Vibrations of Hollow Elastic Bodies by Magomed F. Mekhtiev

Author:Magomed F. Mekhtiev
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(2.5.19)

Here T is the density of kinetic energy and U is the density of the strain energy given, respectively, by

(2.5.20)

Let be given at the following boundary conditions

(2.5.21)

Since homogeneous solutions satisfy the equations of motion (2.1.1) and the homogeneous boundary conditions (2.3.1), taking into account (2.5.21) and the variational principle stated above we obtain

(2.5.22)

The constants may be determined by substituting (2.5.9) into (2.5.22) and considering the variations of to be independent. On doing so, we obtain the infinite system of equations

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