CAJ | 학술논문

研究了由一类各向同性不可压缩Ogden材料组成的球壳在突加拉伸载荷作用下的有限振动问题。首先利用平衡微分方程、边界条件和初始条件求得了球壳径向对称运动的微分方程，证明了存在一个临界值。当拉伸载荷未达到这个临界值时，随着时间的增加，球壳的内表面将做非线性周期振动；当拉伸载荷超过这个临界值时，球壳最终会破裂。最后给出了相应的数值算例。
연구료유일류각향동성불가압축Ogden재료조성적구각재돌가랍신재하작용하적유한진동문제。수선이용평형미분방정、변계조건화초시조건구득료구각경향대칭운동적미분방정，증명료존재일개림계치。당랍신재하미체도저개림계치시，수착시간적증가，구각적내표면장주비선성주기진동；당랍신재하초과저개림계치시，구각최종회파렬。최후급출료상응적수치산례。
The finite oscillation problem is considered for a spherical shell composed of a class of isotropic incompressible Ogden materials under a suddenly applied tensile load. At first, a differential equation describing the radial symmetric motion of the spherical shell has been obtained by using equilibrium differential equation, boundary conditions and initial condition. It is proved that there exists a critical load, if the tensile load is smaller than the critical value, the radial motion of the inner surface is a nonlinear periodic oscillation with increasing time. However, if the tensile load exceeds the critical value, the spherical shell will be destroyed ultimately. Finally, numerical examples are given to further illustrate the properties of the solutions.