An efficient and robust integration technique for applied random vibration analysis

The mode-based finite element formulation of the equations of motion is usually adopted for linear random vibration analysis (RVA). In general, the RVA of large systems requires a large number of numerical integrations which is very time-consuming for a reasonable level of desired accuracy. Moreover, conventional numerical integration methods may fail to converge when the integrands are highly oscillatory due to slow propagation velocities. In this paper, a robust general-purpose RVA integration technique which can overcome these drawbacks is presented. Multi-point base and nodal excitations including wave passage effect and frequency-independent spatial correlation can be taken into account in the analysis. The proposed technique is based on the closed-form solutions for polynomial-type power spectral density functions and has been verified to be efficient and accurate for many engineering problems. This paper describes the implementation details, presents two examples taken from engineering applications and demonstrates the dramatic time-saving in the computation compared to numerical integration solutions. Response statistics, such as standard deviation of structural responses, are computed and displayed over the entire structures for these examples.