擬動態試驗技術在衝擊載重的應用

Applications of Pseudodynamic Technique to Impulsive Loading

張順益(Shuenn-Yih Chang) ； 蔡金盛(Chin-Sheng Tsai)

《中國土木水利工程學刊》 22卷2期 (2010/06) Pp. 187-193

https://doi.org/10.6652/JoCICHE.201006_22(2).0006

摘要

本研究率先將擬動態試驗技術應用在求取衝擊載重的動態歷時反應，因此針對所可能遭遇的困難進行探討並提出解決方法。逐步積分時，衝擊載重作用結束之外力不連續將會引起額外的振幅誤差，此誤差的大小幾乎與積分時間步長的大小成正比，因此，在使用逐步積分法求解衝擊載重的振動反應時，為了減少衝擊載重作用結束時，外力不連續所引起的誤差，往往被迫採用很小的積分時間步長來進行逐步積分，此積分時間步長可能遠小於滿足精確度的要求。事實上，此積分時間步長可能為衝擊載重延時的1/10甚或更小。因此如以擬動態試驗來求取衝擊載重的歷時反應時，為了獲得正確的歷時反應，採用傳統的擬動態試驗技術針對動力平衡運動方程式來進行求解時，需要使用較小的積分時間步長，而較小的積分時間步長將會使得下一步的位移增量也會變得較小，而由於位移計的解析度是有一定的限制，當所求得的位移增量小於或接近此範圍時，將會造成正確解被誤差所掩蓋，而得到不正確的試驗結果。另一方面，試驗時間也會大幅拉長。為了克服此困難，本研究將改用動量平衡運動方程式來進行擬動態試驗，此時因外力對時間積分一次而不再有外力不連續的現象，因此可採用較大的積分時間步長，而得到較大的位移增量以克服位移計之解析度的限制，進而得到可靠的試驗結果。

關鍵字

擬動態試驗 ； 時間步長 ； 外力不連續

並列摘要

In step-by-step integration, the load discontinuity at the end of an impulse will lead to an extra amplitude distortion and the amount of this distortion is almost proportional to the size of time step. Hence, in order to reduce the extra amplitude distortion a very small time step, which might be much smaller than that required for accuracy consideration in period, is generally used to obtain the shock response. In fact, it might be less than 1/10 or even smaller of the loading duration. This implies that a very small time step might be needed in a test if the conventional pseudodynamic technique, where the force equation of motion is solved pseudodynamically, is employed to obtain the shock response. Thus, a displacement control error might be experienced in the pseudodynamic testing since a very small time step may lead to a very small displacement increment, which is probably small than the resolution of the displacement transducer, in a time step. Consequently this small displacement increment may be inaccurately imposed on the specimen due to the limited resolution of the displacement transducer. Thus, inaccurate results are obtained. Alternatively, the momentum equation of motion is solved in conducting a pseudodynamic test for obtaining shock responses. Apparently, the difficulty arising from the discontinuity at the end of an impulse will be eliminated due to the use of the time integral of the external force. As a result, a large time step may be allowed to use for the pseudodynamic testing. Consequently, the displacement control problem automatically disappears and thus reliable test results can be achieved.

並列關鍵字

pseudodynamic test ； time step ； load discontinuity