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The strain compliance of cortical shell is generally not a sensitive indicator to predict risk of fatigue injury if the fatigue loading is mild. The prophylactic augmentation strengthens the osteoporotic vertebrae, decreases the progression of vertebral height loss, reduces the anterior body shift, and hence protects the adjacent intact vertebra from elevated flexion bending. It can be cautiously suggested that if the vertebra is osteoporotic and adjacent level is located at pivot or lordotic level of spinal column, the prophylactic augmentation may be an option to prevent the AVF.

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Friction dampers are often used in turbine design to attenuate blade vibration to acceptable levels so as to prolong blades’ service life. A wedge damper, also called a self-centering, blade-to-blade damper, can provide more design flexibility to meet various needs in different operating conditions when compared with conventional platform dampers. However, direct coupling of the two inclined friction interfaces of the wedge damper often leads to very complex contact kinematics. In Part I of this two-part paper, a dual-interface friction force model is proposed to investigate the coupling contact kinematics. The key issue of the model formulation is to derive analytical criteria for the stick-slip transitions that can be used to precisely simulate the complex stick-slip motion and, thus, the induced friction force as well. When considering cyclic loading, the induced periodic friction forces can be obtained to determine the effective stiffness and damping of the interfaces over a cycle of motion. In Part II of this paper, the estimated stiffness and damping are then incorporated with the harmonic balance method to predict the forced response of a blade constrained by wedge dampers.