DYNAMIC RESPONSE OF A LONG, DISCRETELY SUPPORTED BEAM

Abstract eng:
This paper describes a computational model of a long beam resting on discretely-located flexible supports. The model is suitable for assessing certain types of vibrations in building floors, and for various aerospace and other applications. The model is a finite element model of an arbitrarily long Euler-Bernoulli beam, constructed using the mode shapes of a beam supported by a continuous foundation as basis functions. Thus, the model is efficient, and yields a numerically exact solution when the joist spacing is small (i.e., continuous). The beam configuration is completely described using a fundamental frequency, a characteristic length, and the distribution of the joist stiffnesses, as well as two damping ratios and a dimensionless rotatory inertia parameter. The model is then applied to vibration serviceability behavior of floors, a significant consideration in civil engineering design, which is becoming increasingly more important because of the use of lighter, higher strength steel and concrete. When a floor plate is geometrically regular and supported by identical, equally spaced joists or beams, vibration can propagate in the direction transverse to the joists. Such “vibration transmission” can lead to the perception of poor behavior. Exploiting the model's efficiency, vibration transmission is studied to determine the influence of characteristic length, and joist stiffness on floor response. Two response regimes are identified for the floor system. The practice of varying the stiffness distribution of the supporting joists as a vibration mitigation strategy is also assessed.

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