Reliable dynamic analysis of an uncertain shear beam

In structural engineering, shear beams and their dynamic behaviour play an important role in modelling, analysis and design of various types of structures subjected to a system of dynamic loads such as wind or earthquake excitations. However, in current procedures of dynamic analysis of shear beams, the presence of uncertainty in the system's mechanical properties and/or applied forces is not considered. In this work, a new method for dynamic modal analysis of continuous uncertain shear beams subjected to uncertain external loads is developed. First, an interval formulation is used to quantify the uncertainty present in the system's mechanical characteristics and/or magnitude of dynamic forces. Then, having the interval parameters, the bounds on modal responses of the continuous system are obtained leading to determination of the upper bounds of total response that may be used for design purposes. An example problem that illustrates the behaviour of the method and a comparison with Monte Carlo simulations are presented. Using this new method, it has been shown that obtaining the bounds on the dynamic response of a shear beam does not require an iterative procedure such as Monte Carlo simulations.