earticle

영어

Free vibration of structures includes information on their inherent dynamic characteristics such as natural frequency and damping ratio. Especially, in the case of a structure including the friction damping, in which a strong nonlinearity depending on structural displacement and velocity is inherent, the amount of energy dissipation and equivalent viscous damping can be estimated by analyzing the free vibration from initial displacement to motion stopping. Free vibration displacement and acceleration responses to both single-degree-of-freedom(SDOF) and multi-degree-of-freedom(MDOF) structures containing friction damping are investigated in this paper. Due to the friction damping under an assumed initial condition, the number of cycles that pass before the motion stops and both the permanent displacement and acceleration after the motion ceases are theoretically derived from the equation of motion for SDOF structure, and verified through the numerical analysis. Also, free vibration response to MDOF structure simultaneously considering both viscous and friction damping is analyzed by using its modal decomposition. As the friction force is acting on inter-story of a structure and its sign convention depends on inter-story velocity, the equation of motion for MDOF structure is composed of the story drift coordinates. Structural mass, viscous damping and stiffness matrices that has the form of non-diagonal matrix are converted to diagonal matrix, and structural modal responses are obtained by applying their modal orthogonality. Finally, it is confirmed that free vibration responses to MDOF structure with the story drift coordinates are exactly agreed with those transformed to physical coordinates by the superposition of single modal responses which has been decomposed by the modal orthogonality.