Chiara Grappasonni

Nonlinear normal modes, modal interactions and isolated resonance curves

Abstract The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system. To this end, an energy balance technique is used to predict the amplitude of the harmonic forcing that is necessary to excite a specific nonlinear normal mode. A cantilever beam with a nonlinear spring at its tip serves to illustrate the developments. The practical implications of isolated resonance curves are also discussed by computing the beam response to sine sweep excitations of increasing amplitudes.

Development of a FBG based distributed strain sensor system for wind turbine structural health monitoring

The development of a fiber Bragg grating (FBG) based distributed strain sensor system for real time structural health monitoring of a wind turbine rotor and its validation under a laboratory scale test setup is discussed in this paper. A 1 kW, 1.6 m diameter rotor, horizontal axis wind turbine with three instrumented blades is used in this study. The sensor system consists of strain sensors, surface mounted at various locations on the blade. At first the sensors are calibrated under static loading conditions to validate the FBG mounting and the proposed data collection techniques. Then, the capability of the sensor system coupled with the operational modal analysis (OMA) methods to capture natural frequencies and corresponding mode shapes in terms of distributed strains are validated under various non-rotating dynamic loading conditions. Finally, the sensor system is tested under rotating conditions using the wind flow from an open-jet wind tunnel, for both a baseline wind turbine and a wind turbine with a structurally modified blade. The blade was modified by attaching a lumped mass at the blade tip simulating structural damage or ice accretion. The dynamic characteristics of the baseline (healthy) blade and modified (altered) blade are compared to validate the sensor systems ability for real time structural health monitoring of the rotor.

Identification of nonlinear normal modes of engineering structures under broadband forcing

Abstract The objective of the present paper is to develop a two-step methodology integrating system identification and numerical continuation for the experimental extraction of nonlinear normal modes (NNMs) under broadband forcing. The first step processes acquired input and output data to derive an experimental state-space model of the structure. The second step converts this state-space model into a model in modal space from which NNMs are computed using shooting and pseudo-arclength continuation. The method is demonstrated using noisy synthetic data simulated on a cantilever beam with a hardening-softening nonlinearity at its free end.

Experimental demonstration of a 3D-printed nonlinear tuned vibration absorber

Engineering structures are designed to be lighter and more flexible, hence reducing the extent of application of linear dynamic models. Concurrently, vibration mitigation is required for enhancing the performance, comfort or safety in real-life applications. Passive linear vibration absorbers are purpose-built, often designed using Den Hartog’s equal-peak strategy. However, nonlinear systems are known to exhibit frequency-energy-dependent oscillations which linear absorbers cannot effectively damp out. In this context, the paper introduces a new nonlinear tuned vibration absorber (NLTVA) whose nonlinear functional form is tailored according to the frequency-energy dependence of the nonlinear primary structure. The NLTVA design aims at ensuring equal peaks in the nonlinear receptance function for an as large as possible range of forcing amplitudes, hence generalizing Den Hartog’s method to nonlinear systems. Our focus in this study is on experimental demonstration of the NLTVA performance using a primary structure consisting of a cantilever beam with a geometrically nonlinear component at its free end. The absorber is implemented using a doubly-clamped beam fabricated thanks to 3D printing. The NLTVA performance is also compared with that of the classical linear tuned vibration absorber.

Subspace and Nonlinear-Normal-Modes-Based Identification of a Beam with Softening-Hardening Behaviour

The capability to reproduce and predict with high accuracy the behaviour of a real system is a fundamental task of numerical models. In nonlinear structural dynamics, additional parameters compared to classical linear modelling, which include the nonlinear coefficient and the mathematical form of the nonlinearity, need to be identified to bring the numerical predictions in good agreement with the experimental observations. In this context, the present paper presents a method for the identification of an experimental cantilever beam with a geometrically nonlinear thin beam clamped with a prestress, hence giving rise to a softening-hardening nonlinearity. A novel nonlinear subspace identification method formulated in the frequency domain is first exploited to estimate the nonlinear parameters of the real structure together with the underlying linear system directly from the experimental tests. Then a finite element model, built from the estimated parameters, is used to compute the backbone of the first nonlinear normal mode motion. These numerical evaluations are compared to a nonlinear normal modes-based identification of the structure using system responses to stepped sine excitation at different forcing levels.

Passive linearization of nonlinear resonances

The objective of this paper is to demonstrate that the addition of properly tuned nonlinearities to a nonlinear system can increase the range over which a specific resonance responds linearly. Specifically, we seek to enforce two important properties of linear systems, namely, the force-displacement proportionality and the invariance of resonance frequencies. Numerical simulations and experiments are used to validate the theoretical findings.

Whirl-tower Open-loop Experiments and Simulations with an Adaptive Pitch Link Device for Helicopter Rotor Vibration Control

In the present work are presented both experimental and numerical simulation results obtained with an open-loop control law applied to an individual blade control system that incorporates a mechanism for blade active impedance adaptation at the root, the active pitch link or “smart spring”. It is demonstrated that the active pitch link provides parametric excitation of the blade in the rotating frame and, with it, alters the vibration spectra of the vibration loads both in the blade structure and transmitted to the nonrotating frame by the hub. The experimental results were obtained in whirl tower tests where blade periodic excitation was provided by a fan located at the base of the rotor and generated a transversal flow at a range of blade azimuth angles.

Prediction of Isolated Resonance Curves Using Nonlinear Normal Modes

Isolated resonance curves are separate from the main nonlinear forced-response branch, so they can easily be missed by a continuation algorithm and the resonant response might be underpredicted. The present work explores the connection between these isolated resonances and the nonlinear normal modes of the system and adapts an energy balance criterion to connect the two. This approach provides new insights into the occurrence of isolated resonances as well as a method to find an initial guess to compute the isolated resonance curve using numerical continuation.The concepts are illustrated on a finite element model of a cantilever beam with a nonlinear spring at its tip. This system presents jumps in both frequency and amplitude in its response to a swept sinusoidal excitation. The jumps are found to be the result of a modal interaction that creates an isolated resonance curve that eventually merges with the main resonance branch as the excitation force increases. Excellent insight into the observed dynamics is provided with the NNM theory, which supports that NNMs can also be a useful tool for predicting isolated resonance curves and other behaviors in the damped, forced response.Copyright

Operational Modal Analysis of a Solid Rocket Motor from Firing Test

The firing test of the first stage of the solid rocket motor P80 of the Vega launcher was run successfully in December 2007 at the Guyanese Space Center in Kourou, French Guiana. This research activity demonstrates the capability of the developed operational-modal-analysis methods to identify the dynamic properties of the solid rocket motor, working under its actual operative conditions, by using response data only recorded during the firing test. The main objective was first to prove the applicability and then to evaluate the overall efficiency of different state-of-the-art approaches in operational modal analysis to track changes in the natural frequencies, damping ratios, and mode shapes of the first stage of the Vega launch vehicle undergoing significant mass variation due to the burning propeller. Additionally, a sensitivity of the considered approaches to deal with structures characterized by time-dependent parameters was numerically carried out.

Obtaining Nonlinear Frequency Responses from Broadband Testing

The objective of the paper is to obtain the frequency response curves of nonlinear mechanical systems from broadband testing. The proposed approach consists in coupling an identification method with a continuation method. Specifically, the frequency-domain nonlinear subspace identification (FNSI) method is first used to derive an experimental model of the structure in state space from broadband measurements. The harmonic balance method coupled with arclength continuation then utilizes this experimental model to compute the frequency response curves of the system. The method is demonstrated using a numerical example.