Coupled Thermo-Elastic Large Amplitude Nonlinear Vibrations of Timoshenko Beams Subjected to Thermal and Mechanical Loadings
by
Emil Manoach
Institute of Mechanics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
Coauthors: M. Ferman (Parks College, Saint Louis, University, St. Louis, MO 63103, USA)

Coupled, Thermo-Elastic Large Amplitude Nonlinear Vibrations of Timoshenko Beams Subjected to Thermal and Mechanical Loading by E. Manoach1 and M. Ferman2 1Institute of Mechanics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria 2 Parks College of Engineering and Aviation, Saint Louis University, St. Louis, MO, USA The coupled thermoelastic problems (when the stress/strain state has to be determined simultaneously with the determination of the temperature field) are very important in many branches of the modern engineering design. Prime examples are in the aircraft field, considering the jet flux from the exhaust striking structure near the nozzles. In the space flight area, the launch and re-entry phases subject the structures to severe loadings combining vibratory and acoustic loads with high temperature, much of which is transient. There are applications of severe loads occurring in nuclear applications as well in manufacturing and foundry processes. Thermal loads may significantly change the dynamic behaviour of the structures because they introduce stresses due to thermal expansion and can cause thermal buckling. If the applied loads (thermal and mechanical) lead to vibrations with large amplitudes the problem becomes more complicated.

The objective of this study is to show that we have developed numerical procedures for uncoupled and coupled thermoelastic vibrations of moderately thick beams subjected to dynamic thermal and/or mechanical loadings. The applied loads lead to large amplitude vibrations, i.e., geometrical non-linearity of structures must be taken into account. The thermal and mechanical loads are applied on the upper surface of the beam. The lower surface and the ends of the beam are accepted to be heat-isolated. The stress relation reflects the new coupling, which we have found to be significant.

An iterative procedure based on the pseudo-load mode superposition method (PLMSM) and the finite difference method (FDM) is developed. This approach allows the change of the basis from the nodal spatial displacements to the modal generalized displacement by using a set of vectors based on the “assumed linear system”. The nonlinear terms due to large deflections and temperature loads are grouped together with the mechanical loads thus forming the pseudo-load force vector. The coupled ordinary differential equations for the generalized displacement are solved applying an iterative procedure for determining the non-linear pseudo-load force vector.

The equation describing the heat propagation (considering the influence of the mechanical field) is discretized by FDM and then an implicit algorithm based on backward differentiation formula method (Gear’s method) is applied for its solution.

The obtained numerical results clarify the influence of the coupled terms in the governing equations for large amplitude vibrations of the beams subjected to intensive thermal and mechanical loads. It is shown that considering the coupled terms is more essential when geometrically nonlinear vibrations are taken into account.

The influence of the temperature loading for beams subjected to harmonic mechanical loading with frequencies close to the frequencies of the free vibrations is investigated in detail. The case of beams subjected to periodic thermal loading is also studied. Examples are shown to illustrate the thermo-elastic coupling effect, as compounded by rapidly varying and oscillating temperature fields.

A bulk of this work was conducted under a USA National Academy of Sciences, NSF/ COBASE Grant, Fall 2003.

Date received: December 23, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakt-19.