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Research Papers

Shock Mitigation by Means of Low- to High-Frequency Nonlinear Targeted Energy Transfers in a Large-Scale Structure

[+] Author and Article Information
Mohammad A. AL-Shudeifat

Aerospace Engineering,
Khalifa University of Science, Technology
and Research,
Abu Dhabi 127788, UAE
e-mail: mohd.shudeifat@kustar.ac.ae

Alexander F. Vakakis

Mechanical Science and Engineering,
University of Illinois at Urbana—Champaign,
Urbana, IL 61801
e-mail: avakakis@illinois.edu

Lawrence A. Bergman

Aerospace Engineering,
University of Illinois at Urbana—Champaign,
Urbana, IL 61801
e-mail: lbergman@illinois.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 19, 2015; final manuscript received April 28, 2015; published online August 26, 2015. Assoc. Editor: Haiyan Hu.

J. Comput. Nonlinear Dynam 11(2), 021006 (Aug 26, 2015) (11 pages) Paper No: CND-15-1015; doi: 10.1115/1.4030540 History: Received January 19, 2015

In this computational study, the implementation of passive nonlinear vibro-impact attachments (termed nonlinear energy sinks (NESs)) for shock mitigation of an otherwise linear multistory large-scale structure is investigated. This is achieved by inducing passive targeted energy transfer (TET) from the fundamental (lowest-frequency and most energetic) structural mode to high-frequency modes, through a series of vibro-impacts induced by the attachments. The functionality of the passive attachments is based on single-sided vibro-impacts (SSVIs), enabling rapid and one-way scattering of shock energy from low- to high-frequency structural modes. Hence, redistribution of shock energy in the modal space of the structure occurs as energy gets nonlinearly scattered to high frequencies. In turn, this energy scattering rapidly reduces the overall amplitude of the transient structural response, and increases the effective dissipative capacity of the integrated NES-structure assembly. The effective modal dissipation rates of the integrated assembly can be controlled by the inherent damping of the NESs, and can be qualitatively studied in detail by defining appropriate dissipative measures which track the TETs from low- and high-frequency structural modes. Ideally, the optimized NESs can passively scatter up to 80% of the input shock energy from the fundamental structural mode to high-frequency modes in the limit when their inherent damping is zero and the coefficient of restitution during vibro-impacts is unity. When dissipative effects are introduced into the NESs, additional energy exchanges between the NESs and high-frequency modes occur. Our study facilitates the predictive design of vibro-impact NESs for optimal and rapid shock mitigation of large-scale structures.

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Figures

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Fig. 1

The nine-story structure with an SSVI NES on each of the two top floors; one-dimensional horizontal motions of the floors and the shaker table are assumed [31,32]

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Fig. 2

Optimization of the second floor SSVI NES parameters for maximum low- to high-frequency energy transfer: (a) percentage of impulsive energy transferred from the fundamental mode to modes 2–9 due to the vibro-impacts of the second NES, and (b) study of robustness of optimized NES parameters for a wide range of impulse intensities velocities; a uniform floor initial floor velocity equal to 0.25 m/s was assumed for each floor

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Fig. 3

Percentage of total energy induced and of energy eventually dissipated by (a) the fundamental mode of the structure, and (b) the higher frequency modes; the optimized SSVI NES parameters listed in Table 1 are used for these simulations

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Fig. 4

Percentage of energy eventually dissipated by each of the higher frequency modes (2–9); the optimized SSVI NES parameters listed in Table 1 are used for these simulations

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Fig. 5

Normalized weighted-averaged effective damping measure of each of the modes of the structure; the optimized SSVI NES parameters listed in Table 1 are used for these simulations

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Fig. 6

Transient modal energies of the nine-story structure with attached optimized SSVI NESs for initial velocity of each floor due to the applied base impulsive load equal to 0.25 m/s; sudden changes in modal energies are caused by the occurring vibro-impacts

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Fig. 7

Nonlinear modal energy redistribution for initial floor velocities equal to 0.25 m/s and optimized NESs: (a) percentage of total impulsive energy in each mode at t=0, and (b) percentage of the total energy eventually dissipated by the modal damping of each mode

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Fig. 8

Comparison of transient modal amplitudes of the structure with locked (linear case) and unlocked (strongly nonlinear case) optimized SSVI NESs for initial floor velocities equal to 0.25 m/s; sudden changes in modal amplitudes are caused by the occurring vibro-impacts

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Fig. 9

Comparison of the responses of the nine floors of the structure with locked (linear case) and unlocked (strongly nonlinear case) optimized SSVI NESs for initial floor velocities equal to 0.25 m/s

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Fig. 10

Wavelet spectra of responses of the first, fifth, and ninth floors of the structure with, (a), (c), and (e) locked, and (b), (d), and (f) unlocked optimized SSVI NESs for initial floor velocities equal to 0.25 m/s; the dashed-lines represent the natural frequencies fi (in Hz) of modes of the nine-story structure for the case when the NESs are locked

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Fig. 11

Relative displacements between the two SSVI NESs and the floors to which they are attached; optimized parameters for the SSVI NESs are assumed for initial floor velocities equal to 0.25 m/s

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Fig. 12

Effects of viscous damping and inelastic vibro-impacts of the SSVI NESs on the passive modal energy redistribution from low to high frequencies: contour plots of percentage of total impulsive energy dissipated by (a) modes 2–9, and (b) by the NESs, as functions of the coefficient of restitution and the viscous damping of the NESs for common initial floor velocities equal to 0.25 m/s

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