クーロン摩擦を伴う1自由度強制振動に関する検討

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Analysis of the ocsillating system with combined Coulomb and viscous friction shown in Fig. 1 has already been studied by Dr. Den Hartog, but this paper introduces some new results of calculaiton on the responses from transient to steady state by the method of connecting two linear equations alternately, with a computer. Eq. (1) is the equation of motion, and Eq. (2), Eq. (3) and Eq. (4) are the general solutions of displacement. Eq. (6), the equation of velocity, is obtained by differentiating Eq. (2), whereas Eq. (5) is derived from the condition for balance of forces, and it is necessary for knowing the time at which a mass sets up motion. Integral constants in Eq. (2) and Eq. (6) can be decided by giving initial conditions, and a certain part of the motion as shown in Fig. 2 or Fig. 3 can be culculated precisely. But, whenever the sign of velocity is changed, it is necessary that the sign of Coulomb friction is inverted, and the decision of the integral constants must make fresh start, then various motions can be computed by considering Eq. (5). Consequently, the transinent responses of some sorts of motions are shown in Fig. 7, Fig. 8, Fig. 9 and Fig. 10, and the new type motions, which were able to be obtained from this numerical analysis for the first time, are shown in Fig. 11 and Fig. 12. The motions in Fig. 11 and Fig. 12 are irregular stop motion and unsymmetrical motion, respectively, and differ from already well known motions essentially, but are not existent in case of large viscous damping factor. Fig. 6 is a distribution chart showing the existence region of all kinds of motions including the new type motions, and Fig. 14 is an amplitude diagram of displacement without viscous damping, in which insufficient region is complemented by the numerical computations. Finally the new type motions were examined with an analog computer, and the results are shown in Fig. 16 and Fig. 17.
社団法人日本音響学会の論文
1974-07-01

クーロン摩擦を伴う1自由度強制振動に関する検討

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