A novel sensor design for a cantilevered Mead-Marcus-type sandwich beam model by the order-reduction technique

IF 1.3 3区 数学 Q4 AUTOMATION & CONTROL SYSTEMS
A. Ozer, Ahmet Kaan Aydin
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引用次数: 2

Abstract

A novel space-discretized Finite Differences-based model reduction introduced in \cite{Guo3} is extended to the partial differential equations (PDE) model of a multi- layer Mead-Marcus-type sandwich beam with clamped-free boundary conditions. The PDE model describes transverse vibrations for a sandwich beam whose alternating outer elastic layers constrain viscoelastic core layers, which allow transverse shear. The major goal of this project is to design a single tip velocity sensor to control the overall dynamics on the beam. Since the spectrum of the PDE can not be constructed analytically, the so-called multipliers approach is adopted to prove that the PDE model is exactly observable with sub-optimal observation time.  Next, the PDE model is reduced by the "order-reduced'' Finite-Differences technique. This method does not require any type of filtering though the exact observability as $h\to 0$ is achieved by a constraint on the material constants. The main challenge here is the strong coupling of the shear dynamics of the middle layer with overall bending dynamics. This complicates the absorption of coupling terms in the discrete energy estimates. This is sharply different from a single-layer (Euler-Bernoulli) beam.
采用降阶技术设计了悬臂式mead - marcus夹层梁模型传感器
将\cite{Guo3}中引入的一种新的基于空间离散有限差分的模型约简方法推广到具有无夹固边界条件的多层mead - marcus型夹层梁的偏微分方程模型中。PDE模型描述了夹层梁的横向振动,该夹层梁的外弹性层交替约束粘弹性核心层,从而允许横向剪切。该项目的主要目标是设计一个单尖端速度传感器来控制光束的整体动力学。由于PDE的频谱不能解析构造,采用所谓的乘数法来证明PDE模型在次优观测时间下是精确可观测的。接下来,通过“降阶”有限差分技术对PDE模型进行简化。这种方法不需要任何类型的滤波,虽然精确的可观测性$h\to 0$是通过对材料常数的约束来实现的。这里的主要挑战是中间层剪切动力学与整体弯曲动力学的强耦合。这使离散能量估计中耦合项的吸收变得复杂。这与单层(欧拉-伯努利)梁有很大的不同。
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来源期刊
Esaim-Control Optimisation and Calculus of Variations
Esaim-Control Optimisation and Calculus of Variations Mathematics-Computational Mathematics
自引率
7.10%
发文量
77
期刊介绍: ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations. Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines. Targeted topics include: in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory; in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis; in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.
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