Research Papers

Experimental Rotations of a Pendulum on Water Waves

[+] Author and Article Information
Stefano Lenci, Maurizio Brocchini, Carlo Lorenzoni

Dipartimento di Architettura, Costruzioni e Strutture (DACS),  Università Politecnica delle Marche via Brecce Bianche, 60131 Ancona, ItalyLenci@univpm.itm.brocchini@univpm.itc.lorenzoni@univpm.it Dipartimento di Idraulica, Strade, Ambiente e Chimica (DISAC), Università Politecnica delle Marche via Brecce Bianche, 60131 Ancona, Italy

J. Comput. Nonlinear Dynam 7(1), 011007 (Aug 15, 2011) (9 pages) doi:10.1115/1.4004547 History: Received April 01, 2011; Accepted June 25, 2011; Published August 15, 2011; Online August 15, 2011

The rotations of a parametric pendulum fitted onto a suitable floating support and forced to move vertically under the action of water waves have been studied on the basis of a dedicated wave flume laboratory experiment. An extended experimental campaign has been carried out with the aim of providing insight into the mechanics of the pendulum’s response to the wave forcing and data useful as a benchmark for available theories. A large number of time histories of the pendulum’s angular position have been collected. Rotations have been detected for different values of the frequency and of the amplitude of the excitation, showing the robustness in parameter space, and for different initial conditions, showing the robustness in phase space. This experiment, suggested by the recently developed concept of extracting energy from sea waves, constitutes preliminary experimental proof of that concept’s practical feasibility.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 2

The wave flume at the Laboratorio di Idraulica of the Università Politecnica delle Marche, Ancona, Italy

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Figure 3

A sketch of the wave flume with the pendulum enlarge Fig. 3 of about 30%

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Figure 4

The three different buoy shapes preliminarily tested. The best one was found to be that in (b).

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Figure 5

Design drawing (a) and a photograph (b) of the pendulum

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Figure 6

The experimental rig on the water channel

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Figure 7

The measurement system

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Figure 8

A schematic diagram of the data acquisition system

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Figure 9

Time histories (a) of the pendulum pivot Y0 (T) and (b) of the angular velocity

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Figure 10

The bifurcation diagram of the rotating solution for ω = 1.3 and h = 0.015

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Figure 11

The behavior chart, i.e., the map of where rotations can be found experimentally in the (f,A)-parameter plane

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Figure 12

The basins of attraction of Ref. [4] for h = 0.015, ω = 1.3, and p = 0.1. The phase shift is ωt0  = 1.5π. R1, anti-clockwise rotation; R2, clockwise rotation; O2, period 2 oscillation; R = rest position.

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Figure 13

The measurement of the initial angular displacement. In the present case, θ0  =− 143° =− 0.794π rad.

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Figure 14

Tested initial conditions for f = 0.8 Hz and for (a) A = 73.4 mm and (b) A = 81.1 mm

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Figure 15

Tested initial conditions for f = 0.9 Hz and for (a) A = 52.0 mm, (b) A = 63.0 mm, and (c) A = 76.0 mm

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Figure 16

Tested initial conditions for f = 1.0 Hz and for (a) A = 60.0 mm and (b) A = 70.0 mm



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