具彈性支撐複合材料圓板之振動與聲傳研究

Abstract

本文在討論具彈性支撐之複合材料圓板之振動及聲壓研究。利用同一彈性支撐來探討不同疊層角度之複材圓板及三明治圓板之聲壓曲勢之異同，並了解封閉及非封閉之彈性支撐對同一振動板之聲壓位準有何影響。 本文所使用之彈性支撐是由泡棉所加熱壓製而成的，其形狀為半圓形。在模擬分析中將其模擬、等效為彈簧，並藉由實驗，將其等效彈簧常數求出，以供往後實驗及理論分析使用。 在理論部份，本篇論文使用古典積層板理論及一階剪變形理論來模擬複合材料積層圓板及三明治圓板之力學行為，並以Ritz Method求解複合材料圓板的自然頻率及模態。在聲壓位準(SPL)方面，由有限元素軟體ANSYS建立複合材料圓板之模型進行頻率響應分析，並將各個激振頻率下各元素之振幅、相角輸出，以便由Fortran撰寫之聲壓位準程式計算在各個激振頻率下之聲壓值，進而繪製SPL關係圖。在ANSYS分析時，討論在不同參數下其聲壓曲線之變化，如疊層角度對聲壓位準所造成之影響。 在實驗部份，進行複合積層圓板及三明治圓板製作，及激振實驗和聲壓量測實驗，並將實驗結果與理論分析比較以確定理論分析之正確性。再藉由實驗了解疊層角度、位移響應、重量、圓板結構、彈性支撐對複合材料圓板聲壓位準和趨勢有何影響，以利後續複材振動板之設計研究。

Vibration characteristics and sound radiation of flexibly supported circular laminated composite plates are studied in this thesis. Using both theoretical and experimental means, we investigate how layer angles and laminated composite structure affect the sound radiation of the flexibly supported circular plates. The effects of continuous and discontinuous flexible suspensions on the SPL of the same circular plates were studied. The flexible suspension using PU foam was formed through a process of heating and pressing and the stiffness of the suspension was measured from experiments. In analysis, elastic springs were used to simulate the flexible suspensions. The dynamic behaviors of the circular laminated composite plates and circular sandwich plates were studied based on the Classical Laminated Plate Theory or the First Order Shear Deformation Theory, and the Ritz method was used with a power series as the displacement function to yield natural frequencies and natural models of the circular plates. In the part of SPL calculation, we established the models of the circular composite plates using ANSYS for harmonic response analysis. And then we used the calculated amplitude and phase of each element in the circular plate to construct the SPL spectrum. Furthermore, the effects of different variables, such as lamination angle, plate thickness, stiffness of springs on the trend of the SPL curves were also studied. In the experimental study, we made circular composite laminated plates and sandwich plates. And then we proved that the solutions of theoretical analysis were consistent with the experimental results of SPL and natural frequencies. The results provided in this thesis may be of value for designing circular radiating panels having efficient radiation capability.