MS13.4: Energy Transfer and Harvesting in Nonlinear Systems

The non-linear dynamical behavior of a simply supported box girder bridge is studied. In particular, the Thin-Walled-Beam is treated through the Generalized Beam Theory (GBT) to consider the deformation of the cross-section in its own plane. The non-linearity is introduced by a Nonlinear Energy Sink (NES), properly linked to the beam along its longitudinal axis. The basic ideas of GBT are first introduced and then combined with those relative to the NES. The problem is studied through Complexification-Averaging and Multiple Scales Method, leading to the detection of the Slow Invariant Manifold (SIM) at fast time scale and equilibrium and singular points of the system at slow time scale. The goal is to compare the beam response under a dynamical external load with and without NES.

A nonlinear energy sink (NES) is a mechanical vibration absorber with mass and nonlinear stiffness, typically a cubic hardening spring. This nonlinear stiffness increases the operational bandwidth of the NES compared to linear vibration absorbers. This work presents and experimentally implements the concept of the NES as an electronic shunt for piezoelectric transducers to damp mechanical vibrations. As an analog to the mechanical NES, a cubic nonlinearity is realized by a cubic nonlinear voltage source. A frequency response is derived through the harmonic balancing technique. A saturation of the vibration amplitude of the host system is discovered, and there is a quasi-periodic energy exchange between the mechanical and electrical domains. This behavior and the vibration control performance are experimentally verified with a cantilever beam with bonded piezoelectric patches. The electronic nonlinearity is made with an analog multiplier.

Many relevant structures in engineering are rotationally periodic, meaning that they consist of a discrete number of sectors with the same properties that are circumferentially assembled with cyclic symmetry. Their resonant vibrations can lead to strong fatigue problems, as it is especially known for bladed disks in turbomachinery. We explore the use of vibro-impact absorbers to suppress these forced resonant vibrations by considering a cyclic chain of oscillators with ten sectors of which each consists of a single degree of freedom oscillator that hosts a vibro-impact absorber. Our simulations show that the absorbers are able to synchronize to the global motion of the structure, with a 1:1 resonance between absorbers and oscillators in all sectors, and thus lead to an outstanding reduction of its resonant amplitude. However, this synchronization can also happen locally in a subset of all sectors which then show larger amplitudes than the remaining ones. Based on the single-term Harmonic Balance ansatz, we develop an analytical model of these synchronized solutions and study their practical stability and largest possible amplitudes numerically.

Vibro-impact absorbers are small devices that consist of a small mass which is freely placed inside a cavity of a vibrating host-structure. During operation it undergoes recurrent impacts with the cavity walls that lead to a strong and nearly irreversible scattering of the mechanical energy within the primary structure’s modal space. As higher modes accumulate more vibration cycles within a given time during their free response than the substantially excited lower modes, they are able to dissipate the mechanical energy on a faster timescale. This results in an overall reduction of the amplitude and does theoretically not rely on local dissipation due to e. g. dissipative materials in the contact area. Experimental investigations of this working principle so far lacked a way of quantifying the instantaneous energy transfer to higher modes, which is crucial to develop better predictable models of the absorber. To this end, we measure the response of a harmonically excited beam structure with vibro-impact absorber at multiple points across its span and project it onto its prior experimentally determined linear modes to reconstruct the instantaneous modal energy distribution.