敲擊回音法為目前廣泛應用於土木工程領域，用以檢測混凝土結構內部損傷位置、裂縫範圍、評估完整性等之非破壞檢測設備。然而對於材料性質的檢測，常見是在試驗室中完成，根據ASTM 試驗規範，試體體積必須十分細長且試驗結果不易獲得。

本研究以共振理論、試驗及數值模擬三者為核心，針對實心圓柱與平板進行分析。首先，對於橫截面採不同材料性質以guided-wave 法進行解析，發現第二至六共振頻率與基礎頻率的比例僅與卜松比有關，藉由線性回歸得到一適合檢測各式材料橫截面完整性之公式。次者，由細長桿件一維縱向波傳理論所得之基礎共振頻率，結合與橫截面基礎共振頻率二者關係，提出一對桿件縱向及橫向各進行一次敲擊，即可檢測材料卜松比與彈性模數之計算公式。此外，對於標準圓柱方面，分析Love 彈性波理論後發現，縱向基礎頻率與第二頻率的比例亦僅與卜松比有關，據此發展出一套只需對桿件縱向一次敲擊即能檢測標準圓柱材料性質的公式。最後，解析Lamb wave 方程式過程中同樣地發現第一與第二頻率的比例僅與卜松比相關，進而推導出對混凝土平板表面一次敲擊即可測定板材料性質之公式。

藉由試驗結果以及2D、3D 模態與暫態分析之數值模擬的印證，證明敲擊回音法設備可應用於不僅可以檢測混凝土，其他包括石膏、金屬、合金金屬、塑膠等圓柱相關材料均可測定其橫截面完整性以與材料性質。對於混凝土平板的材料性質亦可藉由簡單的敲擊即可獲得。相較於ASTM 規範的操作程序，本研究的檢測過程是相對精簡與可靠，可於方便工地現場及時進行材料性質的測定。

The impact-echo method is a nondestructive technique and has been widely used in civil engineering to determine the location of the internal defect, extent of flaws, and the integrity of concrete structures, etc. However, the procedures of evaluation of material properties are always finished in laboratory. According to the manual of American Society for Testing and Materials (ASTM), the dimension of specimen must be very slender and test results are hard to attain.

Base on resonant theories, experiments, and numerical simulation, this research focuses on solid cylinder rod and concrete plate. First, the guided-wave method is used to analyze cross-sectional resonant frequency with different material properties, and frequency coefficients for the 2nd to 6th frequencies only relate with Poisson’s ratio. The curve-fitting technique is used to obtain the best fit equations to determine the integrity of a cross-section. The second, according to the longitudinal fundamental frequency from one-dimensional wave equation and cross-sectional fundamental frequency from guided-wave method of slender rod, a new equation for evaluation Poisson’s ratio and modulus of elasticity is led out. The experimental procedures only need one impact respectively on the center of one end and the middle surface of rod. Furthermore, the elastic wave theory for standard cylinder given by Love is solved and the ratio of the 2nd to 1st longitudinal frequency also only concerns with Poisson’s ratio. The equations are developed to determine material properties and the test process is to impact once with one end of cylinder. Finally, The Lamb wave equations are analyzed and similarly the ratio of the 2nd to 1st longitudinal frequency only corresponds with Poisson’s ratio. New equations for evaluation of material properties of concrete plate are led out and the new test procedure proposed in the paper just needs only one impact to surface of plate.

Via verification of test results and 2D/3D of modal and transient analyses of numerical simulation, the impact-echo equipment is suitable for determination of material properties and evaluation of cross-sectional integrity. The applied scope of materials is including concrete, gypsum, metal, alloy metal, plastic, etc. The material properties of concrete plate will also be obtained by a simple impact. Comparison with the manual of ASTM, the experimental procedures of this search are relative simple, reliable, convenient and immediate to determinate the material properties at field.

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