In this paper, we generalize the Koopman–Hill projection method, which was recently introduced for the numerical stability analysis of periodic solutions, to be included immediately in classical real-valued harmonic balance (HBM) formulations. We incorporate it into the Asymptotic Numerical Method (ANM) continuation framework, providing a numerical...
Recent advances have prominently highlighted physics informed neural networks (PINNs) as an efficient methodology for solving partial differential equations (PDEs). The present paper proposes a proof of concept exploring the use of PINNs as an alternative to finite element (FE) solvers in both classical and gradient-enhanced solid mechanics. To thi...
This article addresses the measurement of the nonlinear modes of highly flexible structures vibrating at extreme amplitude, using a Phase-Locked Loop experimental continuation technique. By separating the motion into its conservative and dissipative parts, it is theoretically proven for the first time that phase resonance testing organically allows...
Structural Health Monitoring (SHM) techniques are key to monitor the health state of engineering structures, where damage type, location and severity are to be estimated by applying sophisticated techniques to signals measured by sensors. However, very localized damage detection algorithms applied to dynamics problems when dealing with rigid struct...
In this paper, a novel method for computing the nonlinear dynamics of highly flexible slender structures in three dimensions (3D) is proposed. It is the extension to 3D of a previous work restricted to inplane (2D) deformations. It is based on the geometrically exact beam model, which is discretized with a finite-element method and solved entirely ...
The relentless advancement of electronic devices has led to increased power densities, resulting in thermal challenges that threaten device reliability. This study aims to address this issue through the development of innovative heterogeneous materials for cooling electronic components. We focus on phase change materials (PCMs) impregnated within a...
Topological data analysis (TDA) is a powerful and promising tool for data analysis, but yet not exploited enough. It is a multidimensional method which can extract the topological features contained in a given dataset. An original TDA-based method allowing to monitor the health of structures when equipped with piezoelectric transducers (PZTs) is in...
In this paper, the effect of gravity on the nonlinear extreme amplitude vibrations of a slender, vertically-oriented cantilever beam is investigated. The extreme nonlinear vibrations are modeled using a finite element discretization of the geometrically exact beam model solved in the frequency domain through a combination of harmonic balance and a ...
The direct parametrisation method for invariant manifolds is a nonlinear reduction technique which derives nonlinear mappings and reduced-order dynamics that describe the evolution of dynamical systems along a low-dimensional invariant-based span of the phase space. It can be directly applied to finite element problems. When the development is perf...
In this paper, the effect of gravity on the nonlinear extreme amplitude vibrations of a slender, vertically oriented cantilever beam is investigated. The extreme nonlinear vibrations aremodeled using a finite element discretization of the geometrically exact beam model solved in the frequency domain through a combination of harmonic balance and a c...
