THREE APPROACHES FOR THE AXIAL VIBRATIONS OF BARS ON MODIFIED WINKLER SOIL WITH NONCLASSICAL BOUNDARY CONDITIONS

✍ Scribed by M.A. DE ROSA; M.J. MAURIZI

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 140 KB
• Volume: 231
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2729

✦ Synopsis

In this paper three approximate numerical approaches are compared, for the title problem. The "rst method is a variational one, and it is known as an optimized Rayleigh or Rayleigh}Schmidt method. As such, it belongs to the so-called &&energy approaches''. On the contrary, the second method solves the di!erential equation of motion according to a recent quadrature procedure, and is known as the &&di!erential quadrature method'', or DQM. The last approach reduces the structure to an holonomic n-degree-of-freedom mechanism, the energies of which are easily written, and the resulting equations of motion can be deduced by using the Lagrange equations for discrete systems.