Vibration Suppression By Nonlinear Energy Sinks And Particle Dampers From The View Of Energy Transfer

Nonlinear energy sinks(NESs)have been utilized to passively suppress dynamic responses of mechanical or structural systems through irreversibly transferring and locally dissipating vibrational energy.The NESs acting as passive,adaptive and broadband nonlinear vibration absorbers have a wide application prospect.This dissertation focuses on a primary structure coupled with a NES and emphasizes the weight’s effects.Also,strongly nonlinear absorbers(acting,in essence,as NESs)and particle dampers are adopted in this thesis to regulate energy transaction and passively suppress vibration of structures.The main contents are given below,Chapter 2 investigates the dynamic effects of the weight on a primary structure attached by a NES(called the structure – NES system)in free vibration and forced vibration.The derivation of dynamic equations for the vertically-excited structure –NES system is given.The vibration frequency changes caused by the NES are numerically explored,as well as emphasizing the weight’s effects.When the structure– NES system is harmonically excited,the steady-state responses of the main structure and the NES are computed via the harmonic balance method.The stability of analytical solutions is checked according to the Floquet theory.The analytical steady-state responses are verified by numerical results which are simulated through the RungeKutta method.Results indicate that there are both quantitative and qualitative differences between the cases with and without the weight in harmonically forced vibration.Comparisons between experimental data and theoretical results indicate that the weight should be considered in the vertically-excited structure – NES system.Chapter 3 studies the structure – NES system subjected to a Gaussian white noise excitation and demonstrates the stochastic responses and vibration suppression with emphasis on the effects of the weights.The probability densities of the structure’s responses are simulated via the path integration method which is based on the GaussLegendre scheme.The path integration solutions are validated by Monte Carlo simulation results.Probability densities of the structure’s responses are compared between two cases under various random excitation intensities.Huge differences are found at small levels of the stochastic excitation intensity,whereas similitudes emerge as the excitation intensity increases.Additionally,the differences about the performance of random vibration reduction between two cases decrease with the strength of this excitation increasing.According to discussions on the NES’s parameters,the optimum performance indicates that strongly nonlinear behaviors of the NES contribute to enhancing suppressing random responses.The effects of weights should be taken into consideration when employing a large and reasonable NES mass.In Chapter 4,a primary structure with a NES vibrating vertically or horizontally are discussed.Both strongly nonlinear modal interactions in the underlying undamped system and nonlinear energy transfer phenomena in the damped system are explored.Periodic orbits of this undamped system are numerically computed via the shooting method together with the pseudo-arclength continuation technique.According to the frequency-energy plot,nonlinear modal interactions are compared between verticallyand horizontally-moving cases in order to find similitudes and differences.Transient resonance captures in two coupled systems are numerically estimated.Highly similar energy transfer behaviors are observed when applying high energies while different energy transfer phenomena occur under low input energies.In Chapter 5,the single and two degree-of-freedom(SDOF and Two-DOF)strongly nonlinear absorbers are attached to a linear,large-scale nine-story structure for purpose of shock mitigation.The role of the strongly nonlinear absorber(SNA)is not only to dissipate shock energy,but also to redistribute the shock energy from the lowto high-frequency modes of the structure,which means that essentially it acts as a NES.The effective damping measure is adopted to estimate how input energy is redistributed in the modal space and to estimate the efficacy of modal energy exchanges for shock mitigation.The quantitative results for shock energy redistribution indicate that with strong geometric nonlinearity one can achieve low-to-high frequency nonlinear targeted energy transfer in this structure.The optimized Two-DOF SNA is much more robust when compared to the optimized SDOF SNA.Form the perspective of energy transfer or energy exchange,Chapter 6innovatively studies the particle damper(PD).The PD is placed in a primary structure which is subjected to a shock force.The complicated model is proposed and considers non-smooth nonlinearity including Hertzian effects,impacts and frictional forces due to granule rotations.The strongly nonlinear dynamic responses of the structure and the granules are simulated under the condition of the numerical convergence via the discrete element method.Effects of diverse initial equilibrium positions of granules on the dynamics are discussed.In addition,when using more than two particles,various topologies of granules are proposed as well as optimum sizes of cavities.The shock energy of the primary is transferred into particles through impacts between particles and the structure.Significant energy exchanges are got by designing the sizes of the container,which gives rise to efficient and rapid shock mitigation.To conclude,for purpose of highly efficient nonlinear vibration suppression,some lightweight attachments,including NESs and PDs,which possess strongly nonlinear characteristics are employed to transfer vibrational energy of the primary structure to nonlinear attachments,or to redistribute the input energy from the low-to highfrequency modes of the structure.Nonlinear vibration suppression based on energy transfer in this dissertation provides theoretical guidance for future experimental research works or practical engineering applications.