Exact free vibration of multi-step Timoshenko beam system with several attachments

摘要: Abstract This paper deals with the analysis of natural frequencies, mode shapes an axially loaded multi-step Timoshenko beam combined system carrying several attachments. The influence design and proposed sub-system non-dimensional parameters on characteristics are major part this investigation. effect material properties, rotary inertia shear deformation for each span included. end masses elastically supported against rotation translation at offset point from attachment. A having two degrees freedom is located ends any intermediate stations acts as a support and/or suspension. boundary conditions ordinary differential equation governing lateral deflections slope due to bending including force term, sub-system, have been formulated. Exact global coefficient matrices modal shape discrete derived. Based these formulae, detailed parametric studies carried out. applied mathematical model valid wide range applications especially in mechanical, naval structural engineering fields.