軌道導波的特性研究的數值模擬

Abstract

鐵軌是具有工字型斷面的線性結構，鐵軌導波被侷限沿著軌道的傳遞，擁有多模態及頻散的波傳特性。本研究採用三維有限元素套裝軟體及雙維有限元素法計算JIS 60鐵軌導波的頻散曲線。雙維有限元素法又稱為半解析有限元素法，採用複變指數函數描述導波波傳，波導斷面之有限元素位移則採用一般的內插函數，元素多寡會影響高頻範圍的頻散曲線準確度。頻散曲線是個別模態之波長與頻率的函數，上述兩種方法獲得的軌道導波頻散曲線非常吻合。 簡支撐及週期支撐鐵軌的暫態模擬響應，經小波轉換映射成時頻譜圖，與波包延遲時間解析解比較，發現脈衝訊號可以激發特定的對稱及反對稱導波。LS-DYNA模擬音頻脈衝激振鐵軌導波都會出現低頻暫態響應，採用套裝軟體ANSYS之直接積分法則不會出現低頻響應。模擬鐵軌道床基板的週期支撐會使導波響應在區間發生多次反射

Rail is a linear structure having I-shaped cross section. Guided waves in a rail are characterized by multimodal and frequency dispersive wave propagation since energy is confined within the waveguide. In this study, commercial three-dimensional finite-element (FE) code and bi-dimensional FE approach are used to determine the dispersion curves of guided waves in JIS 60 rails. The latter is also called the semi-analytic FE method. The formulation uses complex exponential functions to describe the wave propagation in the waveguide and conventional interpolation functions for displacement in finite elements across the cross-section. Accuracy of dispersion curves at high frequencies is influenced by the number of finite elements. The dispersion curve of individual guided wave mode is a function of wave length and frequency. Numerical results obtained from both methods are in very good agreement. Transient responses simulated for simply supported and periodically supported rails have been mapped into time-frequency spectrograms by wavelet transform. The spectrograms are compared with analytical delay times of wave packets. Several specific symmetric and anti-symmetric modes can be actuated in impulse excitement. Unexpected low-frequency signals accompanying the tone-burst induced transient responses are discovered in simulation by LS-DYNA. But they do not appear using ANSYS direct integration method. Multiple reflected guided wave responses occur between adjacent periodical supports, which emulate base plate supports for rails.