Critical Double Impulse Input and Bound of Earthquake Input Energy to Building Structure

A theory of earthquake input energy to building structures under single impulse is useful for disclosing the property of energy transfer function. This property shows that the area of the energy transfer function is constant irrespective of natural period and damping of building structures. However, single impulse may be unrealistic from a certain viewpoint because the frequency characteristic of input cannot be expressed by this input. In order to resolve such issue, a double impulse is introduced in this paper. The frequency characteristic of the Fourier amplitude of the double impulse is found in an explicit manner and a critical excitation problem is formulated with an interval of two impulses as a variable. The solution to that critical excitation problem is derived. An upper bound of the earthquake input energy is then derived by taking full advantage of the property of the energy transfer function that the area of the energy transfer function is constant. The relation of the double impulse to the corresponding one-cycle sinusoidal wave as a representative of near-fault pulse-type waves is also investigated.