No abstract

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method doesn't require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at a first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

In this research, the dynamic response of a slightly curved bridges under moving mass load is studied using an analytical approach. A solution method similar to the method of successive approximation has been used. The method has been exemplified for the special values of the variables. The effects of some variables have been specifically investigated. The results reveal that the inertial, centripetal and Coriolis forces must be involved in the analysis especially when the slightly curved bridges under moving loads with high speed are examined. Depending on the convexity and concavity of the initial curve, the effects of these forces become different. In a curved bridge, the moving mass affects the bridge more than that in a straight bridge with increasing the velocity of the moving mass. It has been observed that the forced vibration of the bridge is strongly influenced by the velocity of the moving mass. Many figures have been plotted to show clearly the effects of the variables.

This study is devoted to the investigation of dynamic analysis of a bridge supported with many vertical supports under a moving load. Each vertical support is modelled as a linear spring and a linear damper. The analysis is based on Euler-Bernoulli beam theory. The present method utilises the concept of distributed moving load, spring force and damping force, and avoids the use of matching conditions. Expressing these forces in terms of the unknown function of the problem, it highly simplifies obtaining an exact solution. An important property of Dirac delta distribution function is utilised in order to reach the exact solution. Considering one and three vertical supports, the response of the supported bridge is plotted and compared to different values of parameters. In the case of an undamped bridge with no support, the results are compared with those of previous papers.

This study is devoted to the investigation of the vibration of a cracked cantilever beam under moving mass load. The present formulation contains inertial, centripetal and Coriolis forces that depend on mass and the velocity of the moving load. The existence of crack induces a local flexibility which is a function of the crack depth, thereby changing its vibration behavior and the eigen-values of the system. The response of the system is obtained in terms of Duhamel integral. The differential equation which involves complicated terms on the right side is solved via an iterative procedure. It has been shown that the centripetal and Coriolis forces make an effect to decrease the deformations on the beam since the deformed beam remains concave during the passage of the moving load. It has also been detected that the previous solutions for the case of moving constant force had several mistakes. The results are exemplified for various values of the variables.