doi:10.1016/S0020-7462(02)00219-6 
Copyright © 2003 Elsevier Ltd. All rights reserved.
The dynamics of loosely jointed structures
James F. Wilson
, 
and Eric G. Callis
Department of Civil and Environmental Engineering, School of Engineering, Duke University, Durham, NC 27708-0287, USA
Available online 20 January 2003.
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Abstract
Loosely jointed structures have joint connections that exhibit non-linear lateral force–displacement behavior in bending. Examples include scaffolds, bleachers and other temporary frames. Formulated herein is a lumped parameter, dynamic sway model of a multi-bay, n-story scaffold with bilinear elastic joint connections. Responses are evaluated numerically for an approximate model: a two degree of freedom scaffold in plane sway motion caused by harmonic base excitation. Chaotic, quasi-periodic, and periodic responses are investigated over a practical range of non-dimensional system parameters. The results show that the type of response is especially sensitive to the magnitude of joint damping.
Author Keywords: Bilinear structures; Chaos; Dynamic response; Loose structures; Non-linear structures; Periodic-response; Quasi-periodic response; Scaffolds; Structural dynamics
Fig. 1. A typical plane frame, six-bay, five-story scaffold. The joint detail shows (a) concentric alignment; (b) eccentric alignment.
Fig. 2. Experimental results showing the bilinear behavior of a typical tube-type joint. In the experiment shown in the insert, the joint parameters for the leg segments were:
L=22.9 cm, OD=4.29 cm, wall=2.41 mm; and for the coupling insert were: length=20.6 cm, OD=3.62 cm, wallthickness=2.11 cm.
Fig. 3. Dynamic model of an
n-story scaffold (left) and free body sketches of the two lumped masses for the
ith story (right).
Fig. 4. Peak steady-state responses |
X| showing: (a) folds for increasing and decreasing excitation frequency Ω, and (b) effects of excitation amplitude
A. The common parameters are: ζ=0.01, ζ
a=0.05,
Ka=0.05,
Kb=2, and
M=0.25.
Fig. 5. Steady-state responses |
X| for excitation parameters
A=Ω=1: (a) Poincaré map showing chaotic responses, (b) a sample time history, and (c) Fourier spectrum. Common parameters are ζ=0.01, ζ
a=0.05,
Ka=0.05,
Kb=2, and
M=0.25.
Fig. 6. Steady-state responses
X for excitation parameters
A=Ω=1: (a) Poincaré plots showing quasi-periodic motion for four values of joint damping, (b) a sample time history for ζ
a=0.1, and (c) Fourier spectrum for ζ
a=0.1. Common parameters are ζ=0.01,
Ka=0.05,
Kb=2, and
M=0.25.
Fig. 7. Steady-state responses
X for excitation parameters
A=1.5, Ω=0.5: (a) Poincaré plot of chaotic motion, (b) a sample time history, and (c) Fourier spectrum. Common parameters are ζ=0.01, ζ
a=0.05,
Ka=0.05,
Kb=2, and
M=0.25.
Fig. 8. Steady-state responses
Y for excitation parameters
A=1.5, Ω=0.5: (a) Poincaré plot of chaotic motion, (b) a sample time history, and (c) Fourier spectrum. Common parameters are ζ=0.01, ζ
a=0.05,
Ka=0.05,
Kb=2, and
M=0.25.
Table 1. Typical parameters for a TDOF model
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