Resumen
In this work, vibration prediction of space large-scale membranes from the energy point of view is investigated. Based on the Green kernel of vibrating membranes, a new analytical representation of energy response of infinite membranes is derived. Averaged energy is used as the main variable so that the response fluctuation can be smoothed. Then membranes of various shapes can be taken into account by introducing the mean free path into the formulation to describe travel distances of energy waves. The energy response of finite membranes is obtained with the superposition of energy waves subsequently. Considering uncertainties usually becomes significant in large-scale structures, the formulation expressed with random variables is obtained for membranes with uncertain properties. The mathematical expectation and variance of energy response are derived subsequently. And the confidence interval of random response is obtained. Finally, numerical simulations are performed to validate the proposed formulations and characteristics of the random energy responses are analyzed by taking a space large-scale membrane structure as a model. The developed formulations make the analysis of membranes with uncertainties more convenient than Finite Element Method (FEM) since they are expressed in analytical forms. Compared with existing formulations of energy flow derived from deterministic travel distances of waves that only apply to regular shapes of structures, the proposed formulations are suitable for membranes of various shapes. This work provides an alternative analytical approach to vibration prediction for space large-scale membranes with uncertainties. And the approach is thought helpful for the vibration analysis of other two-dimensional structures.