CAJ | 학술논문

基于Reissner假设，对四边简支的正交各向异性功能梯度夹层板自由振动问题进行了研究。根据功能梯度芯材与正交各向异性表层的应力状态及本构关系，得出了功能梯度夹层板的运动平衡方程表达式；根据四边简支的边界条件，将挠度与横向剪力用双三角级数展开，得到了功能梯度夹层板固有频率的计算式。算例中采用本文方法对四边简支功能梯度夹层板的固有频率进行了求解，其芯材弹性模量在厚度方向上分别呈线性和幂律分布，并分析了芯材材料属性分布参数、结构跨厚比及面内纵横比对夹层板固有频率的影响，通过与有限元解进行对比，表明所提出的理论方法精确有效。
기우Reissner가설，대사변간지적정교각향이성공능제도협층판자유진동문제진행료연구。근거공능제도심재여정교각향이성표층적응력상태급본구관계，득출료공능제도협층판적운동평형방정표체식；근거사변간지적변계조건，장뇨도여횡향전력용쌍삼각급수전개，득도료공능제도협층판고유빈솔적계산식。산례중채용본문방법대사변간지공능제도협층판적고유빈솔진행료구해，기심재탄성모량재후도방향상분별정선성화멱률분포，병분석료심재재료속성분포삼수、결구과후비급면내종횡비대협층판고유빈솔적영향，통과여유한원해진행대비，표명소제출적이론방법정학유효。
Based on the Reissner assumptions , this paper describes the research done on the free vibration analysis of simply supported orthotropic sandwich panels with a functionally graded core .The expressions of the dynamic equations were presented according to the constitutive relations and stress states of the functionally gradient core and orthotropic face sheets.The natural frequencies of functionally graded rectangular sandwich plates were obtained by expanding the deflection, transverse shearing force with double trigonometric series that satisfy the four-sided simply supported bounda-ry conditions.The natural frequencies of two types of functionally graded sandwich plates were calculated with the numer-ical example , in which Young's modulus of the functionally graded core obeys the linear and power-law distribution through the thickness respectively .The impact of the distribution parameters of the functionally graded core's properties, the thickness-side ratio and aspect ratio , on the natural frequency of the sandwich plate was also examined .The proposed solutions were validated and shown to be precise and effective by comparing the results with FEM solutions .