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Experiments on a beam-rigid body structure repetitively impacting a rod

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Abstract

This paper investigates the experimental dynamics of a beam structure that supports an attached rigid body and that can impact a comparatively compliant base structure. The problem area is motivated by impact phenomena that are observed in certain structures internal to nuclear reactors. The assembly is subjected to base excitation at specified frequency and acceleration, and the resulting displacement and velocity time histories are recorded and used to obtain spectra, phase diagrams, and Poincaré sections. The measurements validate simulation results obtained by using a constraint and modal mapping method based on the two sets of modes when the structure is in-contact, and when it is not-in-contact. Generalized coordinates are mapped across the impact discontinuities in the modal representation. The forced response simulation predicts the test specimen’s response over a range of excitation frequencies. The specimens are fabricated as single integral structures from acrylnitrile butadene styrene plastic through rapid prototyping technology in order to eliminate the undesirable dissipation and flexibility arising from joints and connections. The experimental system can exhibit complex response characteristics, and the influences on complexity of deadband clearance and of asymmetry in the point of impact are examined in the experiments.

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Abbreviations

a :

Contact location along the rigid body

A i :

Cross-sectional area of beam i

b i :

Width of beam i

c:

Clearance

e o :

Base excitation amplitude

E i :

Modulus for material of beam i

f o :

Base excitation frequency

f :

Generalized force

h i :

Height of beam i

I i :

Second moment of area of beam i

J :

Moment of inertia of the rigid body

k :

Stiffness of the contact interface

k tip :

Stiffness of the impact hammer’s steel tip

k T :

Rotational stiffness of end conditions

K (j) :

Stiffness operator in S (j)

L i :

Free span length of beam i

L m :

Length of the rigid body

m :

Mass of the rigid body

m′:

Additional modal testing mass

m eff :

Effective mass of the modal testing hammer

M :

Inertia operator

N :

Number of modes included in discretization

S (j) :

Linear vibration state j

t k :

Time of the kth impact or rebound event

T (ij) :

Mapping matrix from S (i) to S (j)

V i :

Modal displacement of beam i

w(j), v(j):

State vector in S (j)

w i , v i :

Displacement of beam i

x i :

Longitudinal coordinate of beam i

y :

Rigid body displacement

Y :

Modal rigid body displacement

α:

Phase

η i (j) :

Generalized time coordinates of the ith mode in S (j)

θ:

Rigid body rotation

Θ :

Modal rigid body rotation

ξ(j) :

Modal damping ratio in S (j)

ρ i :

Density for material of beam i

τ:

Measured force pulse width

ω i (j) :

Natural frequency of the ith mode in S (j)

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Authors and Affiliations

  1. Department of Civil Engineering, University of Mississippi, University, MS, 38677, USA

    Elizabeth K. Ervin

  2. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Jonathan A. Wickert

Authors
  1. Elizabeth K. Ervin
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  2. Jonathan A. Wickert
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Correspondence to Jonathan A. Wickert.

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Ervin, E.K., Wickert, J.A. Experiments on a beam-rigid body structure repetitively impacting a rod. Nonlinear Dyn 50, 701–716 (2007). https://doi.org/10.1007/s11071-006-9180-3

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