On a Bone-Vibration:The first report

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概要

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• This experiment is one step to clarify dynamic mechanical properties of bones, especially femurs.Material: four dry femurs.We designed a method that a mechanical impulse was exerted on a femoral head along the functional axis of femur with a pendulum. Then a femur, whose condyle is fixed and head is free, is placed horizontally.When a mechanical impulse was exerted on a femur in the above position, a bone vibration was developed. This vibration was analyzed, and was similar to a summation of a high- and a low-frequency component. Therefore, we picked out separately the high- and the low-frequency component with a filter circuit. There were vibrations with logarithmic decrement. The vibrations had a natural frequency themselves—the high was about 500cps and the low was about 100cps.Now, a solution of a sort of a second-order differential equation Md2x/dt2+Sdx/dt+Kx=F(t)is also a damping vibration with logarithmic decrement. Then, we added two second-order differential equations with two different constant coefficients, using a desk-top ANALOG computor. Using this solution yielded a similar wave to a bone vibration.Therefore, we think now that a bone vibration under the above conditions may be expressed as a summation of two ordinary second-order differential equations.Furthermore, analysing many more bone-vibrations, we will compare the difference of the damping ratio and the natural frequency of vibration between many bones.

• 西日本整形・災害外科学会の論文

著者

• 楢林 好隆

  長崎大学整形外科

• 森貞 近見

  長崎大学整形外科

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