A Survey on Energy Methods for Vibroacoustic Analysis of Random Dynamic Systems and Applications

Engineering can be considered a field of applied physics, as for the design of dynamic systems several aspects such as the strength, parameters of motion, among others, must be estimated for dimensioning, specifications of construction procedures, and operation. In the search for an appropriate model to estimate the dynamic response of a system to a prescribed input, several energy-based methods have been explored over the last decades to address three main issues. Firstly, it is quite rare that a solution for a purely analytical model exists, particularly for complex built-up structures. Secondly, numerical approaches to solve such complex equations of motion of a structure are computationally expensive. Lastly, even if a numerical or analytical solution can be found, there is no warranty that such estimation would be true for an ensemble of nominally identical built-up systems due to uncertainties that are not usually considered by the models. The aim of this work is to present a survey of existing approaches based on equations of energy rather than motion to simplify the computational process and include the effects of uncertainties in the dynamic response, and improvements to such models in regard of other engineering aspects. Additionally, several engineering applications are presented.