Dynamic Analysis of Beams with Interval Parameters

Abstract

The present study deals with the transient interval analysis of a shallow beam having uncertainty in structural parameters viz. mass density and applied load. It is quite difficult to obtain information regarding the exact values of these parameters in several practical situations. Use of precise (deterministic) values of structural parameters in such a situation leads to erroneous results as the mathematical model built using deterministic structural parameters does not account for the uncertainty present in the system. In the present work, uncertainty present in the system is represented by interval parameters. In the research work carried out in the past quarter century, several methods were developed to model structural response of uncertain structural systems subjected to static loads under conditions of linear elasticity. The partial differential equations of motion of a Euler-Bernoulli beam are solved using Finite difference and finite element methods under conditions of linear elasticity. The resulting interval equations are solved using search and direct methods. Further, direct optimization approach is used to compute the bounds of displacement. The applicability and effectiveness of presented methods is demonstrated by solving example problems.

Keywords

• Euler-Bernoulli beam
• transient vibration
• interval algebra
• direct method
• optimization
• search method