Structural Dynamics in Uncertain Environments

The uncertainties or randomness of the material properties of structural components are of serious concern to engineers. Structural analysis is usually done by taking into account only deterministic or crisp parameters, however, building materials can have aspects of uncertainty. The causes of this uncertainty or randomness can be due to defects in atomic configurations, measurement errors, environmental conditions, and other factors. The influence of uncertainties are more profound for nanoscale and micro structures due to their small-scale effects. Several nanoscale experiments and molecular dynamics studies also support the claim of possible attachment of randomness for various parameters. With regard to these concerns, it is necessary to propose new models that specifically integrate and effectively overcome imprecisely defined parameters of the system. In this book, uncertainty modeling of nanobeams, microbeam, and FG beams is presented using non-probabilistic approaches which include interval and fuzzy concepts. Vibration and stability analysis of the beams are conducted using different analytical, semi-analytical, and numerical methods for finding exact and/or approximate solutions of governing equations arising in uncertain environments. In this context, this book addresses structural uncertainties and investigates the dynamic behavior of micro, nano, and FG beams. Examines the concepts of fuzzy uncertain environments in structural dynamics. Presents comprehensive analysis of propagation of uncertainty in vibration and buckling analyses. Explains efficient mathematical methods to handle uncertainties in the governing equations.