scholarly journals D’Alembert function for exact non-smooth modal analysis of the bar in unilateral contact

2021 ◽  
Vol 43 ◽  
pp. 101115
Author(s):  
David Urman ◽  
Mathias Legrand ◽  
Stéphane Junca
Author(s):  
Anders Thorin ◽  
Mathias Legrand ◽  
Stéphane Junca

The well-known concept of normal mode for linear systems has been extended to the framework of nonlinear dynamics over the course of the 20th century, initially by Lyapunov, and later by Rosenberg and a growing community of researchers in modal and vibration analysis. This effort has mainly targeted nonlinear smooth systems — the velocity is continuous and differentiable in time — even though systems presenting nonsmooth occurrences have been increasingly studied in the last decades to face the growing industrial need of unilateral contact and friction simulations. Yet, these systems have nearly never been explored from the standpoint of modal analysis. This contribution addresses the notion of modal analysis of nonsmooth systems. Developments are illustrated on a seemingly simple 2-dof autonomous system, subject to unilateral constraints reflected by a perfectly elastic impact law. Even though friction is ignored, its dynamics appears to be extremely rich. Periodic solutions are sought for given numbers of impacts per period and nonsmooth modes are illustrated for one and two impacts per period in the form of two-dimensional manifolds in the phase space. Also, an unexpected bridge between these modes in the frequency-energy plots is observed.


2018 ◽  
Vol 91 (4) ◽  
pp. 2453-2476 ◽  
Author(s):  
Carlos Yoong ◽  
Anders Thorin ◽  
Mathias Legrand

2021 ◽  
Vol 147 (3) ◽  
pp. 04020100
Author(s):  
Nasser Heydari ◽  
Panayiotis Diplas ◽  
J. Nathan Kutz ◽  
Soheil Sadeghi Eshkevari

2015 ◽  
Vol 39 (1) ◽  
pp. 145-149 ◽  
Author(s):  
Ewa B. Skrodzka ◽  
Bogumił B.J. Linde ◽  
Antoni Krupa

Abstract Experimental modal analysis of a violin with three different tensions of a bass bar has been performed. The bass bar tension is the only intentionally introduced modification of the instrument. The aim of the study was to find differences and similarities between top plate modal parameters determined by a bass bar perfectly fitting the shape of the top plate, the bass bar with a tension usually applied by luthiers (normal), and the tension higher than the normal value. In the modal analysis four signature modes are taken into account. Bass bar tension does not change the sequence of mode shapes. Changes in modal damping are insignificant. An increase in bass bar tension causes an increase in modal frequencies A0 and B(1+) and does not change the frequencies of modes CBR and B(1-).


2021 ◽  
Author(s):  
David F. Castillo Zuñiga ◽  
Alain Giacobini Souza ◽  
Roberto G. da Silva ◽  
Luiz Carlos Sandoval Góes

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