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＜紀要論文＞
走行荷重に因る橋桁の強制振動論
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| 概要 | The purpose of the present paper is to investigate the forced vibration problem of railway bridges. It is well known that a running locomotive produces in a bridge a greater deflection and greater str...esses than the same load acting statically. Such an impact effect of live loads on bridges is of great practical importance and many elasticians have investigated the problem both from the standpoint of theory and of experiment. But for this subject almost no satisfactory mathematical theories have so far been obtained. Now, there are various causes producing vibratory deflections m a bridge of which the following will be considered in our paper: (1) Deadload effect of the locomotive; (2) Live-load effect of the running locomotive; (3) Impact effect of the balance-weights of the locomotive driving wheels, i.e. the so-called travelling hammer blow effect. Assuming that a single load (locomotive) is moving along a simple beam (bridge) with a uniform velocity, we obtain the fundamental equations (III·5)' for this problem by the aid of Lagrangian equations of motion. These are the most conclusive equations for this subject, since we can . show that the well-known equations of Stokes, Timoshenko and Inglis are respectively derived from (III-5)' as the special cases. By neglecting small quantities included in (III·5)', we get the simplified fundamental equation (IV･5) containing a large parameter 𝝀 Accordingly, by means of the theory of asymptotic solution of a linear differential equation containing a parameter, we get, under the initial conditions (IV･8), · the approximate solutions (V･4) and (VI･2) which represent the central deflection of the bridge as the functions of the position on it of the· loco motive for undamped and damped vibrations respectively. Using the Fourier's expansions of the Jacobian elliptic functions, we can respectively, write these solutions in the forms (V･29) and (VI·9) with sufficient accuracy. Of course, the former is a special case of the latter. Thus, by means of the ' formula (VI·9), the central deflection η can be expressed as the sum of elementary periodic functions of the position of the locomotive,if the bridge constants (mass M, span 𝑙, unloaded natural frequency n_0, and logarithmic decrement h/n_0) and the locomotive constants (mass m, circumference of driving wheels s, travelling velocity υ, maximum value of hammer blow B, and phase constant of hammer blowε) are known. According to Inglis' work "A mathematical treatise on vibrations in railway bridges", the experiment done for the Newark Dyke Bridge on which the locomotive (type 0-8-0) runs with various constant speeds gives the deflection-curves as shown by Pl. III. In this practical case the bridge and the locomotive constants are all known. Hence, using these values and our formula (VI-9), we obtain the deflection formula (VII-10) for this bridge and then we get the theoretical deflection-curves as shown by Pl. V. When we compare Pl. V with Pl. III, it is obvious that the coincidence between the theoretical and experimental deflection-curves is very satisfactory over the whole range of speeds. Thus, our theory seems to give a better explanation for the forced vibration of railway bridges than any other theories hitherto proposed. In the final part of this paper, we show with sufficient accuracy that the dynamical deflection can be put in the form (VIII·4), where the amplitudes A's and B's given by (VIII·5) are plotted in Pl. IV. Furthermore, it is convenient to use the amplitude-velcocity curve, as shown by Pl. VI, for determining the so-called critical speeds and for estimating the value of the greatest impact effect.続きを見る |
| 目次 | 表紙 目次 發刊の辭[三瀨幸三郎(彈性工學研究所長)] 走行荷重に因る橋桁の強制振動論 Ⅰ 緒言 II 各種理論の概観 III 基礎方程式 V 橋桁の非減衰強制振動に對する解法 VI 橋桁の減衰強制振動に對する解法 VII 理論と實験との比較 VIII 動力學的撓度 IX 結語 Summary続きを見る |
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| 登録日 | 2023.10.06 |
| 更新日 | 2023.12.07 |