http://bibli-cloud15.segi.ulg.ac.be/2684-6500 fr http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=320 Modal analysis is the primary means of analyzing structural responses to external forcing, informing decision-making or further physical testing of the structure. Nevertheless, most commercially available solutions assume the test article behaves linearly with excitation amplitude. If significant amounts of nonlinear stiffness or damping are present in the structure, large errors in linear analysis may result which could lead to improper decisions that may be costly. Therefore, it is useful to develop experimental techniques or computational models which account for nonlinearity during modal analysis. This paper describes a method of generating frequency response functions at various excitation energy levels to generate a three-dimensional transfer function surface. The resulting transfer function surface is agnostic of drive-point location, allowing excitations at different drive points to be compared directly. This result holds only if the drive point is sufficiently far from node points. The Brake-Reuss beam is used as the experimental exemplar at various levels of impact testing. Best practices learned during experimentation are included. Mon, 09 Mar 2026 00:00:00 +0100 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=320 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=314 Substructuring is an important step in the analysis of complex built-up structures. It is the process by which individual components are mathematically assembled to build a model of a coupled system. In the frequency domain, admittance or FRF-based substructuring has become the preferred approach, especially when considering experimental components for which FRFs are easily obtained from test data. However, FRFs are not the only way to represent a component in the frequency domain. Often, particularly for layered systems, the so-called transfer matrix (TM) representation becomes more convenient; component coupling is achieved by simply multiplying together their respective TMs. In the present paper we develop a hybrid substructuring scheme that allows the coupling of FRF-based components using a TM representation of the interconnecting junction. Such an approach might be beneficial for structures with complex layered connections (well suited to TM-based coupling), and has the potential to provide additional insight into structural transmission through multiple interconnected elements. Thu, 08 Jan 2026 00:00:00 +0100 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=314 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=306 An interference fit is a common joining technique used to connect a shaft and a hub. In the presence of dynamic loads and vibrations, characteristic variables such as contact pressure and slippage are load and state-dependent quantities. Such effects have either not been investigated using previous simulation methods or have only been addressed in a simplified manner. The reason for this is the nonlinear contact between the shaft and the hub, which makes a Finite Element simulation with fine meshing, while taking all dynamic effects into account, very demanding and significantly increases the computational effort. This work also offers a new and alternative view of contact modes. This perspective is particularly advantageous for structures with initial stresses that occur in the presence of an interference fit. In this paper, so-called contact modes are applied to interference fits with some modifications. This closes the previously mentioned gap in the simulation landscape because it allows nonlinear, accurate, and fast numerical time integration of finely meshed Finite Element models with interference fits, without the need for simplifications regarding contact, friction, and dynamics due to vibrations and nonlinear rigid body motion. Local plasticity and temperature fields were not taken into consideration. Wed, 07 Jan 2026 00:00:00 +0100 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=306 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=300 Vibration testing of nonlinear structures presents various challenges that are not only related to the nonlinear structure itself but also to the exciter. As the exciter and the structure are coupled, the structure's nonlinear behaviour distorts the exciter force amplitude and frequency content, making the test results more difficult to compare with numerical predictions or even less accurate when isolating and identifying nonlinear normal modes (NNMs). This paper uses an adaptive feedforward cancellation (AFC) real-time control algorithm to track multi-harmonic force reference signals accurately. The controller estimates the disturbance generated by the structure and adjusts the exciter's input to compensate for it, recovering the desired force signal. The advantage of this approach is that it does not rely on the knowledge of the exciter and structure models. It only requires knowledge of the phase at the output of the exciter, which is straightforward to estimate experimentally from the force measurements. The effectiveness of the AFC for exciter force control is demonstrated numerically and experimentally on a cantilever beam structure excited by an electromagnetic shaker. The beam's free tip is attached to a spring mechanism, giving rise to geometric nonlinearities and mode interactions resulting in strong harmonic distortions in the excitation force. The method is further demonstrated on a compressor blade from Roll-Royce's aero-engine. Mon, 17 Nov 2025 00:00:00 +0100 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=300 http://bibli-cloud15.segi.ulg.ac.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. Fri, 17 Oct 2025 00:00:00 +0200 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=285 http://bibli-cloud15.segi.ulg.ac.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 00:00:00 +0200 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=282 http://bibli-cloud15.segi.ulg.ac.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 00:00:00 +0200 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=273 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=269 Non-metallic materials display frequency and temperature dependent dynamic properties which must be characterised for use in computer simulations. The characterisation of such properties is important as most modern structures utilise these materials. Hence, a novel test method has been developed, which combines vibration testing with finite element analysis, to yield dynamic modulus of elasticity and damping. Material properties have been measured in the frequency range 2Hz - 2000Hz. The test method involves a cantilever beam. Two samples of the test material sandwich the root of the beam and are held in place between inertial masses. Experimental modal analysis techniques, where an instrumented hammer vibrates the beam, are used to exercise the material. The modulus of elasticity of the material is found by constructing a finite element model of the test setup and tuning the simulated response with that of the experiment. Damping properties are extracted by applying data fitting techniques to the time histories and spectrum. These are then converted into a material damping property by simulating and accounting for the energy balance between the samples and test setup. Doing so also improves damping simulation accuracy by eliminating the need to estimate Rayleigh damping values at each frequency, as now the material damping property at each frequency can be directly used. For test accuracy, it is important that the sample is gripped in a manner that exercises it effectively and is simple to simulate. Eliminating slipping, and thus the difficult to model friction, is a key concern and has been investigated in depth. The best solution found is an axisymmetric bolting arrangement which holds the samples in place. Additionally, the test setup utilises suspension, together with inertial masses and an orthogonal layout to isolate against external vibrations. Polymers and rubbers, which exhibit complex frequency dependent behaviour, have been reliably characterised using this method. The damping material Sorbothane has also been re-characterised and produced results that aligned with manufacturer specifications. This method proves to be a reliable procedure for dynamic material property testing. Mon, 07 Apr 2025 00:00:00 +0200 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=269 http://bibli-cloud15.segi.ulg.ac.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 00:00:00 +0200 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=252 http://bibli-cloud15.segi.ulg.ac.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 00:00:00 +0200 http://bibli-cloud15.segi.ulg.ac.be/2684-6500/index.php?id=260