http://popups.lib.uliege.be/2684-6500/index.php?id=233 Issues fr Mon, 04 Nov 2024 10:20:51 +0100 Wed, 06 May 2026 14:25:24 +0200 http://popups.lib.uliege.be/2684-6500/index.php?id=233 0 http://popups.lib.uliege.be/2684-6500/index.php?id=234 Experimental and hybrid substructuring allow the virtual analysis of complex structures that are rather represented by experimental models than simulations. Coupling the experimental models with other structures requires adequate driving points generally described by six degrees of freedom with three translations and rotations with forces and torques as inputs as well as translational and angular accelerations as outputs. However, the measurement of these driving points is challenging. In particular, experimentally acquiring all six inputs causes the main effort. For example, excitation devices that directly exert a torque are not widely applicable or three translational directions are not accessible. Therefore, adapter structures are frequently used in practice, which increase the experimental effort or can be impractical due to a lack of space and reachability. The proposed strategy is the replacement of active excitation devices, i.e. impulse hammers or shakers, on the driving points, by passive, rigid bodies, simply referred to as masses. Compared to the existing mass uncoupling method which is also based on this fundamental idea, the main improvement is a simplified notation that enables the incorporation of data from multiple masses and parametric state-space systems. The main finding is that the proposed strategy is suited to estimate driving point dynamics that allow to predict the effect of assembled structures on channels that were not used in the estimation of the driving point, indicating the physical relevance of the estimated dynamics. Mon, 04 Nov 2024 10:23:29 +0100 http://popups.lib.uliege.be/2684-6500/index.php?id=234 http://popups.lib.uliege.be/2684-6500/index.php?id=242 This research presents a novel analysis method for calculating nonlinear Frequency Response Functions from a nonlinear frequency response surface (NFRS). The research aims to provide engineers with a user-friendly technique to evaluate the nonlinear frequency responses when the modal parameters as a function of the vibration amplitude are available. The Frequency Response Functions (FRFs) are the most widely used functions to characterise the dynamic behaviour of structures. The experimental modal analysis stands on four pillars 1) measurement, 2) identification, 3) regeneration, and 4) comparison, and these four steps must be ensured under linear and nonlinear vibrations. However, the nonlinear vibrations are challenging for identifying, regenerating, and comparing nonlinear FRFs. This research postulates that a nonlinear FRF solves a geometrical intersection between the nonlinear frequency response surface and any constant amplitude force surface. The paper demonstrates the hypothesis with ONE- and TWO-DoF systems with a cubic stiffness nonlinearity by showing how to generate a nonlinear frequency response surface when the force-displacement relationship is calculated. The verification of the proposed formulation is yielded by comparing nonlinear FRFs generated by the new analysis method (NM) to the ones generated by the Harmonic Balance Method and numerical integration. Furthermore, the paper presents a new identification method, based on the Dobson formulation, for extracting amplitude-dependent modal parameters. These parameters generate an NFRS, from which synthesised nonlinear FRFs are evaluated and compared to the experimental ones. The most important innovation of this research is that the four steps listed earlier can quickly be implemented with the proposed technique. Tue, 21 Jan 2025 17:25:40 +0100 http://popups.lib.uliege.be/2684-6500/index.php?id=242 http://popups.lib.uliege.be/2684-6500/index.php?id=245 Energy dissipation (i.e., damping) is a critical quantity to identify in order to understand the dynamic performance of a mechanical design as the dissipation directly influences response amplification near resonance. In linear systems, dissipation is often modeled with constant viscous damping for each mode and can be extracted directly from modal tests in the form of damping ratio. For nonlinear systems there have been many proposed techniques for characterizing damping from experimental measurements, however researchers have yet to reach a consensus on a unified approach. This work investigates three damping identification methods and evaluates each of their limitations. The context for the identification is the nonlinear force appropriation testing technique. The study conducts virtual experiments utilizing multi-harmonic balance solutions where phase resonance is enforced on single-degree-of-freedom models with different nonlinearities – both conservative and non-conservative. In this way, the calculated damping ratios are compared directly to corresponding analytical approximations from the models to enable a critical assessment of their accuracy and of any limitations of each damping identification technique. Additionally, the effect of higher harmonics (both in phase resonance and uncontrolled) on the damping ratio estimates is explored by including an electro-mechanical model of a shaker. In addition to identifying limitations for each damping identification technique considered, this work shows that the trend in the damping ratio does not necessarily reflect the true nature of the nonlinear damping restoring force. Moreover, the damping ratio trend identified from nonlinear force appropriation experiments is sensitive to higher harmonics in the excitation force regardless of whether they are maintained in phase resonance or uncontrolled. Thu, 13 Mar 2025 17:29:02 +0100 http://popups.lib.uliege.be/2684-6500/index.php?id=245 http://popups.lib.uliege.be/2684-6500/index.php?id=252 This paper addresses the problem of optimal tuning of a tuned mass damper (TMD) attached to a complex structure that is dynamically excited by its base. It proposes new analytical formulae which are based on the reduction of the multiple degree of freedom (MDOF) model of the host-structure into an equivalent single degree of freedom (SDOF) model. As it has been recognized in the literature that the traditional single mode approximation used to perform this reduction is not valid for base-excited systems, we propose an improved version that leads to the definition of two mass ratios instead of one in the traditional approach. Taking into account this new mass ratio, the equal peak method is used to derive analytically the optimal values of stiffness and damping of the TMD for a given mass ratio of the device. The introduction of a second mass ratio leads to the existence of two sets of equations for the optimal parameters, depending on the relative values of the two mass ratios. It is shown, however, that only the first set of equations is of practical use. The application of these new tuning rules is illustrated using a MDOF model of a high-rise building. It demonstrates the efficiency of the approach when the first mode of vibration is targeted. When higher modes are of interest, modal interactions are important, which cause a slight to moderate unbalance of the peaks. Mon, 31 Mar 2025 09:45:31 +0200 http://popups.lib.uliege.be/2684-6500/index.php?id=252 http://popups.lib.uliege.be/2684-6500/index.php?id=260 Brake squeal is an instability that generates self-excited limit cycles which vary with time and operating conditions in real experiments. To analyze test results, it is proposed to use a Harmonic Balance Vector (HBV) signal model. It combines Harmonic Balance Method and analytic signal methodologies. From the Harmonic Balance Method, one uses the space-time decomposition where spatial distribution of each harmonic is described by a complex vector and frequency is common to all sensors. From analytic signal, one keeps the assumption that quantities are slowly varying in time. Synchronous demodulation and principal coordinate definitions are combined in a multistep algorithm that provides an HBV estimation. On an industrial brake test matrix, HBV estimation is shown to be robustly applicable. The HBV signal being slowly varying, time sub-sampling reduces the volume of test data by two orders of magnitude. Limit cycle frequency, amplitude and shapes can thus be added to the parallel coordinates that associate to each time sample the operating parameters: pressure, velocity, temperature, torque, disk position, disk/bracket distance, ... This opens a path to a range of analyzes otherwise difficult to perform. Classification of squeal occurrences is first discussed showing pressure and amplitude dependence. The effect of amplitude on both frequency and shape is next demonstrated. The entry and exit of instability when parameters change are then analyzed by proposing a transient root locus built from test. Thus squeal test results are related to the classical complex eigenvalue analysis. Intermittent growth/decay events are shown to be correlated with wheel position. Furthermore, distance measurements indicate that disk shape variations of a few microns play a clear parametric role. Parametric testing and clustering are then used to map the instability region and its edges. Pressure is shown to have an effect dominating other variations. Prospective uses of these results to combine test results and finite element models are discussed last. Mon, 31 Mar 2025 09:56:54 +0200 http://popups.lib.uliege.be/2684-6500/index.php?id=260 http://popups.lib.uliege.be/2684-6500/index.php?id=273 Multi-input, multi-output (MIMO) testing is used in component qualification to reproduce operational responses in the laboratory. It is often preferred to single-input and base-shake testing because of the potential for equivalent or better tests using smaller actuators and shorter test suites. Given a target response, two key steps in MIMO test design are selecting actuator locations and solving for input loads. Actuator locations are often manually selected using expert judgment. If an automatic method is used, locations are usually determined by simulating the vibration control problem and minimizing a combination of the input energy and control residuals. To select a configuration, the relative importance of input energy and residuals must be specified. Specifying relative weights is, in general, a manual and subjective process. This paper develops an objective function that compares actuator configurations based on control accuracy and required input energy without any manual parameter tuning. The objective function uses an optimally selected tradeoff parameter for each candidate configuration. To choose actuator locations using the new objective function, a pivoting algorithm for integer programming problems is developed. Starting with an initial configuration (such as the one generated by a greedy algorithm), the pivoting algorithm guarantees an objective function decrease in each iteration until convergence is reached. In a simulation featuring a structure excited by a diffuse acoustic field, electrodynamic shaker locations and regularized inputs are solved for without any analyst-specified parameters. Simulations are performed in MIMO configurations where the number of target responses is less than, equal to, and greater than the number of actuators. Mon, 05 May 2025 10:24:51 +0200 http://popups.lib.uliege.be/2684-6500/index.php?id=273 http://popups.lib.uliege.be/2684-6500/index.php?id=282 An equality-based weighted residual formulation is proposed for the periodic responses of vibrating systems subject to two-dimensional dry friction on a plane. Coulomb's law is expressed as two coupled nonsmooth equality conditions which augment the equations of motion, resulting in a mixed displacement-friction force formulation whose periodic solutions are sought using a standard Ritz-Galerkin procedure in time. The shape functions considered are the classical Fourier functions, and a quasi-analytical expression for the Jacobian of the friction terms is derived in a piecewise linear fashion and computed in a weighted residual sense. The method is based on an exact equality representation of Coulomb's law for interfaces with mass, thus avoiding common hypotheses such as regularization, penalization, or massless interfaces. It is entirely carried out in the frequency domain, contrary to existing frequency-time methods which require the calculation of contact forces in the time domain at each iteration of the nonlinear solver. The method is compact and found to be robust and accurate. It is void of convergence or other numerical issues up to very large numbers of harmonics of the response in all cases considered. Periodic responses featuring complex two-dimensional interface motions and multiple stick-slip transitions are calculated accurately at various resonant and sub-resonant excitation frequencies, at a reasonable computational cost. Since the only approximation in the procedure is the finite number of terms in the Ritz-Galerkin expansion, the intricate behavior of the two-dimensional friction force dictated by Coulomb's law can be captured with a high degree of accuracy. Wed, 27 Aug 2025 13:58:28 +0200 http://popups.lib.uliege.be/2684-6500/index.php?id=282 http://popups.lib.uliege.be/2684-6500/index.php?id=285 Additive manufacturing has gained popularity for its ability to produce complicated geometries that distribute material optimally and allow several parts to be consolidated into one. Part consolidation often comes with a large reduction in damping, however, due to the elimination of frictional losses at interfaces between parts. This reduction of damping can be problematic in applications where resonant vibrations lead to early fatigue failure or undesirable noise emission. In recent years, a promising technique for increasing damping in parts made by laser powder bed fusion (LPBF) has been introduced, in which pockets of retained, unfused metal powder act as embedded dampers. This work presents an experimental study of the nonlinear behavior of several 316L stainless steel rectangular beams made by LPBF with embedded powder dampers. In addition to amplitude-dependent nonlinearity, a significant memory effect is observed, thought to be caused by powder settling and unsettling in response to external agitation. A procedure was developed to measure the full range of damping behavior by causing the system to transition between high-damping and low-damping states. This procedure is applied to six beams with varying pocket thicknesses, resulting in a rich dataset that provides insight into the factors that most influence the effective modal damping and natural frequency of these parts. As pocket thickness increases, the damping increases, together with the amount of nonlinearity and the variance in damping and natural frequency. This uncertainty can be reduced by controlling the amplitude range of interest, the powder state, the drive point, the impact force, and the hammer tip. The relative importance of each of these factors is quantified, and each factor is found to be significant in certain cases. Some of the parts are shown to exhibit significant modal interactions, as well as time-varying phenomena, for some modes. Additionally, a study which varied the operating temperature is presented, confirming that the behavior of trapped-powder dampers is largely temperature-independent. Implications of these findings for design and modeling are discussed. Thu, 09 Oct 2025 09:59:01 +0200 http://popups.lib.uliege.be/2684-6500/index.php?id=285