K. Natarajan
H. S. Paul
Dept. of Math., Indian Inst. of Technol., Madras 600 036, India
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.]