In this study, the dynamic behaviour of a beam carrying accelerating mass is investigated. A MATLAB code was developed for numerical solutions. The accelerating moving mass that is travelling on the beam was modelled as a moving finite element in order to include inertial effects beside gravitation force of mass. Since the mass moves along the deflected curve of the beam, these effects are, respectively, the centripetal force, the inertia force, and the Coriolis force components of the moving mass. The effect of longitudinal force due to acceleration of the moving mass is also included. Dynamic response of the beam was obtained depending on the mass ratio (mass of the load / the mass of the beam) and the acceleration of the mass. Numerical results show the effectiveness of the method.

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There are a variety of techniques for estimating the parameters x and K of the Muskingum method of flood routing. One common difficulty in all the approaches is that different storm sequences along the same river reach would typically yield different parameter estimates. The a statistical analysis of these parameters also shows that they are highly variable. As a result achieving of a high level accuracy may not be the principle issue in describing x and K. This paper presents two approximate methods for estimating these parameters rather easily. The first method requires the computation of the slopes of the inflow and outflow hydrographs at their point of intersection, and the computation of the maximum storage within the reach. The second method requires the computation of the inflow and outflow hydrographs at two specific points. Three case studies investigated show that the first method gives estimates for the Muskingum parameters comparable to those derived by traditional estimation procedures for hydrographs showing linear characteristics.

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The aim of this study is to design a Linear Quadratic Regulator (LQR) controller for the active vibration control of a smart flexible cantilever beam. The mathematical model of the smart beam was created on the basis of the Euler-Bernoulli beam theory and the piezoelectric theory. State-space and finite element models used in the LQR controller design were developed. In the finite element model of the smart beam containing piezoelectric sensors and actuators, the beam was divided into ten finite elements. Each element had two nodes and two degrees of freedom were defined for each node, transverse displacement, and rotation. Two Piezoelectric ceramic lead Zirconate Titanate (PZT) patches were affixed to the upper and lower surfaces of the beam element as pairs of sensors and actuators. The location of the piezoelectric sensor and actuator pair changed and they were consecutively placed on the fixed part, the middle part, and the free end of the beam. In each case, the design of the LQR controller was made considering the first three dominant vibratory modes of the beam. The effect of the position of the sensor-actuator pair on the beam on the vibration damping capability of the controller was investigated. The best damping performance was found when the sensor-actuator pair was placed at the fixed end.