The forced vibrations of axisymmetric inhomogenous isotropic viscothermoelastic hollow cylinder under periodic dynamic pressure have been studied. The material was taken inhomogenous due to easy exponent law in radial direction. By applying time harmonics variation technique, the partial differential equations were converted into ordinary differential equations. These ordinary differential equations were solved by applying series solution of matrix Fröbenius method analytically to represent displacement, temperature and stresses. Numerically simulated outcomes were presented graphically to express the effect of functionally graded material disk for different values of grading parameter. With the increase in value of grading index, variation of field functions go on decreasing. The variation of field functions show high variation in homogenous materials in contrast to low variation in inhomogeneous materials.

研究了轴对称非均质各向同性粘弹性空心圆柱在周期性动压力下的强迫振动。由于沿径向的指数规律容易，材料被认为是不均匀的。通过应用时间谐波变化技术，将偏微分方程转换为常微分方程。通过应用矩阵Fröbenius方法的级数解来解析这些常微分方程，以表示位移，温度和应力。图形化地表示了数值模拟的结果，以表达功能分级材料盘对不同等级参数的影响。随着等级指数值的增加，场函数的变化继续减小。