The dynamic analysis of nonuniformly pretwisted Timoshenko beams with elastic boundary conditions

✍ Scribed by Shueei-Muh Lin; Wen-Rong Wang; Sen-Yung Lee

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 205 KB
• Volume: 43
• Category: Article
• ISSN: 0020-7403
• DOI: 10.1016/s0020-7403(01)00018-2

✦ Synopsis

The coupled governing di erential equations and the general elastic boundary conditions for the coupled bending-bending forced vibration of a nonuniform pretwisted Timoshenko beam are derived by Hamilton's principle. The closed-form static solution for the general system is obtained. The relation between the static solution and the ÿeld transfer matrix is derived. Further, a simple and accurate modiÿed transfer matrix method for studying the dynamic behavior of a Timoshenko beam with arbitrary pretwist is presented. The relation between the steady solution and the frequency equation is revealed. The systems of Rayleigh and Bernoulli-Euler beams can be easily examined by taking the corresponding limiting procedures. The results are compared with those in the literature. Finally, the e ects of the shear deformation, the rotary inertia, the ratio of bending rigidities, and the pretwist angle on the natural frequencies are investigated.