Structural control of the fundamental mode and frequency, of discrete vertical shear cantilevers. (1st September 2020) - Miranda, Julio C.
Highlights: Applied to mechanical systems undergoing seismic excitations, this paper proposes a methodologyto achieve the control of the fundamental mode and frequency, of discrete vertical shear cantilevers. Two control strategies are proposed: a) A strategy for which any desired relative modal kinetic energy distribution along the height of the cantilever is retained, and b) A strategy for which any desired relative modal strain energy distribution along the height of the cantilever is retained. Both strategies result in the definition of the fundamental mode and frequency, as well as the corresponding stiffness matrix. Subsequently, after assuming a value for the coefficient of damping of the controlled fundamental mode, the methodology allows for the definition of the damping matrix, as well as the definition of the coefficients of damping for the higher modes. Since the mechanical system discussed is presumed to be close-coupled, and with low classical damping, the resulting procedures are very simple and practical. The discussion includes alternative structural dynamics methods for the calculation of the system's frequencies, and participation factors. Several examples illustrating the control strategies are offered, that demonstrate the validity and simplicity of the proposed procedures. Abstract: In view of applications to mechanical systems undergoing seismic excitations, this paper proposes a methodology to achieve the control of the fundamental mode and frequency, of buildings idealized as discrete vertical shear cantilevers. Two control strategies are proposed: a) A strategy for which any desired relative modal kinetic energy distribution along the height of the cantilever is retained, and b) A strategy for which any desired relative modal strain energy distribution along the height of the cantilever is retained. Both strategies result in the definition of the fundamental mode and related frequency, as well as the corresponding stiffness matrix. Subsequently, after assuming a value for the coefficient of damping of the controlled fundamental mode, the methodology allows for the definition of the damping matrix, as well as the definition of the coefficients of damping for the higher modes. Since the mechanical system discussed is presumed to be close-coupled, and with low classical damping, the resulting procedures are very simple, and practical, since they can be applied to a large building inventory. The discussion includes alternative structural dynamics methods for the calculation of the system's frequencies, and participation factors. Several examples illustrating the control strategies are offered, that demonstrate the validity and simplicity of the proposed procedures.