Node Control of Uniform Beams Subject to Various Boundary Conditions

Abstract

This paper introduces node control, whereby discrete direct feedback control forces are placed at the nodes of the N+1th mode (the lowest N modes participate in the response). Node control is motivated by the node control theorem which states, under certain conditions, that node control preserves the natural frequencies and natural modes of vibration of the controlled system while achieving uniform damping. The node control theorem is verified for uniform beams with pinned-pinned, cantilevered, and free-free boundary conditions, and two cases of beams with springs on the boundaries. A general proof of the node control theorem remains elusive.

Spatial aperture shading of polyvinylidene fluoride applied to distributed systems for uniform damping control

“…The modal control forces derived from uniform damping control are applied in a discrete spatial manner as prescribed by the NCT. The NCT states that the control forces for a structure with M modes participating in the dynamics should be placed at the nodes of the M + 1th mode [2]. Note that a cantilevered beam has M nodes in the M + 1th mode.…”

“…It is advantageous because the eigenquantities are preserved, allowing for energy-efficient vibration control, and because the proper choice of control gains decouples the modes in the control system [1]. When UNDC is coupled with nodal control theory (NCT) a means for actuator and sensor placement is added [2]. Silverberg and Weaver developed the theory for actively damping a beam utilizing UDNC and NCT.…”

“…NCT states that one can control the lowest N modes participating in a response by placing discrete sensor/actuator pairs at the nodes of the (N + 1) mode. Utilizing NCT leads to a controlled system that has frequency and modal invariance and uniform damping [2]. Silverberg and Washington [3] added bias or steady state calibration to this work, and Rosetti and Sun [4] extended the work to rings.…”

Local sensing/control or global error sensing/control in structural acoustics: A comparison of two techniques influence over sound power

“…An approach from the literature which uses the ideal of many localized reductions to produce a global reduction has been called 'nodal control' [12][13][14][15][16]. In that set of work the aim was typically the reducing global vibration, not global sound radiation.…”