http://popups.lib.uliege.be/2684-6500/index.php?id=90 Index terms fr 0 http://popups.lib.uliege.be/2684-6500/index.php?id=84 The aim of this paper is to provide an introduction to using normal form transformations for linear and nonlinear structural dynamics examples. Starting with linear single-degree-of-freedom systems, a series of examples are presented that eventually lead to the analysis of a system of two coupled nonlinear oscillators. A key part of normal form transformations are the associated coordinate transformations.This review includes topics such as Jordan normal form and modal transformations for linear systems, while for nonlinear systems, near-identity transformations are discussed in detail. For nonlinear oscillators, the classical methods of Poincaré and Birkhoff are covered, alongside more recent approaches to normal form transformations. Other important topics such as nonlinear resonance, bifurcations, frequency detuning and the inclusion of damping are demonstrated using examples. Furthermore, the connection between normal form transformations and Lie series is described for both first and second-order differential equations. The use of normal form transformations to compute backbone curves is described along with an explanation of the relationship to nonlinear normal modes. Lastly, conclusions and possible future directions for research are given. Mon, 17 Jan 2022 13:50:12 +0100 Fri, 10 Jan 2025 13:37:03 +0100 http://popups.lib.uliege.be/2684-6500/index.php?id=84 http://popups.lib.uliege.be/2684-6500/index.php?id=154 The Masing conditions establish a criterion to relate the loading curve of a hysteretic system (e.g., systems with friction or plasticity) to its complete hysteresis loop. For the field of joint mechanics, where hysteretic models are often used to describe the dissipative, tangential behavior within an interface, the Masing conditions allow for significant computational savings when the normal load is constant. In practice, though, jointed systems experience time varying normal forces that modify the tangential behavior of the system. Consequently, the hysteretic behavior of jointed structures do not adhere to the Masing conditions. In this work, this discrepancy between the Masing conditions and behavior exhibited by jointed structures is explored, and it is hypothesized that if the Masing conditions accounted for variations in normal force, then they would more accurately represent jointed structures. A new set of conditions is introduced to the original set of Masing conditions, yielding a « Masing manifold » that spans the tangential displacement-tangential force-normal force space. Both a simple harmonic oscillator and a built-up structure are investigated for the case of elastic dry friction, and the results show that the hysteresis of both of these systems conforms to the three dimensional Masing manifold exactly, provided that a set of constraints are satisfied, even though the hysteresis does not conform with the original Masing conditions. Tue, 07 Nov 2023 09:24:21 +0100 Wed, 22 May 2024 14:56:09 +0200 http://popups.lib.uliege.be/2684-6500/index.php?id=154