An interest in free vibration frequencies and mode shapes of rectangular cantilever plates, with step discontinuities in properties, has arisen in connection with modeling the response of certain high-rise buildings during seismic excitation. In the case of long narrow structures, sueh as some office or apartment buildings, the idealized model consists of a vertical cantilever plate, fixed at the base, and with step discontinuities in effective stiffness and mass distribution corresponding to those of the successive floor levels as one moves up the building. It will be appreciated, for example, that lateral stiffness of the building provided by the steel framework will normally decrease from story to story as one moves upward. In this paper, employing the superposition method, accurate analytical type solutions are obtained for free vibration of such cantilever plates. Behaviour of the various uniform segments of the plate is investigated by means of the superposition of a judicious selection of building blocks (rectangular plate forced vibration solutions), each driven by either a harmonic edge rotation or vertical edge reaction, distributed along one edge. The superposition method has been described in detail in numerous publications and more recently in reference.
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