Rapid non-resonant intermodal targeted energy transfer (IMTET) caused by vibro-impact nonlinearity

Nonlinear Dynamics - This paper describes a rapid and efficient nonlinear non-resonance mechanism for low-to-high-frequency energy scattering, which is referred to as intermodal targeted energy...     

Enhanced passive targeted energy transfer in strongly nonlinear mechanical oscillators

Single-degree-of-freedom (SDOF) nonlinear energy sinks (NESs) can efficiently mitigate broadband disturbances applied to primary linear systems by means of passive targeted energy transfer (TET), but for a rather limited range of energies. We demonstrate that the TET can be significantly enhanced for broad range of energies by introducing additional internal degrees of freedom to the NES in a highly asymmetric fashion. Numerical simulations demonstrate that the enhanced performance is due to a positive synergistic effect of the internal degrees of freedom of the proposed NES with highly asymmetric stiffnesses.     

Reflection of short rectangular pulses in the ideal string attached to strongly nonlinear oscillator

The system under consideration is ideal elastic string attached to strongly nonlinear oscillator with cubic nonlinearity by two different ways – immediately and by weak linear spring. The reflection of short rectangular pulses from the oscillator is accompanied by excitation of vibrations. The type of mode excited determines the amount of energy transferred to the oscillator as well as the structure of the reflected wave.     

Escape of a forced-damped particle from weakly nonlinear truncated potential well

Nonlinear Dynamics - Escape from a potential well is an extreme example of transient behavior. We consider the escape of the harmonically forced particle under viscous damping from the benchmark...     

Interaction of elastic system with snap-through vibration absorber

Interaction of essentially non-linear vibration absorber (snap-through truss) with primary 1DOF linear oscillator is investigated. The study covers both free and forced (external excitation applied to the linear oscillator) responses of the system. The analysis is performed by complexification-averaging technique, describing a slow variation of amplitudes of principal harmonic components. Periodic and quasiperiodic oscillations are revealed and investigated. It turns out that for realistic parameters of the system vast majority of the responses, including those suitable for the vibration absorption, is quasiperiodic. The results are verified by means of a direct numeric simulation.     

From Chaos to Ordering: New Studies in the Shannon Entropy of 2D Patterns

Properties of the Voronoi tessellations arising from random 2D distribution points are reported. We applied an iterative procedure to the Voronoi diagrams generated by a set of points randomly placed on the plane. The procedure implied dividing the edges of Voronoi cells into equal or random parts. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of the positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in linear semi-crystalline polymers and metallic glasses. Thus, we can conclude that by applying even a simple set of rules to a random set of seeds, we can introduce order into an initially disordered system. At the same time, the Shannon (Voronoi) entropy showed a tendency to attain values that are typical for completely random patterns; thus, the Shannon (Voronoi) entropy does not distinguish the short-range ordering. The Shannon entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase in the number of iteration steps. The Shannon entropy grew with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Shannon (Voronoi) entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Shannon entropy.     

Bifurcations of Nonlinear Normal Modes of Linear Oscillator with Strongly Nonlinear Damped Attachment

Linear oscillator coupled to damped strongly nonlinear attachment with small mass is considered as a model design for nonlinear energy sink (NES). Damped nonlinear normal modes of the system are considered for the case of 1:1 resonance by combining the invariant manifold approach and multiple scales expansion. Special asymptotical structure of the model allows a clear distinction between three time scales. These time scales correspond to fast vibrations, evolution of the system toward the nonlinear normal mode and time evolution of the invariant manifold, respectively. Time evolution of the invariant manifold may be accompanied by bifurcations, depending on the exact potential of the nonlinear spring and value of the damping coefficient. Passage of the invariant manifold through bifurcations may bring about destruction of the resonance regime and essential gain in the energy dissipation rate.     

Mesoscopic patterning in evaporated polymer solutions: new experimental data and physical mechanisms

Mesoscopically ordered patterns were obtained when polymer solutions were applied to tilted substrates and evaporated immediately under ambient conditions in a slow air current. The patterns were studied with optical, scanning electron, and atomic force microscopy. Shadowgraph visualization of the patterning was carried out, and visualization of the flow with an ink tracer was performed. Restrained and nonrestrained flows of the polymer solution gave rise to very similar patterning. The formation of the patterns on different solid substrates, including substrates wetted with silicon oil, was investigated. The concentration of the polymer solutions exerted an influence on the characteristic dimension of mesoscaled cells. A physical mechanism of the patterning is proposed. The mechanism is based on the mass transport instability occurring under the intensive evaporation of the solvent. The model satisfactorily explains the experimental findings.