### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 5aPAa14. Axisymmetric free vibrations of finite poroelastic bone.

**K. Natarajan
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H. S. Paul
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*Dept. of Math., Indian Inst. of Technol., Madras 600 036, India
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Axisymmetric free vibrations of poroelastic finite cylindrical bone, which
behaves as transversely isotropic material, are investigated. Both curved and
plane end surfaces of the solid cylinder are free from mechanical stresses and
average fluid stresses. Two sets of basic solutions are derived to the equations
of motion and poroelastic equation (due to Biot's theory) by applying variable
separable technique. From the shear stress-free boundary conditions, eigenvalues
for wave numbers are found. Using the basic solutions and eigen wave numbers,
solutions to the mechanical displacements and the fluid velocities are developed
in series form. The series form solutions satisfy the shear stress-free boundary
conditions exactly term by term. Remaining boundary conditions are satisfied by
an orthogonalization procedure using trigonometric functions and first kind
Bessel functions. Natural frequencies of vibrations are calculated for human
bone by varying the number of terms in the series that are tabulated. The series
solutions converge rapidly within few terms. For various half-length to radius
ratios of the finite cylinder, natural frequencies are computed and presented
graphically. [One of the authors (K.N.) acknowledges CSIR, New Delhi, India for
the financial support.]