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Geomechanics and Engineering Volume 1, Number 2, June 2009 , pages 121-142 DOI: https://doi.org/10.12989/gae.2009.1.2.121 |
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Dynamic stiffness based computation of response for framed machine foundations |
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N. Lakshmanan, N. Gopalakrishnan, G.V. Rama Rao and K. Sathish kumar
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| Abstract | ||
| The paper deals with the applications of spectral finite element method to the dynamic analysis of framed foundations supporting high speed machines. Comparative performance of approximate dynamic stiffness methods formulated using static stiffness and lumped or consistent or average mass matrices with the exact spectral finite element for a three dimensional Euler-Bernoulli beam element is presented. The convergence of response computed using mode superposition method with the appropriate dynamic stiffness method as the number of modes increase is illustrated. Frequency proportional discretisation level required for mode superposition and approximate dynamic stiffness methods is outlined. It is reiterated that the results of exact dynamic stiffness method are invariant with reference to the discretisation level. The Eigen-frequencies of the system are evaluated using William-Wittrick algorithm and Sturm number generation in the LDLT decomposition of the real part of the dynamic stiffness matrix, as they cannot be explicitly evaluated. Major | ||
| Key Words | ||
| machine foundations; dynamic stiffness method; spectral finite element; wittrick-william\'s algorithm; sturm number; major | ||
| Address | ||
| N. Lakshmanan: Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai-600113, India N. Gopalakrishnan: Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai-600113, India G.V. Rama Rao: Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai-600113, India K. Sathish kumar: Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai-600113, India | ||