Abstract
AbstractThe free vibration and the forced dynamic responses of a uniform cantilever Timoshenko beam carrying any number of concentrated masses, translational and rotational springs and subjected to various external loadings are studied by means of the analytical‐and‐numerical‐combined method (ANCM), where the locations and the magnitudes of the masses, springs and loadings are arbitrary. First of all, the (exact) closed‐form solutions for the natural frequencies and the normal mode shapes of the ‘unconstrained’ Timoshenko beam (without carrying any concentrated elements) are determined; then the eigenvalue equation for free vibration analysis and the equation of motion for forced vibration analysis of the ‘constrained’ Timoshenko beam (carrying the prescribed concentrated elements) are derived analytically by applying the expansion theorem and the mode superposition methodology; finally the approximate natural frequencies and mode shapes of the ‘constrained’ Timoshenko beam and its dynamic responses due to external excitations are calculated numerically. It is found that the ANCM presented in the paper has the advantages of both the pure analytical method (to be able to save computing time) and the pure numerical method (to be able to solve various practical problems).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Communications in Numerical Methods in Engineering
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.