Effective Placement of a Cantilever Resonator on Flexible Primary Structure for Vibration Control Applications: Part 1: Mathematical Modeling and Analysis

[+] Author and Article Information
Troy Lundstrom

PhD Candidate, Piezoactive Systems Laboratory, Department of Mechanical and Industrial, Engineering, Northeastern University, Boston, MA 02115

Nader Jalili

Professor and Director, Piezoactive Systems Laboratory, Department of Mechanical and Industrial, Engineering, Northeastern University, Boston, MA 02115

1Corresponding author.

ASME doi:10.1115/1.4039531 History: Received February 15, 2017; Revised February 09, 2018


In this first part of a two-part series, the theoretical modeling and optimization are presented. More specifically, the effect of attachment location on the dynamics of a flexible beam system is studied using a theoretical model. The application of piezoelectric bender actuators as active resonators may prove to be advantageous over typical, uniaxial actuators as they can dynamically apply both a localized moment and translational force to the base structure attachment point; this minimizes the likelihood that the attachment location is the node of a mode (rotary or translational). Assuming unit impulse force disturbance, potential actuator/sensor performance for the secondary beam can be quantified by looking at fractional root mean square (RMS) strain energy in the actuator relative to the total system, and normalized RMS strain energy in the actuator over a frequency band of interest with respect to both disturbance force and actuator beam mount locations. Similarly, by energizing the actuator beam piezoelectric surface with a unit impulse, one can observe RMS base beam tip velocity as a function of actuator beam position. Through such analyses, one can balance both sensor/actuator performance and make conclusions about optimally mounting the actuator beam sensor/actuator. Accounting for both sensing and actuation requirements, the actuator beam should be mounted in the following region: From this analysis, the ideal mounting region for the actuator beam is: 0.4=e=0.5.

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