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Analytical framework for probabilistic assessment of dynamical system under base- and mass- excitations with equal input energy is presented with reference to multi-hazard engineering. Closed-form solutions for equivalent undamped and damped dynamical systems under harmonic sinusoidal base- and mass- excitations are obtained. Uncertainties are considered in the excitation frequency and peak amplitude for sinusoidal base excitations, whereas for the mass excitations, the input forcing functions have variations in excitation frequency, mean speed, and fluctuating wind speeds. Dynamic response quantities (acceleration and displacement) are obtained under the suite of stochastic base and mass excitation forces. Structural failure under the independent excitations is determined as joint probability density functions and fragility surfaces. Under equal input energy from such separate dynamic excitations, dissimilar vulnerability is exhibited by the structure when exposed to two independent time-dependent excitations, base-induced earthquake and mass-induced wind forces. Moreover, the uncertainty in the input excitation parameters has significant influence on the probability of failure in the design life of structure under the non-simultaneous excitations.

Analytical stochastic framework for assessment of base- and mass-excited structures under equal input energy pertinent to multi-hazard engineering