In the automotive industry uniaxial vibration testing is a common method used to predict the lifetime of components. In reality truck components work under multiaxial loads meaning that the excitation is multiaxial. A common method to account for the multiaxial effect is to apply a safety margin to the uniaxial test results. The aim of this work is to find a safety margin between the uniaxial and multiaxial testing by means of virtual vibration testing and statistical methods. Additionally to the safety margin the effect of the fixture’s stiffness on the resulting stress in components has been also investigated.

In this thesis a novel approximate/analytical approach based on the concepts of stochastic averaging and of statistical linearization is developed for the response determination of nonlinear/hysteretic multi-degree-of-freedom (MDOF) systems subject to evolutionary stochastic excitation. The significant advantage of the approach relates to the fact that it is readily applicable for excitations possessing even non-separable evolutionary power spectra (EPS) circumventing ad hoc pre-filtering and pre-processing excitation treatments associated with existing alternative schemes of linearization. Further, the approach can be used, in a rather straightforward manner, in conjunction with recently developed design spectrum based analyses for obtaining peak response estimates without resorting to numerical integration of the nonlinear equations of motion. Furthermore, a novel approximate/analytical Wiener path integral based solution (PIS) is developed and a numerical PIS approach is extended to determine the response and first-passage probability density functions (PDFs) of nonlinear/hysteretic systems subject to evolutionary stochastic excitation. Applications include the versatile Preisach hysteretic model, recently applied in modeling systems equipped with smart material (shape memory alloys) devices used for seismic hazard risk mitigation. The approach is also applied to determine the capsizing probability of a ship, whose rolling dynamics is captured by a softening Duffing oscillator. Finally, novel harmonic wavelets based joint time-frequency response analysis and identification approaches are developed capable of determining the time-varying frequency content of non-stationary complex stochastic phenomena encountered in engineering applications. Specifically, a harmonic wavelets based statistical linearization approach is developed to determine the EPS of the response of nonlinear/hysteretic systems subject to stochastic excitation. In a similar context, an identification approach for nonlinear time-variant systems based on the localization properties of the harmonic wavelet transform is also developed. It can be construed as a generalization of the well established reverse multiple-input/single-output (MISO) spectral identification approach to account for non-stationary inputs and time-varying system parameters. Several linear and nonlinear time-variant systems are used to demonstrate the reliability of the approach.

This paper is devoted to the computation of statistical characteristics of the response of discrete vibration systems with a random external excitation. The excitation can act at multiple points and is modeled by a time-shifted random process and its derivatives up to the second order. Statistical characteristics of the response are given by expansions as to the correlation length of a weakly correlated random process which is used in the excitation model. As the main result analytic expressions of some integrals involved in the expansion terms are derived.

This work deals with composite sandwich panels, which are currently used as supporting structures for satellites. This type of panel contains an aluminum honeycomb core and two thin laminate coatings, reinforced with carbon fibers. Laminate sandwich panel coatings offer an alternative to conventional aluminum coatings, which is advantageous mainly due to the reduction of weight and increase of the flexural stiffness of the panels. The work is a parametric study of mechanical properties for several variants of the coating of sandwich panels. These are laminate coatings, differing in the orientation of the fibers in the individual layers, as well as an aluminum alloy coating. The study is divided into two parts. The first part examines the deformation-stress response of a sandwich panel, which is simply supported at the edges and loaded with pressure. The response calculation is performed using FEM and verified by the method of sum of an infinite series. The second part investigates the deformation-stress response of the joint, (node) of two sandwich panels, which is loaded by random vibrations, aimed at simulating the mechanical environment of the rocket carrier during the takeoff of the launch vehicle. The response is calculated using FEM and verified by an experiment on a vibrating stool for a selected variant of the laminate coating of sandwich panels. The results of the work can be used for the design of baffle of the X-ray imaging device (SXI), which is part of the equipment of the space satellite of the SMILE project.

Cette thèse porte sur l'analyse de l'endommagement par fatigue et optimisation fiabiliste des structures soumises à des vibrations aléatoires. Le but de l'optimisation fiabiliste est de trouver le compromis entre le coût et la fiabilité. Plusieurs méthodes, telles que la méthode hybride et la méthode OSF ont été développées. Ces méthodes ont été appliquées dans des cas statiques et certains cas dynamiques spécifiques. Dans la réalité les structures sont soumises à des vibrations aléatoires qui peuvent provoquer un endommagement par fatigue. Dans cette thèse on présente la stratégie numérique de calcul de l'endommagement par fatigue dans le domaine fréquentiel et on propose une extension des méthodes RBDO dans le cas des structures soumises à des vibrations aléatoires. Aussi, une méthode RHM est développée. Enfin,une application industrielle qui porte sur la modélisation de la partie mécanique du banc HALT est présenté. / This thesis deals with the fatigue damage analysis and reliability-based design optimization (RBDO) of structures under random vibrations. The purpose of an RBDO method is to find the best compromise between cost and safety. Several methods, such as Hybrid method and OSF method have been developed. These methods have been applied in static cases and some specific dynamic cases. In fact, structures are subject to random vibrations which can cause a fatigue damage. In this thesis we present the strategy of calculation of the fatigue damage based on the Sines criterion in the frequency domain developed in our laboratory. Then, an extension of the RBDO methods in the case of structures subjected to random vibrations is proposed. Also, an RHM method is developed. Finally, we present an industrial application where we propose a model of the mechanical part of the HALT chamber.

Este trabalho de pesquisa apresenta um modelo numérico para a análise de estruturas planas sob excitação aleatória induzida pelo vento. O comportamento não-linear da estrutura é considerado adotando-se um modelo constitutivo elasto-plástico para o material, aço estrutural. Os elementos das estruturas estudadas estão sujeitos ao surgimento e desaparecimento de rótulas plásticas, levando a um dimensionamento mais econômico. O conhecimento a respeito de vibrações aleatórias de estruturas lineares encontra-se estabelecido. Por outro lado, poucos resultados encontram-se disponíveis para o caso não linear considerado. Para a simulação de vibrações aleatórias uma análise de Monte Carlo é utilizada. Uma função de densidade espectral de potência das velocidades do vento é usada para gerar um certo número de funções harmônicas de carregamento. Os ângulos de fases destes harmônicos são gerados por um algoritmo pseudo-aleatório. Para cada função de carregamento realiza-se uma integração direta no tempo pelo método de Newmark. A grande quantidade de dados de resposta é tratada estatisticamente de modo a permitir a obtenção de conclusões, a respeito da possibilidade de ocorrência de eventos desfavoráveis, do ponto de vista da engenharia. / This work presents a numerical model to analyze structures under random dynamic excitation induced by the wind. The structure is considered to have nonlinear behavior due to the elastic-plastic constitutive law adopted for the material, structural steel. The members of the studied structures may experience formation or disappearance of plastic hinges, leading to a more economic design. Random vibrations of linear structures is a well established subject. On the other hand, very few results are available for the nonlinear case as the one considered. To simulate random vibrations a Monte Carlo type analysis is used. A power spectral density function for wind velocity is used to generate a large number of harmonic input functions. Their phase angles are generated via a pseudo-random algorithm. Numerical time integration using Newmark’s method is performed for each input function. The large amount of response data obtained is statistically treated to allow for useful engineering conclusions on the probability of occurrence of unfavorable events.

Este trabalho de pesquisa apresenta um modelo numérico para a análise de estruturas planas sob excitação aleatória induzida pelo vento. O comportamento não-linear da estrutura é considerado adotando-se um modelo constitutivo elasto-plástico para o material, aço estrutural. Os elementos das estruturas estudadas estão sujeitos ao surgimento e desaparecimento de rótulas plásticas, levando a um dimensionamento mais econômico. O conhecimento a respeito de vibrações aleatórias de estruturas lineares encontra-se estabelecido. Por outro lado, poucos resultados encontram-se disponíveis para o caso não linear considerado. Para a simulação de vibrações aleatórias uma análise de Monte Carlo é utilizada. Uma função de densidade espectral de potência das velocidades do vento é usada para gerar um certo número de funções harmônicas de carregamento. Os ângulos de fases destes harmônicos são gerados por um algoritmo pseudo-aleatório. Para cada função de carregamento realiza-se uma integração direta no tempo pelo método de Newmark. A grande quantidade de dados de resposta é tratada estatisticamente de modo a permitir a obtenção de conclusões, a respeito da possibilidade de ocorrência de eventos desfavoráveis, do ponto de vista da engenharia. / This work presents a numerical model to analyze structures under random dynamic excitation induced by the wind. The structure is considered to have nonlinear behavior due to the elastic-plastic constitutive law adopted for the material, structural steel. The members of the studied structures may experience formation or disappearance of plastic hinges, leading to a more economic design. Random vibrations of linear structures is a well established subject. On the other hand, very few results are available for the nonlinear case as the one considered. To simulate random vibrations a Monte Carlo type analysis is used. A power spectral density function for wind velocity is used to generate a large number of harmonic input functions. Their phase angles are generated via a pseudo-random algorithm. Numerical time integration using Newmark’s method is performed for each input function. The large amount of response data obtained is statistically treated to allow for useful engineering conclusions on the probability of occurrence of unfavorable events.

In support of society's technological evolution, the study of nonlinear systems in engineering and sciences has become a vital research area. Aiming to contribute in this field, this thesis investigates the behaviour of nonlinear systems using the 'Wiener theories'. As a useful example the Duffing oscillator is investigated in this work. In many real-life applications, nonlinear systems are excited randomly so this work examines systems under white-noise excitation using the Wiener series. Equivalent Linearisation (EL) is a well-known and simple method that approximates a nonlinear system by an equivalent linear system. However, it has deficiencies which this thesis attempts to improve. Initially, the performance of EL for different types of nonlinearities will be assessed and an alternative method to enhance it is suggested. This requires the calculation of the first Wiener kernel of various system defined quantities. The first Wiener kernel, as it will be shown, is the foundation of this research and a central element of the Wiener theory. In this thesis, an analytical proof to explain the interesting behaviour of the first Wiener kernel for a system with nonlinear stiffness is included using an energy transfer approach. Furthermore, the method mentioned above to enhance EL known as the Single-Pole Fit method (SPF) is to be tested for different kinds of systems to prove its robustness and validity. Its direct application to systems with nonlinear stiffness and nonlinear damping is shown as well as its ability to perform for systems with two degrees of freedom where an extension of the SPF method is required to achieve the desired solution. Finally, an investigation to understand and replicate the complex behaviour observed by the first Wiener kernel in the early chapters is carried out. The groundwork for this investigation is done by modelling an isolated nonlinear spring with a series of linear filters and certain nonlinear operations. Subsequently, an attempt is made to relate the principles governing the successful spring model presented to the original nonlinear system. An iterative procedure is used to demonstrate the application of this method, which also enables this new modelling approach to be related to the SPF method.

This document reflects the results of evaluating three computational methods to analyse the fatigue life of components mounted on the cylinder block; two currently in use at Scania and one that has been further developed from its previous state. Due to the cost of testing and the exponential increase in computational power throughout the years, the cheaper computational analyses have gained in popularity. When a component is mounted in a fairly complex assembly such as an engine, simplifications need to be made in order to make the analysis as less expensive as possible while keeping a high degree of accuracy. The methods of Virtual Vibrations, VROM and VFEM have been evaluated and compared in terms of accuracy, computational cost, user friendliness and general capacities. Additionally, the method VFEM has been further developed and improved from its previous state. A in-depth investigation regarding the differences of the methods has been conducted and improvements to make them more efficient are suggested herein. The reader can also find a decision matrix and recommendations regarding which method to use depending on the general characteristics of the component of interest and other factors. Two components, which differ in complexity and mounting nature, have been used to do the research.

This paper is devoted to the computation of statistical characteristics of the response of discrete vibration systems with a random external excitation. The excitation can act at multiple points and is modeled by a time-shifted random process and its derivatives up to the second order. Statistical characteristics of the response are given by expansions as to the correlation length of a weakly correlated random process which is used in the excitation model. As the main result analytic expressions of some integrals involved in the expansion terms are derived.