CAJ | 학술논문

基于改进傅立叶级数方法，将矩形板振型函数表示为包含正弦三角级数的改进傅立叶级数，从而有效地克服结构在边界处存在的不连续性，建立了一般边界条件下矩形薄板结构振动声辐射的分析方法，并对薄板结构的振动声辐射特性进行了研究。文中还建立了薄板结构的位移容许函数，然后基于最小势能原理求解了系统的Lagrange函数，最后利用Rayleigh-Ritz法对方程求解从而获得薄板自由振动的模态信息；在此基础上，基于Rayleigh积分公式推导出了薄板振动、辐射声压和声功率的表达式，研究了结构特性参数及边界条件对薄板振动声辐射的影响，通过有限元软件和参考文献的比对分析，验证了改进方法的正确性和有效性。
기우개진부립협급수방법，장구형판진형함수표시위포함정현삼각급수적개진부립협급수，종이유효지극복결구재변계처존재적불련속성，건립료일반변계조건하구형박판결구진동성복사적분석방법，병대박판결구적진동성복사특성진행료연구。문중환건립료박판결구적위이용허함수，연후기우최소세능원리구해료계통적Lagrange함수，최후이용Rayleigh-Ritz법대방정구해종이획득박판자유진동적모태신식；재차기출상，기우Rayleigh적분공식추도출료박판진동、복사성압화성공솔적표체식，연구료결구특성삼수급변계조건대박판진동성복사적영향，통과유한원연건화삼고문헌적비대분석，험증료개진방법적정학성화유효성。
Based on the theory of plates, a new method called Improved Fourier Series Method (IFSM) is presented to study the vibration and acoustic characteristics of rectangular plates with arbitrary boundary conditions. The plate admissible functions is presented, which is invariantly sought as an improved Fourier cosine series, and a sine series is introduced to overcome the discontinuities of the structure. And then the Lagrange equation is established according to the principle of the minimum potential energy. Finally, by us-ing the Rayleigh-Ritz technique the vibration characteristics can be easily acquired. Under these circum-stances, with the help of Rayleigh integral formula, the expressions of sound pressure and acoustic power are derived. The effects of structural parameters and boundary conditions that have great impact on the acous-tic radiation are also studied. The comparisons among numerical simulation results, which obtained with FEM and reposed in literatures, validate the correctness of the method.