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The response of a shear rod to a transient sinusoidal excitation

OBSERVATORIO ASTRONOMICO UNIVERSIDAD NACIONAL DE LA PLATA Republica Argentina, S. A.

Abstract

Taking into account that the behavior of a building under the action of ground acceleration may be represented in a first approximation by the behavior of a rod, the latter was investigated by the author in three previous papers. To extend the results obtained previously, the response of an undamped shear rod, fastened at one end and excited by a transient sinusoidal acceleration, has been considered and a closed expression, which may be useful as a reference for more complicated cases, has been obtained. The expression was found following a method similar to D'Alembert's of solving the equation of the vibrating string. Formulae for the case of resonance and for the seismic load are also given.