Dynamic Response Bound Estimation of Structures with Interval Parameters

This study aims to evaluate the result of mechanical vibration problems in presence of an interval of values for parameters such as mass, length, modulus of elasticity, moment of inertia. A possibility and computationally efficient method is proposed to obtain the limits of natural frequency of systems with interval parameters. The interval eigenvalue problem is formulated by the Finite Element Method (FEM) which stiffness and mass matrices are submitted to disturbance by Perturbation Theory of Matrices (PTM). At each stage of the analysis, the existence of uncertainty in matrix formulation is considered as the presence of disorder in a pseudo-deterministic system capable of providing technically reliable and efficient results. Numerical results are presented using a tool developed by the author in MATLAB ®. This program works with dynamic structures with interval uncertainty. The numerical results are compared with the literature and with a Monte Carlo simulation. Experimental tests were conducted to validate the results of the proposed method.