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<p>Tall, flexible bridge piers are particularly vulnerable to excessive vibrations resulting from intense seismic activity, necessitating the development of effective mitigation strategies. Nonlinear energy sinks (NESs) emerge as prominent passive control mechanisms for mitigating vibrations in various engineering structures. However, a substantial auxiliary mass is typically considered necessary to achieve adequate damping, which is inadvisable because of the resultant increased moment forces. This study proposes a novel nonlinear energy sink-inerter (NESI) device for attenuating random vibrations in a tall bridge pier subjected to stochastic ground motions. Specifically, the Euler–Bernoulli beam theory and Kane’s method are employed to derive the stochastic kinetic equations of the pier-NESI system, from which the reduced Fokker–Planck–Kolmogorov (FPK) equation is formulated and solved using the radial basis function neural network (RBFNN) method in conjunction with the optimal sampling technique to yield the stationary probability density function (PDF) of the system. Concurrently, numerous Monte Carlo simulations (MCS) are conducted to verify the accuracy of the RBFNN solutions. Subsequently, parameter optimization of the NESI is performed to minimize the root mean square (RMS) of the pier-top displacement in an analytical form. Additionally, the vibration absorption effect of NESI is compared with that of NES. To demonstrate the proposed procedure, a tall bridge pier with a height of 132&#xa0;m is adopted as an example. The numerical results clearly indicate that the optimal NESI can effectively mitigate the RMS of the pier-top displacement. Furthermore, NESI outperforms NES with a higher vibration mitigation effect and lower mass requirements. This study establishes a foundation for both the application and optimal design of NESI in the context of tall bridge piers.</p>

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Random vibration mitigation of tall pier by nonlinear energy sink-inerter under seismic excitation

  • 期刊论文

  • 发表日期：

    2025年4月25日

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  • Shushen Ye,
  • Lincong Chen,
  • Zi Yuan

摘要

Tall, flexible bridge piers are particularly vulnerable to excessive vibrations resulting from intense seismic activity, necessitating the development of effective mitigation strategies. Nonlinear energy sinks (NESs) emerge as prominent passive control mechanisms for mitigating vibrations in various engineering structures. However, a substantial auxiliary mass is typically considered necessary to achieve adequate damping, which is inadvisable because of the resultant increased moment forces. This study proposes a novel nonlinear energy sink-inerter (NESI) device for attenuating random vibrations in a tall bridge pier subjected to stochastic ground motions. Specifically, the Euler–Bernoulli beam theory and Kane’s method are employed to derive the stochastic kinetic equations of the pier-NESI system, from which the reduced Fokker–Planck–Kolmogorov (FPK) equation is formulated and solved using the radial basis function neural network (RBFNN) method in conjunction with the optimal sampling technique to yield the stationary probability density function (PDF) of the system. Concurrently, numerous Monte Carlo simulations (MCS) are conducted to verify the accuracy of the RBFNN solutions. Subsequently, parameter optimization of the NESI is performed to minimize the root mean square (RMS) of the pier-top displacement in an analytical form. Additionally, the vibration absorption effect of NESI is compared with that of NES. To demonstrate the proposed procedure, a tall bridge pier with a height of 132 m is adopted as an example. The numerical results clearly indicate that the optimal NESI can effectively mitigate the RMS of the pier-top displacement. Furthermore, NESI outperforms NES with a higher vibration mitigation effect and lower mass requirements. This study establishes a foundation for both the application and optimal design of NESI in the context of tall bridge piers.