Stochastic Optimal Bounded Parametric Control of Periodic Viscoelastomer Sandwich Plate with Supported Mass Based on Dynamical Programming Principle

IF 3.1 3区工程技术 Q2 CONSTRUCTION & BUILDING TECHNOLOGY

Buildings Pub Date : 2024-07-25 DOI:10.3390/buildings14082309

Z. Ruan, Z. Ying, Zhao-Zhong Ying, Hua Lei, Wen Wang, Lei Xia

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引用次数: 0

Abstract

The sandwich plate (SP) with supported mass can model structural systems such as platform or floor with installed vibration-sensitive apparatus under random loading. The stochastic optimal control (in time domain) of periodic (in space) viscoelastomer (VE) SP with supported mass subjected to random excitation is an important research subject, which can fully use VE controllability, but it is a challenging problem on optimal bounded parametric control (OBPC). In this paper, a stochastic OBPC for periodic VESP with supported mass subjected to random base loading is proposed according to the stochastic dynamical programming (SDP) principle. Response-reduction capability using the proposed OBPC is studied to demonstrate further control effectiveness of periodic SP via SDP. Controllable VE core modulus of SP is distributed periodically in space. Differential equations for coupling vibration of periodic SP with supported mass are derived and transformed into multi-dimensional system equations with parameters as nonlinear functions of bounded control. The OBPC problem is established by the system equations and performance index with bound constraint. Then, an SDP equation is derived according to the SDP principle. The OBPC law is obtained from the SDP equation under bound constraint. Optimally controlled responses are calculated and compared with passively controlled responses to evaluate control effectiveness. Numerical results on responses and statistics of SP via the proposed OBPC show further remarkable control effectiveness.

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基于动态编程原理的带支撑质量的周期性粘弹性夹层板的随机优化有界参数控制

带支撑质量的夹层板（SP）可以模拟随机载荷下的结构系统，如安装了振动敏感器械的平台或地板。带支撑质量的周期性（空间）粘弹体（VE）SP 在随机激励下的随机最优控制（时域）是一个重要的研究课题，它可以充分利用粘弹体的可控性，但它是一个具有挑战性的最优约束参数控制（OBPC）问题。本文根据随机动力学程序设计（SDP）原理，提出了一种针对周期性 VESP 的随机有界参数控制方法。研究了利用所提出的 OBPC 降低响应的能力，以证明通过 SDP 进一步控制周期性 SP 的有效性。SP 的可控 VE 核心模量在空间呈周期性分布。推导出周期性 SP 与支撑质量耦合振动的微分方程，并将其转化为多维系统方程，其中参数为有界控制的非线性函数。通过系统方程和带约束条件的性能指标，建立了 OBPC 问题。然后，根据 SDP 原理推导出 SDP 方程。在约束条件下，由 SDP 方程得到 OBPC 法则。计算最佳控制响应，并与被动控制响应进行比较，以评估控制效果。通过提议的 OBPC 对 SP 响应和统计的数值结果显示了进一步显著的控制效果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Buildings Multiple-

CiteScore

3.40

自引率

26.30%

发文量

1883

审稿时长

11 weeks

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