Original scientific paper

https://doi.org/10.17559/TV-20160209175450

Influence of the longitudinal displacement on the nonlinear principal parametric resonance of the woodworking bandsaw

Roberto Žigulić orcid.org/0000-0003-3052-6794 ; Department of Mechanical Engineering, Faculty of Engineering Rijeka, University of Rijeka Vukovarska 58, 51000 Rijeka, Croatia
Cristiano Fragassa orcid.org/0000-0003-0046-8810 ; Department of Industrial Engineering, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
Ante Skoblar orcid.org/0000-0003-2230-3398 ; Department of Mechanical Engineering, Faculty of Engineering Rijeka, University of Rijeka Vukovarska 58, 51000 Rijeka, Croatia

Abstract

The transverse vibrations of axially moving Timoshenko beam, as suitable mathematical models for woodworking bandsaws, are investigated. Special attention is paid to the influence of longitudinal displacement effect, as opposed to most models which can be usually encountered in the literature. This influence is introduced through the integro-partial differential equations. The expressions for the mode shapes in the case of hybrid supports with different torsion spring stiffness on the support points are also derived. The influence of mean beam velocity and axial tension on its natural frequencies and mode shapes is also investigated. Based on the nonlinear model, the amplitudes of the steady-state response are calculated for the case of principal parametric resonance. Developed program solution was tested on a number of earlier known examples. Present theoretical considerations, with the help of the program solution, is also used to analyse an example from industrial practice.

Keywords

hybrid boundary conditions; method of multiple scales; numerical examples; principal parametric resonance; travelling Timoshenko beam

Hrčak ID:

174733

URI

https://hrcak.srce.hr/174733

Publication date:

10.2.2017.

Article data in other languages: croatian

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