THE FORCED VIBRATION AND BOUNDARY CONTROL OF PRETWISTED TIMOSHENKO BEAMS WITH GENERAL TIME DEPENDENT ELASTIC BOUNDARY CONDITIONS

✍ Scribed by S.M. LIN; S.Y. LEE

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 226 KB
• Volume: 254
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2001.4084

✦ Synopsis

The governing di!erential equations and the general time-dependent elastic boundary conditions for the coupled bending}bending forced vibration of a pretwisted non-uniform Timoshenko beam are derived by Hamilton's principle. By introducing a general change of dependent variable with shifting functions, the original system is transformed into a system composed of four non-homogeneous governing di!erential equations and eight homogeneous boundary conditions. The transformed system is proved to be self-adjoint. Consequently, the method of separation of variables can be used to solve the transformed problem. The physical meanings of these shifting functions are explored. The orthogonality condition for the eigenfunctions of a pretwisted non-uniform beam with elastic boundary conditions is also derived. The relation between the shifting functions and the sti!ness matrix is derived. The boundary control of a pretwist Timoshenko beam is studied. The e!ects of the total pretwist angle, the position of loading and the boundary spring constants on the energy required to control the performance of a pretwisted beam are investigated.