Guided waves at high frequency are used in structural health monitoring systems to detect damage. The successful application of the technique, however, requires a deep understanding of wave mode propagation and scattering, as this allows the correct choice of frequency range and wave types to be used to interrogate the structure. Often, this is not the case and systems are developed in an ad hoc way. There is, thus, a greater need to understand the way in which guided waves interact with, and are scattered by, damage. This paper aims to contribute to knowledge in this area. A wave finite element method is applied in a study of wave scattering from symmetric and asymmetric changes of cross-sectional area over a finite length in a waveguide, which are intended to be crude models of corrosion damage. To facilitate analysis of the results, Lamb wave scattering is first investigated in such a system for a point discontinuity involving a change in cross-sectional area. The wave scattering characteristics are evaluated by using the time-averaged kinetic energy of the reflected and transmitted wave fields considering components in the vertical and horizontal directions. This, together with the traditionally used displacement and energy flow coefficients, allows an investigation into the rich wave scattering behaviour due to multi-mode behaviour and wave mode conversion which can complicate the interpretation of the results. In particular, it is shown that care needs to be taken in the interpretation of a sudden increase in the amplitude of a reflected wave from damage. At certain frequencies, this can be due to evanescent waves starting to propagate, rather than an increase in the severity of the damage.

Landing gear shimmy is a self excited vibration phenomenon which must be avoided during aircraft design due to its potentially catastrophic behaviour. In a preliminary specification of structural properties of a landing gear, if shimmy is verified through the engineering process of analysis, typically is a difficult task to identify how its mechanical property must be modified to get a shimmy free system. In this sense, this article introduces an adaptation of the eigenstructure assignment theory (EAT) to design a nose landing gear free of the dynamic behaviour of shimmy. EAT is a classical theory employed to compute a feedback control gain which represents a linear transformation of the system states to control forces. The common application of this theory involves active and semi-active controllers, which require electro-mechanical actuators and additional source of energy. However, in this article EAT is adapted to write the matrix of gain in terms increments of structural stiffness and damping of the landing gear to update a previous design to get a shimmy free system. The proposed process allows to specify a desired new structural mode (though an eigenvector) and both frequency and damping ratio (through an eigenvalue). The strategy allows to compute new values of stiffness and damping to redesign a stable system with better vibration response of landing gear. The proposed approach can be applied in the eigenstructure assignment of any linear system, by means a practical process of changing the system properties (stiffness and damping), in the case of this article, to avoid landing gear shimmy. The results shows the effectiveness of the method.

A simple loop shaping technique is applied to design an optimal, robust feedback controller to reduce the interior noise of an acoustic cavity. It is a data-based technique that uses the measured plant response to tune the parameters of a fixed-structure controller in a graphical way. The two cases studied are narrowband noise control in a small cavity and broadband noise control in a long duct. Each control system consists of a microphone, a loudspeaker, and a controller connecting the two transducers that are further collocated. The fixed-structure of each controller should be chosen ahead of loop shaping and is determined in this paper solely based on the Nyquist plot of each plant measured. It turns out that a single band (high) pass filter of second order is suitable for the narrowband (broadband) noise control case considered. It is finally demonstrated with experiments that the technique is practical and a second order filter can be effectively used for active control of cavity noise in a single narrow or broad frequency band.

Frequency domain modeling has been developed to different engineering applications. In particular, the Spectral Element method (SEM) has been discussed in literature mainly for vibration control design and structural health monitoring once it allows to study unlimited range of frequencies. However, although different authors discuss classical control techniques like PID for SEM formulations there is a limited number of works involving modern control theory based on state space representation. In this context, this work introduces a new approach that allows to use feedback techniques in vibration control design based on SEM. The formulation is presented and numerical simulations are performed using the Timoshenko beam model with two PZT patch bonded. The PZT transducer effects are included too. Results show vibrations reductions of the first three modes of a campled-clamped beam and the proposed approach offers promise to control design using SEM.

This paper concerns an experimental investigation into the active vibration control of a flexible truss structure. Two active strut members, consisting of piezoelectric ceramic stack actuators, are installed at the base of a vertical ten-bay, laboratory scale, truss structure. They are integrated into the structure and are each connected to the truss at one end through a force gauge. Integrated force signals were fed back through decentralized controllers to the co-located actuators to actively add damping to two modes of vibration. To determine the optimum gains for each controller, a model of the structure was needed. A state-space model was derived using the Observer/Kalman Filter Identification (OKID) method together with the Eigensystem Realization Algorithm (ERA). To test the efficacy of the control system, the truss was impacted at its free end by the impact hammer and the responses of the truss were measured by the force sensors, both with and without control. Experimental results illustrate that the modal damping ratio could be increased from 0.0098 to 0.0775 for the first mode and from 0.0053 to 0.0778 for the second mode.

This article presents a novel approach for damage detection applied to structural health monitoring systems exploring the residues obtained from singular spectrum analysis. In this technique, a lead zirconate titanate patch acting as actuator excites the structure, and three other patches are used as sensors to receive the structural responses. This method is based on a high-frequency excitation range in order to overcome the problem caused when the low-vibration modes are excited. In this method, a wideband chirp signal, with low amplitude and variable frequency, is used to excite the structure. The response signals are acquired in the time domain, and the singular spectrum analysis procedure is performed. The residues obtained between the reconstructed and original time series are used to compute statistical metrics. The residues calculated from singular spectrum analysis are used to compute the root mean square deviation and correlation coefficient deviation metric indices, rendering the damage detection approach more reliable. Tests were carried out on an aluminum plate, and the results have demonstrated the effectiveness of the proposed method making it an excellent approach for structural health monitoring applications. The results exploring different numbers of components used during the reconstruction process of time series are obtained, and the highlights are presented.

Attempts are being made to improve mechanical design by using nonlinearity rather than eliminating it, especially in the area of vibration control and in energy harvesting. In such systems, there is a need to both predict the dynamic behavior and to estimate the system properties from measurements. This paper concerns an experimental investigation of a simple identification method, which is specific to systems in which the behavior is known to be similar to that of a Duffing-type system. It involves the measurement of jump-down frequencies and the amplitudes of displacement at these frequencies. The theoretical basis for the method is briefly described as, is an experimental investigation on a beam-shaker system. The results are comparable with those determined by the restoring force surface method. The method described in this article has the advantage that the data can be collected and processed more easily than the restoring force surface method and can be potentially more suitable for the engineering community than existing identification measures.

This paper presents a nonlinear control algorithm for accurate angular positioning of a sectioned airfoil actuated by Shape Memory Alloys (SMAs). The main objective of the proposed control system is to modify the shape of the profile based on a reference angle. The change of the sectioned airfoil angle is resultant by the effect of shape memory of the alloy due to heating of the wire caused by an electric current that changes its temperature by Joule effect. The general model includes nonlinear dynamics of the sectioned airfoil, a constitutive model of shape memory alloy, and electrical and heat transfer behavior of SMA wire. Due to nonlinear behavior of the system, especially in the mathematical model of the alloy, this work proposes the application of a robust control algorithm based on a switching controller. Simulation results show fast, accurate, and robust performance of the control system for different angular stabilization. Keywords— Nonlinear tracking control, sectioned airfoil, shape memory alloy, switching controller.

This paper addresses a novel approach for damage identification in Structural Health Monitoring (SHM) systems based on Principal Component Analysis (PCA) and Delaunay Triangulation (DT). The proposed method explores Electromechanical Impedance (EMI) principle, in the time domain, to identify structural damage in an aircraft aluminum panel. The procedure is carried out exciting the PZT (Pb-Lead Zirconate Titanate) transducers using a wide band chirp signal and measuring their time responses. The PCA is performed using structural response signals and PCA loadings are considered as input to compute the DT. Root Mean Square Deviation (RMSD) metrics are computed from the area formed by the triangles obtained from the DT. Such areas vary due to the displacement of loadings caused by changes in the structural condition for each PZT sensor. These variations have provided good evidence about the effectiveness of the proposed method applied to SHM systems.

This paper introduces a new method for Structural Health Monitoring using error functions computed from guided waves reflected from damage. The approach is experimentally tested on anisotropic specimens such as composite plates. The baseline and test signals of each sensing path (between two PZT transducers) are measured and the energy of the scattered signal for each path is calculated in a given frequency range. Assuming that there is damage in the evaluated position, the wave will reflect at this point and travel to the next transducer. According to the distance between the first transducer to the evaluated point plus the distance between same point to the second transducer (pitch-catch configuration) the time-of-flight is calculated for each grid point on the structure. The wave speeds in anisotropic specimens are propagation direction dependent. The wave speed for different angles were experimentally computed and incorporated in the algorithm in order to calculate the proper time-of-flight. The energy of the scattered signal is computed in a time range based on the time of flight of each analyzed position. Finally, a resultant error function for an estimation of the damage location in the monitoring area is applied. As the error function is based on the interference of the damage in the propagation of guided waves, the higher value of the error implies the less likelihood of damage in that position. An image is generated with an error value for each mesh position in the plate. This error function compares the energy in the given ranges for each pair of transducers. The experiment was performed in a 500x500x2mm carbon/epoxy composite formed by 10 plain-weave layers with 9 PZT transducers in the surface. The resultant error function at each driving frequency is calculated as a sum of all error functions. In addition, several frequencies were tested and the results for each one were combined in order to get a better result.

The main objective of this work is to illustrate an application of angular active control in a sectioned airfoil using shape memory alloys. In the proposed model, one wants to establish the shape of the airfoil profile based on the determination of an angle between its two sections. This angle is obtained by the effect of the shape memory of the alloy by passing an electric current that modifies the temperature of the wire through the Joule effect, changing the shape of the alloy. This material is capable of converting thermal energy into mechanical energy and once permanently deformed, the material can return to its original shape by heating. Due to the presence of nonlinear effects, especially in the mathematical model of the alloy, this work proposes the application of a control system based on fuzzy logic. Through numerical tests, the performance of the fuzzy controller is compared with an on-off controller applied in a sectioned airfoil model.

This paper presents design, implementation and experimental results of active vibration control of a truss structure using a pair of piezoelectric ceramic stack actuators. To reduce the vibrations caused by an impulse force, two active strut members are installed along a vertical of the base bay of the truss. The active strut element consists of a piezoelectric ceramic actuator stack, a force transducer and mechanical interfaces. A self-organizing fuzzy controller (SOFC) is designed to suppress vibration of the truss. The SOFC, which uses the input and output history in its fuzzy rules, is designed to maximize modal damping of a constructed truss structure. Experimental results illustrate that the active piezoceramic strut actuators and the SOFC can effectively reduce vibration of the truss.

Departamento de Engenharia Mecânica Faculdade de Engenharia de Ilha Solteira UNESP - Univ Estadual Paulista, Av. Brasil 56

The present work illustrates an application of shape memory alloys and nonlinear controller applied to the active angular control of a sectioned airfoil. The main objective of the proposed control system is to modify the shape of the profile based on a reference angle. The change of the sectioned airfoil angle is resultant by the effect of shape memory of the alloy due to heating of the wire caused by an electric current that changes its temperature by Joule effect. Considering the presence of plant’s nonlinear effects, especially in the mathematical model of the alloy, this work proposes the application of an on-off control system.

The way in which a nonlinear spring affects the reflection coefficients at the end of a rod and a beam is investigated in this paper. The specific type of nonlinearity considered is of the hardening and softening Duffing-type, which has both linear and cubic stiffness. The magnitudes and the phases of the reflection coefficients for longitudinal and flexural waves are determined. This is achieved by using the harmonic balance approach and the results are verified by comparing the incoming and the outgoing power from the boundary. It is shown that the main effect of the nonlinearity is to change the phase, except in the case of an incident evanescent wave when there is also a jump in the magnitude of the reflection coefficient. In addition, when the nonlinearity is of the softening type, a jump phenomenon occurs in the reflection coefficients.

Mathematical modeling of mechanical structures is an important research area in structural dynamics. The goal is to obtain a model that accurately predicts the dynamics of the system. However, the nonlinear effects caused by gaps, backlash, joints, as well as large displacements are not as well understood as the linear counterpart. In this sense, the Volterra series is an interesting tool for the analysis of nonlinear systems, since it is a generalization of the linear model based on the impulse response function. This paper applies the discrete-time Volterra series expanded in orthonormal Kautz functions to identify a model of a nonlinear benchmark system represented by a Duffing oscillator. The input and output data are used to identify the Volterra kernels of the structure. After the identification of the model, the linear and nonlinear components of the response of the system can be analyzed separately. The paper concludes by indicating the main advantages and drawbacks of this technique to model the behavior of nonlinear systems.

Este trabalho consiste em investigar técnicas de monitoramento de integridade estrutural baseadas em Índices de Falha para detectar danos estruturais. Inúmeros problemas estruturais intensamente noticiados pela mídia, alguns resultando em vítimas fatais, demonstram a importância de se desenvolver metodologias confiáveis de monitoramento da integridade estrutural a fim de evitar catástrofes que resultem em perdas de vidas humanas, danos ao meio ambiente ou prejuízos financeiros. Trata-se, portanto, de um tema atual e de grande interesse tecnológico, em virtude das questões econômicas e de segurança. Em particular, o trabalho consiste em estudar, implementar e aplicar uma metodologia de monitoramento da condição estrutural (do inglês Structural Health Monitoring, SHM) baseado em medidas da norma H2, RMSD (Root-Means-Square Deviation), IFM (Índice de Falha Métrica) e CCDM (Correlation Coefficient Deviation). A metodologia é baseada no cálculo de uma das normas para a estrutura com e sem falha e na avaliação da diferença entre elas. Assim, o dano estrutural é detectado.

Mathematical modeling of mechanical structures is an important research area in structural dynamics. The goal is to obtain a model that accurately predicts the dynamics of the system. However, the nonlinear effects caused by large displacements and boundary conditions like gaps, backlash, joints, as well as large displacements are not as well understood as the linear counterpart. This paper identifies a non-parametric discrete-time Volterra model of a benchmark nonlinear structure consisting of a cantilever beam connected to a thin beam at its free end. The time-domain data of the modal test are used to identify the Volterra kernels. To facilitate the identification process, the kernels are expanded with orthogonal Kautz functions to decrease the number of parameters to be identified. The nonlinear parameters are also estimated by a nonlinear model updating technique involving optimization of residue of the numerical and experimental kernels. The capability of the representation of the nonlinear phenomena is investigated through numerical simulations. The paper concludes by indicating the advantages and drawbacks of the Volterra series for modeling the behavior of nonlinear structures with suggestions to overcome the disadvantages found during the tests.