星形蜂巢狀結構是一種具有負泊松比特性的週期性多孔結構，該類型的負泊松比多孔結構又統稱為膨脹材料，其組成皆為彈性材料的週期排列，所分析對象為彈性波，包含縱波、橫波及其耦合現象等，學者將此類型結構視為聲子晶體的一種，進而透過有限元素分析與布洛赫定理分析此類型週期結構的波傳行為，發現在某些頻段下的彈性波在此週期結構中無法傳遞，產生彈性波的能隙現象。本文將星形蜂巢狀結構其內部空隙部分填入基材，分析填入基材對其整體結構機械性質的變化，針對填入不同基材與不同填入區域兩部份，並分別討論其泊松比、楊氏模數及剪力模數變化關係。進而對填入基材的星形蜂巢狀結構分析其波傳現象，在特定的頻寬下外圍填滿的星形蜂巢狀結構會具有準直的現象。
為了設計可主動式控制的聲子晶體元件，在星形蜂巢狀結構相互連接梁的兩側加上壓電材料，並利用壓電材料外加經過設計的負電容電路會使壓電材料的剛性改變之特性，藉由調變外加負電容電路中的可變電阻，達到改變壓電材料的楊氏模數，調變聲子晶體完全能隙的作用頻率範圍，可用於設計聲波開關或濾波器等，最後透過有限元素軟體COMSOL分析聲子能帶及進行全波模擬，證明可調式膨脹聲子晶體元件的可行性。

The development of star-shaped honeycombs filled with matrix in the void area is presented. Divide into two parts, the different matrix be filled and the different area be filled. The effects of the matrix on the effective constants such as Poisson’s ratio, Young’s modulus, and shear modulus are investigated and discussed. Then the wave propagation of star-shaped honeycombs filled with matrix are investigated, and the outside-filled star-shaped honeycombs exhibit collimate phenomenon in certain frequency. In order to design phononic crystals device, we proposed a tunable piezoelectric materials which is connected to a separate negative capacitance circuit. Making use of the characteristic which change the effective modulus by tuning the variable resistor in the circuit, we introduce piezoelectric materials into star-shaped honeycombs. The phononic bandgap depends on the tunable effective modulus, giving rise to prospective applications such as elastic/acoustic filters and sonic switch. The performance obtained by COMSOL Multiphysics Finite Element simulations confirmed the feasibility of the sonic devices proposed.

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