Passive targeted energy transfers and strong modal interactions in the dynamics of a thin plate with strongly nonlinear attachments

Abstract

We study Targeted Energy Transfers (TETs) and nonlinear modal interactions attachments occurring in the dynamics of a thin cantilever plate on an elastic foundation with strongly nonlinear lightweight attachments of different configurations in a more complicated system towards industrial applications. We examine two types of shock excitations that excite a subset of plate modes, and systematically study, nonlinear modal interactions and passive broadband targeted energy transfer phenomena occurring between the plate and the attachments. The following attachment configurations are considered: (i) a single ungrounded, strongly (essentially) nonlinear single-degree-of-freedom (SDOF) attachment – termed nonlinear energy sink (NES); (ii) a set of two SDOF NESs attached at different points of the plate; and (iii) a single multi-degree-of-freedom (MDOF) NES with multiple essential stiffness nonlinearities. We perform parametric studies by varying the parameters and locations of the NESs, in order to optimize passive TETs from the plate modes to the attachments, and we showed that the optimal position for the NES attachments are at the antinodes of the linear modes of the plate. The parametric study of the damping coefficient of the SDOF NES showed that TETs decreasing with lower values of the coefficient and moreover we showed that the threshold of maximum energy level of the system with strong TETs occured in discrete models is by far beyond the limits of the engineering design of the continua. We examine in detail the underlying dynamical mechanisms influencing TETs by means of Empirical Mode Decomposition (EMD) in combination with Wavelet Transforms. This integrated approach enables us to systematically study the strong modal interactions occurring between the essentially nonlinear NESs and different plate modes, and to detect the dominant resonance captures between the plate modes and the NESs that cause the observed TETs. Moreover, we perform comparative studies of the performance of different types of NESs and of the linear Tuned-Mass-Dampers (TMDs) attached to the plate instead of the NESs. Finally, the efficacy of using this type of essentially nonlinear attachments as passive absorbers of broadband vibration energy is discussed

Numerical and experimental investigations of a rotating nonlinear energy sink

“…Unlike the tuned mass damper (TMD), the NES is a broadband frequency-energy device that is capable of mitigating high vibration amplitudes in structures over broad frequency and energy ranges [33]. In addition, the NES has another unique advantage over the TMD, namely its capability to redistribute a significant portion of the initial shock energy from low to high vibration modes.…”

Control of primary and subharmonic resonances of a Duffing oscillator via non-linear energy sink

“…Discussion on energy transfer between linear and essentially nonlinear oscillators is given in [14][15][16][17], while extension of the use of NES to control non-ideal main structures is presented in [18,19]. NES attached to continuum primary linear structures, such as string, beams or plates, is considered in [20][21][22][23][24][25][26][27]. Multi-d.o.f.…”

Passive Vibration Control of Pipes Conveying Fluid with Parallel Nonlinear Energy Sinks

“…The passive methodologies are intrinsically simple and stable to design. Targeted energy transfer (TET) is a one-way irreversible form, in which the vibration energy directly comes from a source (oscillator) to a receptor (receiver) [19][20][21][22] . Then, the nonlinear energy sink was put forward on the basis of the TET theory, which owns small supplementary mass and suits for a wide frequency range.…”