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Port-Hamiltonian Modelling for Buckling Control of a Vertical Flexible Beam with Actuation at the Bottom

机译：底部驱动的垂直挠性梁屈曲控制的哈密顿港口建模

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The use of beams and similar structural elements is finding increasing application inmany areas, including micro and nanotechnology devices. For the purpose of buckling analysis and control, it is essential to account for nonlinear terms in the strains while modeling these exible structures. Further, in modeling of micro and nanotechnology devices, the micro length scale parameter effects can be accounted by the use of a 2 dimensional stress-strain relationship. This paper studies the buckling effect for a slender, vertical beam with a tip-mass at one end and fixed on a movable platform at the other. For the purpose of illustration, the movable platform is assumed to be a cart. Accounting for a 2 dimensional stress-strain relationship, nonlinear expressions for strains, and incorporating an inextensibility constraint of the beam, the Hamiltonian equations of motion are obtained. The equations of motion are then cast in a port-Hamiltonian form with appropriately defined flows and efforts. We then carry out a preliminary modal analysis of the system to describe candidate post-buckling configurations and study the stability properties of these equilibria. The vertical configuration of the beam under the action of gravity is without loss of generality, since the objective is to model a potential field that determines the equilibria.
机译：在许多领域，包括微米和纳米技术设备中，梁和类似结构元件的使用正在发现越来越多的应用。为了进行屈曲分析和控制，在对这些可变形结构进行建模时，必须考虑应变中的非线性项。此外，在微米和纳米技术装置的建模中，可以通过使用二维应力-应变关系来解释微观长度尺度参数的影响。本文研究了细长的垂直梁的屈曲效果，该梁的一端具有尖端质量，另一端固定在可移动平台上。为了说明的目的，假定可移动平台是推车。考虑到二维应力-应变关系，应变的非线性表达式，并结合了梁的不可伸缩性约束，得出了哈密顿运动方程。然后，以适当定义的流量和作用力将运动方程式转换为汉密尔顿港形式。然后，我们对该系统进行了初步的模态分析，以描述候选的屈曲后构型并研究这些平衡的稳定性。光束在重力作用下的垂直构型不会失去一般性，因为目的是为确定平衡的势场建模。

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