Free vibration analyses of curved beams and rings carrying various concentrated elements with shear deformation and rotary inertia effects considered by using FEM

• Main Authors: Yung-Chuan Chen, 陳勇全
• Other Authors: Jong-Shyong Wu
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/28975845367387337191

碩士 === 國立成功大學 === 系統及船舶機電工程學系碩博士班 === 95 === The purpose of this thesis is to determine the natural frequencies and mode shapes of the Timoshenko curved beams (or arcs) and rings carrying various concentrated elements in various boundary conditions by using the finite element method (FEM). The above-mentioned concentrated elements include lumped masses, translational springs, rotational (bending) springs and torsional springs. First of all, a uniform continuous curved beam (or ring) is replaced by many straight beam elements and any two adjacent straight beam elements is connected by a node. Next, the aforesaid concentrated elements are attached to each of the nodes, so that the mathematical model for a curved beam or ring carrying any number of lumped masses, translational springs, rotational springs and or torsional springs with various supporting conditions can easily be obtained. Based on the last mathematical model, the natural frequencies and mode shapes of a ring or a curved beam with any cross-sections, subtended angles and radii of curvature carrying various concentrated elements are determined. The influence of shear deformation, rotary inertia and slenderness ratio on the free vibration characteristics of the curved beams and rings are studied.