• Structural Engineering and Mechanics
• /
• v.30 no.4
• /
• pp.427-444
• /
• 2008

A mathematical model for the nonlinear dynamics of a rotating beam with flexible root attached to a rotating hub with elastic foundation is developed. The model is developed based on the large planar and flexural deformation theory and the potential energy method to account for axial shortening due to bending deformation. In addition the exact nonlinear curvature is used in the system potential energy. The Lagrangian dynamics and the assumed mode method is used to derive the nonlinear coupled equations of motion hub rotation, beam tip deflection and hub horizontal and vertical displacements. The derived nonlinear model is simulated numerically and the results are presented and discussed for the effect of root flexibility, hub stiffness, torque type, torque period and excitation frequency and amplitude on the dynamic behavior of the rotating beam-hub and on its stability.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.14 no.2
• /
• pp.288-297
• /
• 1990

The method of analyzing flexible mechanisms with clearances was studied considering flexibility of beams in the mechanism using finite elements. Both ends of a beam were modeled as free following Dubowsky's impact pair model. Instead some force constraints were imposed at imposed at the connections between adjoining links. Coulomb model has been developed using dry frictions in place of tangential damping forces in the impact pair model and the contact compliance and damping coefficient approximated in a form of root function were used. As examples, impacts of a rigid ball in a cylinder, impact beam model and four-bar mechanisms made up of three flexible links with clearance connections were simulated numerically. The results from examples showed similar but a little bit smaller magnitude of impact forces compared with published studies.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.1
• /
• pp.263-270
• /
• 1995

The use of the shape memory alloy, Nitinol wire, is investigated as an actuator for enhancing the damping in structural vibration systems. The first-order mathematical model of the Nitinol wire is obtained from the experimental data for an actuator. Finite element method is utilized for the strain gage sensor model, which is installed at the root of cantilever beam. A simple system, cantilever beam, is built as a flexible structural system to implement a control law with the Nitinol wire actuator. The system model including sensor and actuator is derived, which agrees with the experimental results. The actuator dynamics is augmented with the system so as to design PI controller and the one of robust controllers, LQG/LTR controller, and the control laws are implemented experimentally. The experimental study shows the feasibility of utilizing the Nitinol wire as an actuator for the purpose of vibration control.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2008.11a
• /
• pp.256-263
• /
• 2008

The assumed modes method is developed to derive a set of linear differential equations describing the motion of a flexible wind turbine blade and to propose an approach to investigate the forced responses result from various wind excitations. In this work, we have adopted Euler beam theory and considered that the root of the blade is clamped at the rigid hub. And the aerodynamic parameters and forces are determined based on Blade Element Momentum (BEM) theory and quasi-steady airfoil aerodynamics. Numerical calculations show that this method gives good results and it can be used fur modeling and the forced vibration analysis including the coupling effect of wind-turbine blades, as well as turbo-machinery blades, aircraft propellers or helicopter rotor blades which may be considered as straight non-uniform beams with built-in pre-twist.