An analytic methodology was developed to predict the fatigue life of a structure experiencing stationary, Gaussian random vibration excitation. This method allows the estimation of fatigue life using a frequency domain method, where only the input power spectral density and damping factor are required. The methodology uses linear elastic fracture mechanics for fatigue crack propagation and accounts for the frequency shifting that occurs due to fatigue crack evolution. Good results have been obtained comparing the analytic model to both finite element analysis (FEA) and experimental results, for mild‐steel cantilever beams.

A review of past and recent developments in multiaxial excitation of linear and nonlinear structures is presented. The objective is to review some of the basic approaches used in the analytical and experimental methods for kinematic and dynamic analysis of flexible mechanical systems, and to identify future directions in this research area. In addition, comparison between uniaxial and multiaxial excitations and their impact on a structure’s life-cycles is provided. The importance of understanding failure mechanisms in complex structures has led to the development of a vast range of theoretical, numerical, and experimental techniques to address complex dynamical effects. Therefore, it is imperative to identify the failure mechanisms of structures through experimental and virtual failure assessment based on correctly identified dynamic loads. For that reason, techniques for mapping the dynamic loads to fatigue were provided. Future research areas in structural dynamics due to multiaxial excitation are identified as (i) effect of dynamic couplings, (ii) modal interaction, (iii) modal identification and experimental methods for flexible structures, and (iv) computational models for large deformation in response to multiaxial excitation.

Multiaxial and uniaxial vibration experiments were conducted in order to study the differences in failure modes and fatigue life for the two types of excitation. An electrodynamic (ED) shaker capable of controlled vibration in six degrees of freedom (DOF) was employed for the experiments. The test specimen consisted of six large inductors insertion mounted on a printed wiring board (PWB). Average damage accumulation rate (DAR) in the inductor leads was measured for random excitations in-plane, out-of-plane, and both directions simultaneously. Under simultaneous multiaxial excitation, the average DAR was found to be 2.2 times greater than the sum of the in-plane and out-of-plane DARs. The conclusion was that multiple-step sequential uniaxial testing may significantly overestimate the durability of large/heavy structures with high center of mass in a multiaxial dynamic environment. Additionally, a test method utilizing uniaxial vibration along a direction other than the principal directions of the structure was examined. This method was found to have significant limitations, but showed better agreement with simultaneous multiaxial vibration experiments.

This paper presents a set of experimental data comparing repetitive shock (RS) vibration, single-axis electrodynamic (ED) vibration, and multi-axis ED vibration. It was found that multi-axis testing is more severe than single-axis testing at the same level. In addition, weaknesses were found in the RS system at low frequency. Smoothing of the data or poor line resolution was also shown to change the overall severity of a test. A poor correlation was shown between the power spectral density (PSD) and the rate of natural frequency change (RFC) over a wide frequency shift. The change in natural frequency caused the initial PSD to be an ineffective indicator of test severity. Quantification of the severity of the test profile can be accomplished through characterization of the RFC.

During fatigue damage accumulation, cracks propagate through the material leading to catastrophic failure. As the cracks propagate, the natural frequency lowers, leading to a changing stress state. A new method has been developed where the damage accumulation rate is computed in the frequency domain using Linear Elastic Fracture Mechanics (LEFM), stress intensity, and the natural frequency. A finite element model was developed to predict the stress intensity and natural frequency during damage accumulation. Validation of the LEFM technique was done through comparison to experimental data. Reasonably good correlations between the FEM and the analytic model were achieved for the stress intensity and natural frequency.