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Fatigue damage in engineering structures is universal. The occurrence of fatigue cracks brings unpredictable hidden dangers to a structure in terms of safety and service performance. Traditional damage identification methods, such as power spectrum analysis, are mostly based on linear elasticity theory that cannot reflect the typical nonlinear characteristics of fatigue cracks and cannot meet the higher requirements of the signal analysis method put forward by current mass detection data. To solve this problem, a numerical model of a cantilever beam with a breathing crack is established in this study. A method for diagnosing fatigue damage is studied by combining bispectral analysis and a statistical normal cloud model, which characterize the nonlinear characteristics of the structure. This method can effectively describe the nonlinear characteristics of the structure and reasonably evaluate the degree of fatigue damage in the structure. The bispectrum-normal cloud model method proposed in this study overcomes the limitations of existing linear damage detection methods in nonlinear damage detection, and can improve the efficiency of signal analysis from a statistical point of view. It has good prospects for structural nonlinear damage assessment.

Fatigue damage is a type of damage usually occurring to repeatedly loaded elements of structures in various engineering fields. Accumulation of fatigue damage may cause failure of structural elements. Identification of incipient fatigue damage is essential to ensure safety of structures. Fatigue crack under repeated loads commonly behaves in a nonlinear dynamic manner, typically manifested by both occurrence of higher harmonic components and interaction of harmonic components. Interrogation of nonlinear dynamic manner provides a promising way to characterize structural fatigue damage. This study aims at developing a new method to interrogate nonlinear dynamic manner for fatigue damage identification. This method is based on bispectral analysis of structural vibrational responses. This method portrays fatigue damage by inspecting the presence of higher harmonic components and quantifying the interaction of these harmonic components. The method can precisely locate and quantify a small-sized fatigue damage in a cantilever beam, presenting great accuracy in fatigue damage identification.

In this paper a new damage index for detection and location of damage is introduced. It is improved version of the earlier developed Poincare map method based on forced response of the structure. The proposed method is compared with the most popular modal based methods for damage detection: the modal displacements, modal curvatures and the strain energy methods. A finite element model of intact and damaged composite beams is used in order to validate correctness and efficiency of the method. Moreover, the modal based and forced response are tested experimentally by using a scanning laser vibrometer. The advantages of the offered method and its application in SHM are demonstrated by numerical simulations and experimental tests.

Hidden damage severely threatens the safety of structures due to its invisibility and indistinguishability. Debonding is typical hidden damage in steel-reinforced bridges. Detection of multiple debondings in steel-reinforced bridges poses a challenge for traditional nondestructive methods that require damage location as prior knowledge, but this condition is usually not satisfied for debonding located within the bridge. Differing from existing studies, this study explores a vibrational method of detecting multiple debondings needing no prior knowledge, that uses a scanning laser vibrometer to acquire densely-sampled operating deflection shapes of bridges. The operating deflection shape carries richer information than mode shapes for damage characterization. Nevertheless, densely-sampled deformed quantities are commonly susceptible to noise when used to identify damage. To detect multiple debondings, a new feature is developed, the wavelet-transform curvature operating deflection shape. This feature is used to identify multiple debondings in a steel-reinforced concrete slab dismantled from a bridge, clearly demonstrating the strengths of suppressing noise, intensifying the signatures of debonding, and requiring no prior knowledge of damage location. The proposed method holds promise for detecting multiple hidden damage in various structures besides bridges.

An effect of thermal loading on vibrations of beams is investigated in the paper. A beam is considered as an extended Timoshenko beam model with nonlinear terms resulted from large deflections. Dynamics of the structure is analysed under thermal and mechanical loadings considering transient dynamics due to a heat pulse imposed to the beam. The numerical method for solving coupled thermo-mechanical problem is presented. On this basis the importance of the heat pulse intensity around the first resonance condition is demonstrated. The effect of the heat on the the complex transient dynamics of the beam and its qualitatively different response is shown as well.

A 3D beam model, i.e. a beam that may deform in space and experience longitudinal and torsional deformations, is developed considering Timoshenko's theory for bending and assuming that the cross section rotates as a rigid body but may deform in longitudinal direction due to warping. The cross sectional properties are firstly calculated and then inserted at the equation of motion. The beam is assumed to be with an arbitrary cross section, with linearly varying thickness and width, and with an initial twist. The model is appropriate for open and closed thin-walled cross sections, and also for solid cross sections. The objective of the current research is to demonstrate that complex beam structures can be modeled accurately with reduced number of degrees of freedom.

This special issue is a result of discussions performed during a workshop (with the same name) held in Lublin, February 2014. This meeting served as the seed to invite several experts in the field to present contributions for this Special Topics issue which reflect the present state of the art for research and development of smart materials and their possible applications for energy control and energy harvesting.

This engineering research focus issue was inspired by the workshop organised by us on March 19th 2012 at the Lublin University of Technology (in the framework of CEMCAST) titled “Dynamics of functionally graded materials and systems with hysteresis” The collection of the present research papers followed our fruitful discussions focussing on “Dynamics of composite nonlinear systems and materials for engineering applications and energy harvesting” which is now the title of the present volume. In the next two sections we briefly discuss the topics included in this focus issue.

In this work dynamic behaviour of a composite beam having delamination is presented. The model of delamination takes into account a contact interaction between sublaminates including normal forces, shear forces and additional damping. Numerical calculations are performed in order to estimate the influence of the new terms included into the model.

Vibration based damage detection methods are among the most popular and promising approaches for health monitoring of structures. In this work a critical review of different methods for damage detection methods of structures is presented. The theoretical bases of the most popular methods based on the changes in the modal properties of the structures are deduced. The review includes the modal displacements, the mode shape slopes, the modal curvatures and the strain energy methods. The efficiency of all these methods is compared by using a finite element analysis of intact and damaged beams. The methods are tested experimentally by using a scanning laser vibrometer to measure the modal properties of specially prepared composite beams with defects. All this methods are compared with the damage detection method based on the analysis of the Poincare maps of the motion of the structures). Conclusions concerning the advantages and the applicability of the considered methods are deduced.

In this work numerical and experimental study of the vibration of laminated beams with damage, subjected to dynamic loading and temperature variations is presented. The goal of the study is to check the applicability of the damage detection technique based on an analysis of the Poincare maps of the beam response. The geometrically nonlinear version of the Timoshenko beam theory is used to model the beam behavior. The damage is represented as a reduction of the effective elastic modulus of the beam material in a small area of the structure. The beams are subjected to a harmonic loading, leading to large amplitude vibrations and to temperature changes. The main results are focused on establishing the influence of the damage on the vibration response of heated or unheated structures and the change in the time-history diagrams and the Poincare maps, caused by a damage and elevated temperature. The damage detection criterion formulated earlier for nonheated plates, based on analysing of the Poincare maps of the damaged and healthy plate, is modified and tested for the case of beams additionally subjected to elevated temperatures. The importance of taking into account the actual temperature in the process of damage detection is shown. Performed experimental tests (by an optical method) confirm the applicability and sensitivity of the proposed method.

The main aspect of the paper is to give an answer to the question of what specific kind of defect has actually occurred in a structure and how to distinguish between different kinds of discontinuities. For this purpose composite rods and beams with fatigue cracks, step changes in cross-sectional area and small changes in material properties have been investigated. The objective of the work has been to propose a signal processing methodology based on wavelet transformation for identification of specific discontinuity. The identification of a fatigue crack from other discontinuities has been demonstrated. It has been also found that the proposed methodology might be useful for precise indication of the size of the identified fatigue damage.

This study investigates a possibility for representing, interpreting and visualising the vibration response of aircraft panels using time domain measurements. The aircraft panels are modelled as thin orthotropic plates and their vibration response is simulated using FE modelling. The vibration response of a thin aluminium panel is simulated using FE modelling. The first ten resonant frequencies are estimated for the FE model and for the dynamically tested panel. They were found to show somewhat low sensitivity to damage. Then the simulated vibration response of the panel is transformed and expanded in a new phase space. This presents an alternative way to study and analyse the dynamics of a structure. A two dimensional phase space is used in this investigation. Thus instead of studying the single dimension measured vibration characteristics one is faced with expanded two dimensional variables which can be visualised and this facilitates the comparison between the damaged and the non-damage states.

This work was motivated by the recent NATO funded research on preventing disasters from collapse and improving the safety of aircraft structures. It considers the problem for vibrationbased damage detection in aircraft panels modelled as isotropic plates. The explored method does not use any assumptions of model or linearity, it is simply based on pure signal analysis of the vibration response of plates. FE modelling is used to model the plate’s dynamic response in its intact and in its damaged state. The signals obtained are analysed using multivariate analysis applied in the measured frequency domain. This reduces the data dimensionality and is expected to have a clustering effect. At this stage the measured data is transformed into features – new variables- which have smaller dimension than the initial ones and make the categories more distinguishable. Then a very simple pattern recognition (PR) method is applied to discriminate between the two categories of data -data coming from the undamaged plate and data coming from the damaged plate. This is the second stage when the obtained features are used for the actual recognition between the defined categories. The paper suggests the use of the Karhunen-Loeve transform in order to extract features from the measured frequency response functions of the plate. When the data dimensionality is brought down to two the response of the plate can be visualised. The clustering effect on the features coming from undamaged plate and those from the damaged is obvious.

This paper discusses and illustrates the influence of transverse shear on the response of a thick elastic-plastic beam when it is subjected to a pulse load. The pseudo-normal mode superposition method is used for solving the equations of motion. Numerical results are obtained for simply supported and clamped beams subjected to a pulse load of finite duration.

The dynamic elastic-plastic response of a thick circular plate has been investigated by using the Mindlin plate theory. The normal modes and frequencies of free vibrations of an "assumed elastic" plate are used to transform the space displacements into modal generalized displacements. In each time subinterval the non-linear terms are grouped together with external loads and the pseudo-loads so obtained are interpolated by a quadratic polynomial of time and are determined by an iterative procedure. Numerical results are obtained for simply supported and clamped plates subjected to different type of pulse loads (rectangular and two types of triangular pulses). The influence of the pulse shape, pulse duration and inelastic strains on the plate response is considered.

The dynamic contact interaction between an elastic-plastic beam with a variable cross-section and a two-parametric elastic foundation with a finite thickness is studied. The beam is subjected to an impulsive loading and its plastic properties are described by a linear isotropic strain-hardening model. The finite difference approximation is applied to the spatial domain and the fourth-order Runge-Kutta method is used to solve the nonlinear problem in the time domain. The development of the contact spot in time and the influence of the contact forces and foundation properties on the elastic and elastic-plastic beam response are presented.

The problem of thermally induced vibrations of a simply supported elastic-plastic Timoshenko beam with a linear work hardening is studied. The applied load is a short time thermal flow acting on the upper beam surface. The problem is solved using two models: the joint thermo-elasto-plastic equations and decoupled ones. Numerical results are obtained for three types of heat flow pulse loads (rectangular and two triangular pulses) with different durations and amplitudes. The coupling effects on the transverse beam displacements and on the temperature bending moment are studied. The influence of the pulse shape and pulse duration on the beam response is considered also.

This study aimed at the development of vibration-based health monitoring methodology for thin circular plates. The possibility of using the first several natural frequencies of a circular plate for damage detection purposes was investigated first. The study then suggested a damage detection method, which considered a vibrating plate as a dynamic system and used its time-domain response represented in a new phase (state) space to extract damage sensitive characteristics. The paper introduced the idea of using large amplitude vibrations and nonlinear time series analysis for damage detection purposes. The suggested damage detection approach explored the possibility to use certain characteristics of the distribution of phase space points on the attractor of the system. It studied the histograms of this distribution and attempts to extract damage sensitive features. Three damage features were suggested and they are shown to detect damage at a rather low level using a finite element model of the plate. The method suggested was rather generic and permits development and application to more complex structures and real data.

This paper deals with the problem of vibration health monitoring (VHM) in structures with nonlinear dynamic behaviour. It aims to introduce two viable VHM methods that use large amplitude vibrations and are based on nonlinear time series analysis. The methods suggested explore some changes in the state space geometry/distribution of the structural dynamic response with damage and their use for damage detection purposes. One of the methods uses the statistical distribution of state space points on the attractor of a vibrating structure, while the other one is based on the Poincare map of the state space projected dynamic response. In this paper both methods are developed and demonstrated for a thin vibrating plate. The investigation is based on finite element modelling of the plate vibration response. The results obtained demonstrate the influence of damage on the local dynamic attractor of the plate state space and the applicability of the proposed strategies for damage assessment. The approach taken in this study and the suggested VHM methods are rather generic and permit development and applications for other more complex nonlinear structures.

PURPOSE Evidence is emerging that the abrupt compliance mismatch that exists at the junction between the stent ends and the host arterial wall disturbs both the vascular hemodynamics and the natural wall stress distribution. These stent-induced alterations are greatly reduced by smoothing the compliance mismatch between the stent and host vessel. A stent that provides this smooth transition in compliance, the compliance matching stent (CMS), has been developed. This study attempts to evaluate the hemodynamics and wall mechanical consequences of the CMS both in vitro and in vivo. MATERIALS AND METHODS Finite element analysis was used to assess the solid mechanical behavior (compliance and stress) of the CMS in a stent/artery hybrid structure. A similar analysis was performed with a Palmaz stent. In vivo hemodynamics and wall mechanical changes induced by the CMS were investigated in a swine model from direct measurements of flow, pressure, diameter, and histology in the stented segment of superficial femoral arteries after 7 days. RESULTS Finite element analysis showed that the abrupt compliance mismatch was substantially smoothed between the vessel portions with and without the stent with CMS segments. Circumferential stress was also markedly reduced with the CMS compared to other stent. The in vivo results showed that the CMS was efficient in compliance matching and did not dampen flow or pressure waves downstream the stent. Concurrent histology showed limited thrombus and inflammatory cell accumulation around the stent struts. CONCLUSION These results indicate that the stent/artery hybrid structure can be compliance matched with proper stent design and that this structure limits solid mechanical stress and hemodynamic disturbances. It remains to be seen whether compliance-matched vascular stents reduce in-stent restenosis.