A framework for the analysis of vibrations of structures with uncertain attachments

Attachments affect the dynamic response of an assembled structure. When engineers are modelling structures, small attachments will often not be included in the “bare” model, especially in the initial design stages. The location of these attachments might be poorly known, yet they affect the response of the structure. This paper considers how attachments jointed to the structure at uncertain points, can be included in the dynamic model of a structure. Two approaches are proposed. In the time domain, a combination of component mode synthesis, characteristic constraint modes and modal analysis gives a computationally efficient basis for subsequent analysis using, for example, Monte Carlo simulation. The frequency domain approach is based on assembly of frequency response functions of bare structure and attachment. Numerical examples of a beam and a plate with a point mass added at an uncertain location are considered and predictions compared with experiment results

Wave propagation in one-dimensional waveguides with slowly varying random spatially correlated variability

This paper investigates structural wave propagation in waveguides with randomly varying material and geometrical properties along the axis of propagation. More specifically, it is assumed that the properties vary slowly enough such that there is no or negligible backscattering due to any changes in the propagation medium. This variability plays a significant role in the so called mid-frequency region for dynamics and vibration, but wave-based methods are typically only applicable to homogeneous and uniform waveguides. The WKB approximation is used to find a suitable generalization of the wave solutions for finite waveguides undergoing longitudinal and flexural motion. An alternative wave formulation approximation with piecewise constant properties is also derived and included, so that the internal reflections are taken into account, but this requires a discretization of the waveguide. Moreover, a Fourier like series, the Karhunen–Loeve expansion, is used to represent homogeneous and spatially correlated randomness and subsequently the wave propagation approach allows the statistics of the natural frequencies and the forced response to be derived. Experimental validation is presented using a cantilever beam whose mass per unit length is randomized by adding small discrete masses to an otherwise uniform beam. It is shown how the correlation length of the random material properties affects the natural frequency statistics and comparison with the predictions using the WKB approach is given

Nationally Coordinated Program of Highway Research, Development and Technology: Annual Progress Report, Executive Summary, Fiscal Year 1989

Nationally Coordinated Program of Highway Research, Development and Technology: Annual Progress Report, Executive Summary, Fiscal Year 198