Research Papers

Micropolar Continuous Modeling and Frequency Response Validation of a Lattice Structure

[+] Author and Article Information
A. Salehian

Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1salehian@uwaterloo.ca

D. J. Inman

Department of Mechanical Engineering, Center for Intelligent Material Systems and Structures, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061dinman@vt.edu

J. Vib. Acoust 132(1), 011010 (Jan 13, 2010) (7 pages) doi:10.1115/1.4000472 History: Received September 20, 2008; Revised June 18, 2009; Published January 13, 2010; Online January 13, 2010

A simple approach is employed here to determine an equivalent continuum representation of a lattice type structure with flexible joints. Kinetic and strain energy expressions are written in terms of the nodal velocities and strain components of the beam members, as well as the joints stiffness values. Necessary assumptions are made to reduce the order of the strain variables while retaining the effects of the microrotations that are coupled to the primary strain terms. As a result, an equivalent one-dimensional model has been found, which takes the assumptions of a micropolar continuum into account rather than an ordinary continuum. The frequency response function of the presented model has been validated experimentally and is shown to be in good agreement with the experimental results for a planar truss with Pratt girder configuration.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Schematic of the element of a planar truss in bending and nodal deflections

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Figure 2

A comparison between a regular and a micropolar continuum (θi and θj microrotations) and (φ macrorotation)

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Figure 3

Schematic of the bar members and joints in truss element

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Figure 4

An n-degree of freedom mass-spring system

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Figure 5

View of the experimental setup

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Figure 6

Frequency response functions (ordinary continuum theory, and experiment)

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Figure 7

Frequency response functions (micropolar continuum theory, and experiment)

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Figure 8

Strain of the diagonal member due to various truss strain components

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Figure 9

Bending deflection components of the longeron and batten members

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Figure 10

Bending deflection components of the diagonal member

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Figure 11

Experiment setup for joint stiffness measurements

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Figure 12

A line fit of torque and torsional strain values of joints



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