex structures. Such a concept thus presents the potential for numerous implementations in a large variety of technological applications, whereas further potential may emerge in a multi-physics environment.status: publishe

Simplifying transformations for nonlinear systems: Part I, an optimisation-based variant of normal form analysis

This paper introduces the idea of a ‘simplifying transformation’ for nonlinear structural dynamic systems. The idea simply stated; is to bring under one heading, those transformations which ‘simplify’ structural dynamic systems or responses in some sense. The equations of motion may be cast in a simpler form or decoupled (and in this sense, nonlinear modal analysis is encompassed) or the responses may be modified in order to isolate and remove certain components. It is the latter sense of simplification which is considered in this paper. One can regard normal form analysis in a way as the removal of superharmonic content from nonlinear system response. In the current paper, this problem is cast in an optimisation form and the differential evolution algorithm is used

Targeted Energy Transfer and Modal Energy Redistribution in Automotive Drivetrains

The new generations of compact high output power-to-weight ratio internal combustion engines generate broadband torsional oscillations, transmitted to lightly damped drivetrain systems. A novel approach to mitigate these untoward vibrations can be the use of nonlinear absorbers. These act as Nonlinear Energy Sinks (NESs). The NES is coupled to the primary (drivetrain) structure, inducing passive irreversible targeted energy transfer (TET) from the drivetrain system to the NES. During this process, the vibration energy is directed from the lower-frequency modes of the structure to the higher ones. Thereafter, vibrations can be either dissipated through structural damping or consumed by the NES. This paper uses a lumped parameter model of an automotive driveline to simulate the effect of TET and the assumed modal energy redistribution. Significant redistribution of vibratory energy is observed through TET. Furthermore, the integrated optimization process highlights the most effective configuration and parametric evaluation for use of NES

A machine learning approach to nonlinear modal analysis

Although linear modal analysis has proved itself to be the method of choice for the analysis of linear dynamic structures, extension to nonlinear structures has proved to be a problem. A number of competing viewpoints on nonlinear modal analysis have emerged, each of which preserves a subset of the properties of the original linear theory. From the geometrical point of view, one can argue that the invariant manifold approach of Shaw and Pierre is the most natural generalisation. However, the Shaw–Pierre approach is rather demanding technically, depending as it does on the construction of a polynomial mapping between spaces, which maps physical coordinates into invariant manifolds spanned by independent subsets of variables. The objective of the current paper is to demonstrate a data-based approach to the Shaw–Pierre method which exploits the idea of independence to optimise the parametric form of the mapping. The approach can also be regarded as a generalisation of the Principal Orthogonal Decomposition (POD)

Bridging the Gap Between Nonlinear Normal Modes and Modal Derivatives

Nonlinear Normal Modes (NNMs) have a clear conceptual relation to the classical linear normal modes (LNMs), yet they offer a solid theoretical framework for interpreting a wide class of non-linear dynamical phenomena with no linear counterpart. The main difficulty associated with NNMs is that their calculation for large-scale models is expensive, particularly for distributed nonlinearities. Repeated direct time integrations need to be carried out together with extensive sensitivity analysis to reproduce the frequency-energy dependence of the modes of interest. In the present paper, NNMs are computed from a reduced model obtained using a quadratic transformation comprising LNMs and Modal Derivatives (MDs). Previous studies have shown that MDs can capture the essential dynamics of geometrically nonlinear structures and can greatly reduce the computational cost of time integration. A direct comparison with the NNMs computed from another standard reduction technique highlights the capability of the proposed reduction method to capture the essential nonlinear phenomena. The methodology is demonstrated using simple examples with 2 and 4 degrees of freedom.BeIPD-COFUND outgoing fellowship: Managing bifurcations of nonlinear mechanical systems using experimental continuation technique

On the dynamics of a nonlinear energy harvester with multiple resonant zones

The dynamics of a nonlinear vibration energy harvester for rotating systems is investigated analytically through harmonic balance, as well as by numerical analysis. The electromagnetic harvester is attached to a spinning shaft at constant speed. Magnetic levitation is used as the system nonlinear restoring force for broadening the resonant range of the oscillator. The system is modelled as a Duffing oscillator with linear frequency variation under static, as well as harmonic excitation. Behaviour charts and backbone curves are extracted for the fundamental harmonic response and validated against frequency response curves for selected cases, using direct numerical integration. It is found that variation in stiffness, together with asymmetric forcing, gives rise to a novel structure of multiple resonant zones, incorporating mono-stable and bi-stable dynamics. Contrary to previously considered bi-stable energy harvesters, cross-well oscillations are realized through a transition from single-well potential energy to double-well with forward frequency sweep. Furthermore, in-well_oscillations present a hardening behaviour, unlike the well-known softening in-well response of bi-stable Duffing oscillators. The analysis shows that the proposed system has multiple resonant responses to a frequency sweep, influenced by consecutive interacting backbone curves similar to a multi-modal system. This combined effect of the transition to bi-stable dynamics and the hardening in-well oscillations induces resonant response of the harvester over multiple distinct frequency ranges. Thus, the system exhibits a broadened frequency response, enhancing its energy harvesting potential

Nonlinear dynamics of a spinning shaft with non-constant rotating speed

Research on spinning shafts is mostly restricted to cases of constant rotating speed without examining the dynamics during their spin-up or spin-down operation. In this article, initially the equations of motion for a spinning shaft with non-constant speed are derived, then the system is discretised, and finally a nonlinear dynamic analysis is performed using multiple scales perturbation method. The system in first-order approximation takes the form of two coupled sets of paired equations. The first pair describes the torsional and the rigid body rotation, whilst the second consists of the equations describing the two lateral bending motions. Notably, equations of the lateral bending motions of first-order approximation coincide with the system in case of constant rotating speed, and considering the amplitude modulation equations, as it is shown, there are detuning frequencies from the Campbell diagram. The nonlinear normal modes of the system have been determined analytically up to the second-order approximation. The comparison of the analytical solutions with direct numerical simulations shows good agreement up to the validity of the performed analysis. Finally, it is shown that the Campbell diagram in the case of spin-up or spin-down operation cannot describe the critical situations of the shaft. This work paves the way, for new safe operational ‘modes’ of rotating structures bypassing critical situations, and also it is essential to identify the validity of the tools for defining critical situations in rotating structures with non-constant rotating speeds, which can be applied not only in spinning shafts but in all rotating structures