Stochastic dynamics of veering modes in a symmetric coupled system

ABSTRACT

A conceptual model of a coupled symmetric system consisting of three beams coupled using a common base beam was developed. The purpose was to analyse the behaviour of close modes of the repeated system. A study on variation in the dynamic behaviour due to parametric uncertainty was carried out experimentally and theoretically. Experimentally the mass of the system was perturbed and the frequency response function (FRF) was analysed. Theoretically the mean and standard deviation of the frequency response function was determined using stochastic finite element (SFEM). Stochastic finite element analysis was carried out considering uncertainty in stiffness and the system response. Karhunen–Loeve (KL) expansion and polynomial chaos (PC) were carried out for Young's modulus uncertainty and the response uncertainty respectively. Optimal number of KL terms and PC order were determined. Using the optimal SFEM model, the influence of uncertainty in the individual subsystem on the dynamic response was determined. The results from the study indicated that a relaxed manufacturing tolerance could reduce the possibility of shock amplification. The frequency range over which high system response was observed in the FRF increased with lower tolerance, however, the maximum amplitude in the mean response was reduced.

KEYWORDS:

• SFEM
• symmetric system
• KL expansion
• polynomial chaos

Acknowledgements

Kiran Vijayan gratefully acknowledges the support and funding received for the work from SERB and NRB.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Naval Research Board [NRB-470/Mar/2020-21] and Science and Engineering Research Board [ECR/2016/001531].