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The lateral vibration of cracked isotropic thick beams is investigated. Generally, the analysis of thick beam based on line elements can be undertaken using either Timoshenko beam theory or a third order beam theory (TSDT) such as Reddy beam theory. TSDT is superior to Timoshenko beam theory, as it eliminates the need for a shear correction coefficient. However, there is no available solution for a cracked beam based on Reddy beam theory which is the main focus of this paper. The investigated beam is divided into several elements where their stiffness and mass matrices are derived using Reddy beam theory. Each element has two nodes with 3 degrees of freedom (1 lateral and 2 rotational) at each node. The crack was modeled using two rotating springs with stiffnesses that varied with crack depth. These elements are used to connect the adjacent beam elements. The impact of boundary conditions, slenderness ratio, crack location, and crack depth are investigated. In addition, experimental and finite element analyses of cracked steel beams is undertaken to validate the results of the present model. The results show that the maximum deviation between the analytical and the experimental results is less than 3% up to the third mode shape. [ABSTRACT FROM AUTHOR]

In the air drilling process, the pre-bent pendulum bottom hole assembly (PBP-BHA) has excellent performance in controlling the well deviation and improving the wellbore quality, but the mechanism that is closely related to the dynamics of the PBP-BHA has not been ascertained. In this paper, an effective technique combining the weighted residuals method with the finite element method is presented to study the PBP-BHA lateral vibration. First, a three-dimensional nonlinear static model of pre-bent BHA is established under small deformation condition and solved by the weighted residuals method and optimization method, so as to define the tangent point according to the deformation characteristics of the PBP-BHA. This tangent point determines the end of the effective PBP-BHA length that starts from the drill bit. Subsequently, the finite element model of PBP-BHA is established to solve the lateral natural frequencies and mode shapes of the PBP-BHA. After considering the borehole wall constraint, the modal superposition technique is used to obtain the steady dynamic responses of the PBP-BHA. Meanwhile, the dynamic performance of the PBP-BHA used in the actual air drilling process is calculated to obtain its critical speeds and working status chart. The critical speeds of the PBP-BHA are 80 r/min and 190 r/min, which are far away from the surface rotary speed in the actual drilling site. Through comparing with the dynamic characteristics of regular BHA with the same structural parameters, it is discovered that the bend angle in the PBP-BHA plays a crucial role in improving the dynamic performance of the PBP-BHA. Moreover, the technique presented in this study can be used to make a reasonable design of BHA configuration and optimize drilling parameters. [ABSTRACT FROM AUTHOR]

Chaos control of a spinning disk having transverse vibration is considered in this article by stabilizing the system on its corresponding unstable periodic orbit (UPO). At the first step, the system continuous-time dynamic equations are quantized by utilizing a proper Poincare map. Then, using the regression method a linear description from the obtained cross points is achieved around the corresponding fixed point of the target UPO. Finally, through solving the Riccati equation, an optimal controller is introduced which stabilizes the system on its unstable fixed point. At the end, the effectiveness of the proposed control method is examined through numerical simulations. [ABSTRACT FROM AUTHOR]

Starting from the analysis of tire ground contact characteristics, the formulas of ground contact patch of tires are obtained, which are verified by tests, and the calculation formula of lateral stiffness of tread element is determined using the energy method. On this basis, a dynamic model of tread's lateral vibration is established, and the effects of vehicle speed, vertical load and tire pressure are analyzed. The results show that: the lateral self-excited vibration will occur under certain conditions, and vehicle speed, vertical load and tire pressure have great influence on the vibration characteristics; the lateral self-excited vibration of tread is a kind of stable periodic vibration caused by Hopf bifurcation of system. [ABSTRACT FROM PUBLISHER]