Frequency domain analysis offers a very efficient method for the fatigue durability assessment of structures subjected to vibration loading. It also allows engineers to gain valuable insight into system behavior and characteristics that are not easily recognized in the time domain. With some reasonable assumptions, most importantly linearity and steady state behavior, the response of a structure in many engineering applications can be simply evaluated through the “scaling” of the input signal by the Frequency Response Functions (FRFs). In cases where the input is random or stochastic in nature additional assumptions are needed to assess the behavior of the system. Usually such cases assume a stationary and ergodic input signal with a zero mean Gaussian distribution. When making such assumptions the system is still characterized by its FRFs. However, since the input signal is random it can be best described by its Power Spectral Density (PSD). Furthermore, the system response (characterized by the stress tensor) can be evaluated by “scaling” the PSD of the input signal(s) by the magnitude squared of the stress FRFs. The linearity assumption also allows the evaluation of a system response due to multiple inputs through superposition principles.
When using stress based fatigue (to assess the durability of a component or a structure) there are several damage evaluation methodologies that can be used. Traditionally, for time domain analysis the von Mises equivalent stress had been the methodology of choice. More recently critical plane search methods have gained popularity and have shown much better correlation with laboratory experiments and field failures, especially under multi-axial and non-proportional loading. Some of these methods have found their way into frequency domain analysis. This paper highlights the application of critical plane methods for the multi-axial fatigue assessment of engineering structures that are subjected to non-deterministic random vibration. A case study is presented to illustrate the process and shows how the proposed method works.