Dynamic Response of Beams to Interval Load

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Parameters of mathematical models are most often represented by real numbers, while in practice it is impossible or at least very difficult to get reliable information about their exact values. Hence, it is unreasonable to take point data for that may lead to incorrect results, which is not welcome especially when inaccuracy cannot be neglected. Depending on available information, one can use different ways of modelling of uncertainty. Interval computing plays an important role in this field, because very often the only available information are lower and upper bounds on a physical quantity. This paper focuses on a transient dynamic analysis of a beam with uncertain parameters. Finite difference and finite element methods are used to solve partial differential equation which represents the model for the motion of a straight elastic beam. In order to compute the time-history response of the beam under uncertainty, interval dynamic beam equations are solved using Search method, Gradient method, Taylor method, adaptive Taylor method, direct optimisation and Direct method for solving parametric interval linear systems. The applicability, i.e. effectiveness and accuracy, of those methods is illustrated through solution of beams with interval value of modulus of elasticity and mass density and subjected to interval dynamic loading.