Nonlinear and Time-Varying Dynamics of High-Dimensional Models of a Translating Beam With a Stationary Load Subsystem

Abstract

Nonlinear vibration and dynamic stability analyses of distributed structural systems have often been conducted for their low-dimensional spatially-discretized models, and the results obtained from the low-dimensional models may not accurately represent the behavior of the distributed systems. In this work the incremental harmonic balance method is used for the first time to handle a variety of problems for high-dimensional models of distributed structural systems, including determination of linear and nonlinear frequency responses, optimization of system parameters, determination of simple parametric instability region boundaries, analysis of parametrically-excited nonlinear systems, and determination of linear and nonlinear frequency responses under combined parametric and forcing excitations. The methodology is demonstrated on a translating tensioned beam with a stationary load subsystem and some related systems. With sufficient numbers of included trial functions and harmonic terms, convergent and accurate results are obtained in all the cases. The effect of nonlinearities due to the vibration-dependent friction force between the translating beam and the stationary load subsystem, which results from non-proportionarity of the load parameters, decreases as the number of included trial functions increases. A low-dimensional spatially-discretized model of the nonlinear distributed system can yield quantitatively and qualitatively inaccurate predictions. The methodology can be applied to other nonlinear and/or time-varying distributed structural systems.