Nonlinear free vibration analysis of the functionally graded beams

Nonlinear natural oscillations of beams made from functionally graded material (FGM) are studied in this paper. The equation of motion is derived according to the EulerBernoulli beam theory and von Karman geometric nonlinearity. Subsequently, Galerkin’s solution technique is applied to obtain the corresponding ordinary differential equation (ODE) for the FGM beam. This equation represents a kind of a nonlinear ODE containing quadratic and cubic nonlinear terms. This nonlinear equation is then solved by means of three efficient approaches. Homotopy perturbation method is applied at the first stage and the corresponding frequency-amplitude relationship is obtained. Frequency-amplitude formulation and Harmonic balance method are then employed and the consequent frequency responses are determined. In addition, Parameter Expansion Method is utilized for evaluating the nonlinear vibration of the system. A parametric study is then conducted to evaluate the influence of the geometrical and mechanical properties of the FGM beam on its frequency responses. Different types of material properties and boundary conditions are taken into account and frequency responses of the system are evaluated for different gradient indexes. The frequency ratio (nonlinear to linear natural frequency) is obtained in terms of the initial amplitude and compared for different materials and end conditions

The requirements and challenges in preventing of road traffic injury in Iran. A qualitative study

<p>Abstract</p> <p>Background</p> <p>Road traffic injuries (RTIs) are a major public health problem, especially in low- and middle-income countries. Among middle-income countries, Iran has one of the highest mortality rates from RTIs. Action is critical to combat this major public health problem. Stakeholders involved in RTI control are of key importance and their perceptions of barriers and facilitators are a vital source of knowledge. The aim of this study was to explore barriers to the prevention of RTIs and provide appropriate suggestions for prevention, based on the perceptions of stakeholders, victims and road-users as regards RTIs.</p> <p>Methods</p> <p>Thirty-eight semi-structured interviews were conducted with informants in the field of RTI prevention including: police officers; public health professionals; experts from the road administrators; representatives from the General Governor, the car industry, firefighters; experts from Emergency Medical Service and the Red Crescent; and some motorcyclists and car drivers as well as victims of RTIs. A qualitative approach using grounded theory method was employed to analyze the material gathered.</p> <p>Results</p> <p>The core variable was identified as "The lack of a system approach to road-user safety". The following barriers in relation to RTI prevention were identified as: human factors; transportation system; and organizational coordination. Suggestions for improvement included education (for the general public and targeted group training), more effective legislation, more rigorous law enforcement, improved engineering in road infrastructure, and an integrated organization to supervise and coordinate preventive activities.</p> <p>Conclusion</p> <p>The major barriers identified in this study were human factors and efforts to change human behaviour were suggested by means of public education campaigns and stricter law enforcement. However, the lack of a system approach to RTI prevention was also an important concern. There is an urgent need for both an integrated system to coordinate RTI activities and prevention and a major change in stakeholders' attitudes towards RTI prevention. The focus of all activities should take place on road users' safety.</p

Analityczne rozwiązania problemu drgań swobodnych belek umieszczonych na sprężystym podłożu wyznaczone za pomocą iteracyjnej metody wariacyjnej

Closed form expressions are obtained for the dynamic response of an elastic beam rested on a nonlinear foundation in this paper. The nonlinear governing equation is solved using the Variational Iteration Method (VIM). An iteration formulation is constructed based on the VIM and the dynamic responses are then obtained. Frequency responses are presented in a closed form and their sensitivity with respect to the initial amplitudes are investigated. A number of numerical simulations are then carried out and performance and validity of the solution procedure is evaluated in the time domain. It is proved that the VIM is quite a reliable and straightforward technique to solve the corresponding set of coupled nonlinear differential equations.W pracy przedstawiono zamknięte formy rozwiązań opisujących odpowiedź dynamiczną elastycznej belki spoczywającej na nieliniowo sprężystym podłożu. Równanie ruchu rozwiązano przy pomocy iteracyjnej metody wariacyjnej (VIM). Sformułowanie iteracyjne skonstruowane w oparciu o tę metodę pozwoliło na wyznaczenie odpowiedzi dynamicznej belki. Charakterystyki częstościowe przedstawiono w zamkniętej formie i podkreślono ich wrażliwość na wartość amplitud początkowych. Następnie zaprezentowano wyniki kilku symulacji numerycznych w celu oszacowania wydajności i dokładności zastosowanej procedury rozwiązywania równań ruchu w dziedzinie czasu. Wykazano, że metoda VIM jest wystarczająco prosta i wiarygodna w rozwiązywaniu układu sprzężonych, nieliniowych równań różniczkowych

Ride comfort of high-speed trains travelling over railway bridges

The ride comfort of high-speed trains passing over railway bridges is studied in this paper. A parametric study is carried out using a time domain model. The effects of some design parameters are investigated such as damping and stiffness of the suspension system and also ballast stiffness. The influence of the track irregularity and train speed on two comfort indicators, namely Sperling's comfort index and the maximum acceleration level are also studied. Two types of railway bridges, a simple girder and an elastically supported bridge are considered. Timoshenko beam theory is used for modelling the rail and bridge and two layers of parallel damped springs in conjunction with a layer of mass are used to model the rail-pads, sleepers and ballast. A randomly irregular vertical track profile is modelled, characterized by its power spectral density (PSD). The ‘roughness' is generated for three classes of tracks. Nonlinear Hertz theory is used for modelling the wheel-rail contact. The influences of some nonlinear parameters in a carriage-track-bridge system, such as the load-stiffening characteristics of the rail-pad and the ballast and that of rubber elements in the primary and secondary suspension systems, on the comfort indicators are also studied. Based on Galerkin's method of solution, a new analytical approach is developed for the combination between the rigid and flexural mode shapes, which could be used not only for elastically supported bridges but also other beam-type structures

Nonlinear vibration and comfort analysis of high-speed trains moving over railway bridges

The ride comfort of high-speed trains passing over railway bridges is studied in this paper. The effects of some nonlinear parameters in a carriage-track-bridge system are investigated such as the load-stiffening characteristics of the rail-pad and the ballast, rubber elements in the primary and secondary suspensions systems. The influence of the track irregularity and train speed on two comfort indicators, namely Sperling's comfort index and the maximum acceleration level, are also studied. Timoshenko beam theory is used for modelling the rail and bridge and two layers of parallel damped springs in conjunction with a layer of mass are used to model the rail-pads, sleepers and ballast. A randomly irregular vertical track profile is modelled, characterised by a power spectral density (PSD). The 'roughness' is generated for three classes of tracks. Nonlinear Hertz theory is used for modelling the wheel-rail contact