An adaptive harmonic balance method for predicting the nonlinear dynamic responses of mechanical systems—Application to bolted structures
Aeronautical structures are commonly assembled with bolted joints in which friction phenomena, in combination with slapping in the joint, provide damping on the dynamic behavior. Some models, mostly nonlinear, have consequently been developed and the harmonic balance method (HBM) is adapted to compute nonlinear response functions in the frequency domain. The basic idea is to develop the response as Fourier series and to solve equations linking Fourier coefficients. One specific HBM feature is that response accuracy improves as the number of harmonics increases, at the expense of larger computational time. Thus this paper presents an original adaptive HBM which adjusts the number of retained harmonics for a given precision and for each frequency value. The new proposed algorithm is based on the observation of the relative variation of an approximate strain energy for two consecutive numbers of harmonics. The developed criterion takes the advantage of being calculated from Fourier coefficients avoiding time integration and is also expressed in a condensation case. However, the convergence of the strain energy has to be smooth on tested harmonics and this constitutes a limitation of the method. Condensation and continuation methods are used to accelerate calculation. An application case is selected to illustrate the efficiency of the method and is composed of an asymmetrical two cantilever beam system linked by a bolted joint represented by a nonlinear LuGre model. The practice of adaptive HBM shows that, for a given value of the criterion, the number of harmonics increases on resonances indicating that nonlinear effects are predominant. For each frequency value, convergence of approximate strain energy is observed. Emergence of third and fifth harmonics is noticed near resonances both on vibratory responses and on approximate strain energy. Parametric studies are carried out by varying the excitation force amplitude and the threshold value of the adaptive algorithm. Maximal amplitudes of vibration and frequency response functions are plotted for three different points of the structure. Nonlinear effects become more predominant for higher force amplitudes and consequently the number of retained harmonics is increased.
Identification of bolted lap joints parameters in assembled structures
Bolted lap joints have significant influence on the dynamical behaviour of the assembled structures due to creation of strong local flexibility and damping. In modelling the dynamical behaviour of assembled structures the joint interface model must be represented accurately. A nonlinear model for bolted lap joints and interfaces is proposed capable of representing the dominant physics involved in the joint such as micro/macro-slip. The joint interface is modelled using a combination of linear and nonlinear springs and a damper to simulate the damping effects of the joint. An estimate of the response of the structure with a nonlinear model for the bolted joint under external excitations is obtained using the method of multiple scales. The parameters of the model, i.e. the spring constants and the damper coefficient, are functions of normal and tangential stresses at the joint interface and are identified by minimizing the difference between the model predictions and the experimentally measured data.
Laboratory Animal Models for Brucellosis Research
Brucellosis is a chronic infectious disease caused by Brucella spp., a Gram-negative facultative intracellular pathogen that affects humans and animals, leading to significant impact on public health and animal industry. Human brucellosis is considered the most prevalent bacterial zoonosis in the world and is characterized by fever, weight loss, depression, hepato/splenomegaly, osteoarticular, and genital infections. Relevant aspects of Brucella pathogenesis have been intensively investigated in culture cells and animal models. The mouse is the animal model more commonly used to study chronic infection caused by Brucella. This model is most frequently used to investigate specific pathogenic factors of Brucella spp., to characterize the host immune response, and to evaluate therapeutics and vaccines. Other animal species have been used as models for brucellosis including rats, guinea pigs, and monkeys. This paper discusses the murine and other laboratory animal models for human and animal brucellosis.