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Service performance evaluation is of great significance to the safety, durability, and reliability of bridge engineering. Over the last decade, structural health monitoring (SHM) systems have been widely used for condition monitoring of cable-stayed bridges, massive monitoring data are measured and stored by the sensing subsystems, which provides the basis for service performance evaluation of bridge engineering. Meanwhile, the load test is a common method to assess the construction and service performance of bridges. Combined the SHM systems and a load test of a thousand-meter level cable-stayed bridge after ten years of service, this paper investigates the operating conditions of main structures, including bridge towers, main girders, and steel cables. 52 trucks were used to conduct a quasi-static load on three key sections of bridges. Meanwhile, the GPS displacement of towers and main girders, stress of the main girders and acceleration responses of cables were measured synchronously by the SHM systems. Based on the health monitoring data, the dynamic responses, structural deformation, and cable tension of the bridge were investigated and evaluated by comparing with the finite element (FE) model load test at construction stage. The results show that the service performance of the bridge is basically within the designed conditions.

This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived by the von Karman theory, with the central part-through crack being simulated by a modified line-spring model for characterizing the crack-induced reduction in stress values. Second, the acquired partial differential equations are discretized by the Galerkin method combined with a simply supported boundary condition. Third, the harmonic balance method and the fourth-order Runge–Kutta algorithm are used to obtain the analytical and numerical approximations of the structural responses, respectively. For cases of small harmonic loads, the plate shows a hardening nonlinear frequency response. Influences of various parameters on this hardening nonlinearity are presented, including crack stage, aspect ratio, plate thickness, excitation location, and excitation amplitude. In cases of large harmonic loads, the bifurcations and chaotic dynamics of the cracked plate are explored by considering the effects of excitation amplitude and excitation frequency. Both analytical and numerical results indicate that a thick plate with a large aspect ratio is more sensitive to damage, especially when the crack parallels to the long side of the plate. Besides, the excitation that occurs far from the plate center with a large amplitude is beneficial for the damage characterization. Particularly, the damage-induced periodic-chaotic transition provides a novel insight into characterizing structural damage from perspectives of chaotic dynamics.

Characterization of dynamical systems remains a central challenge in real-world applications because, in most cases, governing equations of the systems cannot be obtained explicitly. Moreover, the behaviors of the systems are complex and possibly unpredictable, even when the system is deterministic. In this situation, nonlinear time series analysis provides an efficient tool for characterizing such dynamical systems. As one of the key techniques in nonlinear time series analysis, phase space reconstruction (PSR) can represent a univariate time series by a multidimensional phase space. Nevertheless, such representation relies on the conscientious selection of the time delay and embedding dimension. Although various algorithms have been developed to optimize these embedding parameters, there are still some limitations restricting their applicability, such as subjective effects, erratic results, and the consumption of time. Herein, we propose a novel Constant embedding parameters and Principal component analysis-based PSR (CPPSR) method, to characterize the low-dimensional ( $$ \le $$ 3) dynamical systems. The effectiveness and accuracy of the CPPSR method are numerically verified on various dynamical systems. The numerical results demonstrate that the CPPSR method can produce reconstructed attractors with precise correlation dimension and the largest Lyapunov exponent. The comparison with conventional and Hankel matrix-based PSR methods shows the superiority of the CPPSR method, demonstrating greater accuracy, higher efficiency, and stronger reliability. Moreover, the CPPSR method shows a high potential for the detection of singularity in applications such as structural health monitoring and abnormality diagnosis in ECG signals.

The work is devoted to study 2D pressure driven rarefied gas flow in a microchannel having an elastic obstacle. The elastic obstacle is clamped at the bottom channel wall and its length is half of the channel height. The gas flow is simulated by Direct Simulation Monte Carlo (DSMC) method applying the advanced Simplified Bernoulli Trial (SBT) collision scheme. The elastic obstacle is modelled as geometrically nonlinear Euler Bernoulli beam. A reduced 3 modes reduction model of the beam is created. The influence of the gas flow on the beam vibration is studied, considering the linear and nonlinear beam theories.

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.

A nonlinear thermoelastic model of a circular plate is presented in the paper. The model, based on the Mindlin plate theory, is extended by taking into account nonlinear geometrical terms. Partial differential equations of plate’s dynamics are derived for a fully coupled thermal and mechanical fields. Then the model is reduced to a set of ordinary differential equations taking into account the first three natural modes and assuming a constant thermal field. The influence of elevated temperature on the resonance curves and the mode involvement due to nonlinear and thermal couplings is presented. The analysis shows that the increased temperature may lead to various bifurcation scenarios. The buckling phenomenon and post-buckling nonlinear regular and chaotic oscillations are studied.

The main goal of this work is to develop a theoretical and numerical approach, to study the geometrical nonlinear vibration of bi-material beams under the combined action of mechanical and thermal loads. The geometrically nonlinear version of the Timoshenko beam theory is used to describe the theoretical model of the problem. Starting from the geometrical, constitutive and equilibrium equations of each layer the governing equations of the bi-material beam are derived. The beam is subjected to heat flux and dynamic mechanical loading. The influence of the elevated temperature or the heat propagation along the beam length and thickness on the response of the beam was studied.

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.

The early detection and localization of damages is essential for optimal operation and efficient maintenance of structures. The methods for damage detection and localization should be able to work for wide range of frequencies since the frequency of oscillation cannot be controlled in majority of real-life applications. The current work presents two new approaches for damage localization of beams. The approaches are based on comparison of time responses of intact and damaged beams. The first approach is called selective index method and considers the curvature of the beam and its time derivatives. The second approach considers the fact that the damage of the beam introduces discontinuity of the shear force and uses these discontinuities to localize the damage. Two types of damages are considered - damage modeled by reduced thickness and by reduced stiffness. Several examples are presented and it is demonstrated that both approaches localize correctly the damage.

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.

Numerical approach and computer code are developed to study 2D rarefied gas flow in a microchannel having an elastic obstacle. A Couette rarefied gas flow passing an elastic beam clamped to the fixed bottom wall is considered as a test case. The gas flow is simulated by the direct simulation Monte Carlo (DSMC) method applying the advanced Simplified Bernoulli Trial (SBT) scheme. The elastic obstacle is modelled as a geometrically nonlinear Euler–Bernoulli beam. The beam displacements and velocities are synchronized in both models. The proposed approach guarantees a full coupling of gas–elastic beam interaction for unlimited time of simulation. The influence of the gas flow on the beam vibration is studied for a long period of simulation. The amplitude of vibration and the frequency response functions are strongly influenced by the velocity of the flow.

Nonlinear vibrations of a circular plate subjected to mechanical and thermal loadings are presented in the paper. A model of the plate is based on the extended Mindlin theory, taking into account nonlinear geometrical terms and acting heat uniformly distributed along the plate span. The dynamics of a coupled thermo-mechanical problem is reduced from a set of partial differential equations to ordinary differential equations. Considering oscillations around the first natural frequency just one mode reduction is proposed. The analysis shows that elevated temperature shifts the resonance curve and new post-buckling oscillations arise. Depending on initial conditions for the post-buckling state various scenarios of bifurcations take place and transient irregular oscillations may occur. The proposed one degree of freedom model shows a good agreement with response of the model based on three or five-modes reduction.

In this paper the detection and localization of damage in vibrating plates is analysed. The new improved version of the recently developed Poincare map method based on forced response of the beams is developed and tested for rectangular plates the proposed method is compared with ones of the most popular modal based methods for damage detection: the modal displacements and modal curvatures methods. The advantages of the new offered method and its application in health monitoring of plates are demonstrated by numerical simulations.

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.

In this work, the large amplitude vibration of a heated Timoshenko composite beam having delamination is studied. The model of delamination considers the contact interaction between sublaminates including normal forces, shear forces, and additional damping due to the interaction of sublaminates. This work is an extension of the previous analysis based on a model of the dynamic behavior of a beam with delamination considering additionally the nonlinearities due to large displacements and temperature changes. Numerical calculations are performed in order to estimate the influence of the delamination, the geometrically nonlinear terms, and elevated temperature on the response of the beam.

Dynamics of a Timoshenko beam under an influence of mechanical and thermal loadings is analysed in this paper. Nonlinear geometrical terms and a nonuniform heat distribution are taken into account in the considered model. The mathematical model is represented by a set of partial differential equations (PDEs) which takes into account thermal and mechanical loadings. The problem is simplified to two PDEs and then reduced to ordinary differential equations (ODEs) by means of the Galerkin method taking into account three modes of a linear Timoshenko beam. Correctness of the analytical model is verified by a finite element method. Then, the nonlinear model is studied numerically by a continuation method or by a direct numerical integration of ODEs. An effect of the temperature distribution on the resonance near the first natural frequency and on stability of the solutions is presented. The increase of mechanical loading results in hardening of the resonance curve. Thermal loading may stabilise the beam dynamics when the temperature is decreased. The elevated temperature may transit dynamics from regular to chaotic oscillations.

Large amplitude vibrations of a Timoshenko beam under an influence of temperature are analysed in this paper. In the considered model the temperature increases instantly and the heat is uniformly distributed along the beams length and cross-section. The mathematical model, represented by partial differential equations takes into account thermal and mechanical loadings. Next, the problem is reduced by means of the Galerkin method, considering the first three natural vibration modes of a simply supported beam in the both ends. The influence of the temperature on amplitudes and localisation of the resonance zones and stability of the solutions is studied numerically and analytically by the multiple time scale method. The bifurcation points, existence of unstable lobes and transition from regular to chaotic oscillations are shown.

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 numerical and experimental study of the dynamic behaviour of a composite laminated 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. In order to verify the model special samples of multilayered beams have been manufactured. Small parts of adjacent layers have been cut and replaced by inclusions from different materials modelling delamination. The mechanical properties of the inclusions have been considered during the numerical calculations. The beams were subjected to a short pulse loading and then their response was registered. The results from the numerical simulation were in a good agreement with the experimental results. The significance of the additional damping due to delamination on the response of the beam was confirmed numerically and experimentally.

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.

In this work, geometrically nonlinear vibrations of fully clamped rectangular plates are used to study the sensitivity of some nonlinear vibration response parameters to the presence of damage. The geometrically nonlinear version of the Mindlin plate theory is used to model the plate behaviour. Damage is represented as a stiffness reduction in a small area of the plate. The plate is subjected to harmonic loading with a frequency of excitation close to the first natural frequency leading to large amplitude vibrations. The plate vibration response is obtained by a pseudo-load mode superposition method. The main results are focussed on establishing the influence of damage on the vibration response of the plate and the change in the time-history diagrams and the Poincaré maps caused by the damage. Finally, a criterion and a damage index for detecting the presence and the location of the damage is proposed. The criterion is based on analyzing the points in the Poincaré sections of the damaged and healthy plate. Numerical results for large amplitude vibrations of damaged and healthy rectangular and square plates are presented and the proposed damage index for the considered cases is calculated. The criterion demonstrates quite good abilities to detect and localise damage.

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.

Recent NATO funded research on methods for detection and interpretation methodologies for damage detection in aircraft panel structures has motivated work on low-order nonlinear analytical modelling of vibrations in cracked isotropic plates, typically in the form of aluminium aircraft panels. The work applies fundamental aspects of fracture mechanics to define an elliptical crack, and the local stress field and loading conditions, arbitrarily located at some point in the plate, and then derives an analytical expression for this that can be incorporated into the PDE for an edge loaded plate with various possible boundary conditions. The plate PDE is converted into a nonlinear Duffing-type ODE in the time domain by means of a Galerkin procedure and then an arbitrarily small perturbation parameter is introduced into the equation in order to apply an appropriate solution method, in this case the method of multiple scales. This is used to solve the equation for the vibration in the cracked plate for the chosen boundary conditions, which, in turn, leads to an approximate analytical solution. The solution is discussed in terms of the perturbation approximations that have been applied and highlights the phenomenology inherent within the problem via the specific structures of the analytical solution.

The thermoelastic, geometrically nonlinear vibrations of isotropic, straight and curved beams are studied using p-version, hierarchical finite elements. First-order shear deformation theory is followed, and both the longitudinal displacements and inertia are taken into account. The nonlinear equations of motion are solved in the time domain by Newmark's method. The influence of parameters like the temperature variation, the thickness and the ratio of curvature on the beams nonlinear dynamics is studied. Periodic and non-periodic motions are found.

The main goal of this work is to develop accurate and time efficient numerical approaches to study geometrically nonlinear vibrations of moderately thick beams under the combined action of mechanical and thermal loads. The influence of the thermal loading duration and thermal loading amplitude on the response of the structures is studied. Beams subjected to short heat flux and mechanical harmonic loading, with the excitation frequencies close to the natural frequencies of the beams, are investigated.

Large amplitude vibrations of a Timoshenko beam under an influence of thermal and mechanical loadings are studied in the paper. The structural parameters of the beam are considered enabling internal resonance conditions. Moreover, it is assumed that the beam gets instantly temperature which is distributed along its length and thickness. The mathematical model represented by a set of partial differential equations takes into account coupled mechanical and thermal fields. The problem is transformed to a set of ODEs by the Galerkin method and three modes of a simply supported beam at both ends are studied. The effect of temperature on internal and external resonances is analysed on the basis of the proposed reduced model.Copyright © 2014 by ASME

The goal of this paper is to study large amplitude vibrations of a Timoshenko beam under an influence of the elevated temperature. It is assumed that the beam gets the elevated temperature instantly and the temperature is uniformly distributed along the beam’s length and cross-section. The mathematical model represented by a set of partial differential equations is derived taking into account boundary conditions for a simply supported beam in the both ends. Next, the problem is reduced by the Galerkin method by means of free vibration modes. The influence of the temperature on a resonance localisation and nonlinear oscillations is studied numerically and analytically by the multiple time scale method.

A rotating thin-walled beam with piezoelectric element is analysed. The beam is considered to vibrate in space, hence the longitudinal, transverse and torsional deformations are taken into account. The bending deformations of the beam are modelled by assuming Timoshenko's theory. Torsion is included by considering that the cross section rotates as a rigid body but can deform in longitudinal direction due to warping. The warping function is computed preliminary by the finite element method. The equation of motion is derived by the principle of virtual work and discretized in space by the Ritz method. Electro-mechanical coupling is included in the model by considering the internal electrical energy and the electric charge output. The piezo-electric constitutive relations are used in reduced form. The beam is assumed to rotate about a fixed axis with constant speed. The equation of motion is derived in rotating coordinate system, but the influence of the rotation of the coordinate system is taken into account through the inertia forces. Results in time domain are presented for different speeds of rotation and frequencies of vibration. The influence of the speed of rotation and of the frequency of vibration on the electrical output is presented and analysed.

This study explains and demonstrates the utilisation of different nonlinear-dynamics-based procedures for the purposes of structural health monitoring as well as for monitoring of robot joints.

The dynamic behavior of moderately thick elastic-plastic circular plates has been investigated within the context of the geometrical non-linear version of the Mindlin plate theory. For this purpose, an algorithm is developed based on the pseudo-normal mode superposition method. The plastic yielding is controlled by the von Mises yield criterion. 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. The numerical examples of the forced axisymmetric vibrations of simply supported and clamped plates subjected to a different type of pulse loads clarify the influence of the material and geometrical non-linearities on the plate response.

In this work, the geometrically nonlinear vibrations of fully clamped composite beams subjected to thermal changes are used to study the sensitivity of selected vibration response parameters to the presence of delamination (damage) and elevated temperature. The damage detection criterion formulated earlier for non-heated plates, based on analyzing the points in the Poincare sections of the damaged and healthy plate, is modified and tested for the case of beams additionally subjected to elevated temperatures. The importance of the actual temperature in the process of damage detection is shown.

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.

In this work, geometrically nonlinear vibrations of fully clamped rectangular plates subjected to thermal changes are used to study the sensitivity of some vibration response parameters to the presence of damage and elevated temperature. The geometrically nonlinear version of the Mindlin plate theory is used to model the plate behaviour. Damage is represented as a thickness reduction in a small area of the plate. The plates are subjected to harmonic loading leading to large amplitude vibrations and temperature changes. The plate vibration response is obtained by a pseudo-load mode superposition method. The main results are focussed on establishing the influence of damage on the vibration response of the heated and the unheated plates and the change in the time-history diagrams and the Poincare maps caused by damage and elevated temperature. The damage criterion formulated earlier for non-heated plates, based on analyzing the points in the Poincare sections of the damaged and healthy plate, is modified and tested for the case of plates additionally subjected to elevated temperatures. The importance of taking into account the actual temperature in the process of damage detection is shown.

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.