Response of nuclear structural systems to transient and random excitations, using both deterministic and probabilistic methods☆

Abstract The finite element is commonly used for the static analysis of reactor components and the same ideas can be applied to the dynamic analysis. The formation of various damping matrices for both internal and external damping is discussed. For the most part only the linearized form of the equations of motion is considered giving M x + C x + (K + iG)x = F(t) . The type of solution adopted depends upon both the force input and the required response. For a short period transient input usually only the initial response is required which is best found from a step-by-step integration. A method involving a Taylor series and curve fitting over a series of steps is developed and applied to the solution of a beam subject to a pressure transient. For a periodic force input the steady state response is needed requiring the determination of the damped eigenvectors. An efficient algorithm, using the undamped vectors, is given and the response to an arbitrary force input developed. This method is applied to the previous example and the two solutions are compared illustrating the advantages and disadvantages of each method. For random excitation methods of presenting information are discussed standard results for the stationary problem are presented in terms of the first part of the paper. As an example the spectral density of the response due to random imposed movements is given illustrated by a series of heat exchange tubes excited by random forces. The response due to a non-stationary force input such as an earthquake is discussed. The step-by-step method of analysis is used to predict the probability density function of the response of a simple system at any time under such a non-stationary input. Possible modes of failure with reference to reactor components are discussed and indications of how the proceeding theory can be applied to predicting failures are given.