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Research Papers

An Analytical Study of Dynamic Characteristics of Multi-Story Timoshenko Planar Frame Structures

[+] Author and Article Information
C. Mei

Department of Mechanical Engineering,
The University of Michigan-Dearborn,
4901 Evergreen Road,
Dearborn, MI 48128
e-mail: cmei@umich.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 24, 2011; final manuscript received February 27, 2014; published online May 19, 2014. Assoc. Editor: Jiong Tang.

J. Dyn. Sys., Meas., Control 136(5), 051004 (May 19, 2014) (10 pages) Paper No: DS-11-1365; doi: 10.1115/1.4027087 History: Received November 24, 2011; Revised February 27, 2014

This paper concerns in-plane vibration analysis of coupled bending and longitudinal vibrations in multi-story planar frame structures based on the advanced Timoshenko bending theory. It takes into account the effects of both rotary inertia and shear distortion. A wave based vibration analysis approach is proposed. From a wave vibration standpoint, vibrations propagate along a uniform waveguide (or structural element), and are reflected and transmitted at discontinuities (such as joints and boundaries). Reflection matrices at various boundaries, as well as transmission and reflection matrices at joint discontinuities are derived. Natural frequencies of coupled bending and longitudinal in-plane vibrations are obtained by assembling these propagation, reflection, and transmission matrices. Numerical examples are presented along with comparisons to results available in literature. The examples show good agreement with the results presented in the available literature.

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Figures

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Fig. 1

(a) A plane n-story frame, (b) a half-frame model for symmetrical vibration mode, and (c) a half-frame model for anti-symmetrical vibration mode

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Fig. 2

Sliding (a) and rolling (b) boundaries

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Fig. 3

Free body diagram of an “L” joint

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Fig. 4

Free body diagram of a “T” joint

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