UTM Centre for Industrial and Applied Mathematics, Ibnu Sina Institute for Scientific & Industrial Research, Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia.
Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia.
PLoS One. 2019 Jul 3;14(7):e0219089. doi: 10.1371/journal.pone.0219089. eCollection 2019.
Vibrational behaviour of symmetric angle-ply layered circular cylindrical shell filled with quiescent fluid is presented. The equations of motion of cylindrical shell in terms of stress and moment resultants are derived from the first order shear deformation theory. Irrotational of inviscid fluid are expressed as the wave equation. These two equations are coupled. Strain-displacement relations and stress-strain relations are adopted into the equations of motion to obtain the differential equations with displacements and rotational functions. A system of ordinary differential equation is obtained in one variable by assuming the functions in separable form. Spline of order three is applied to approximate the displacement and rotational functions, together with boundary conditions, to get a generalised eigenvalue problem. The eigenvalue problem is solved for eigen frequency parameter and associate eigenvectors of spline coefficients. The study of frequency parameters are analysed using the parameters the thickness ratio, length ratio, angle-ply, properties of material and number of layers under different boundary conditions.
呈现了充满静止流体的对称角铺设层状圆柱壳的振动行为。圆柱壳的运动方程是根据第一阶剪切变形理论从应力和弯矩结果推导出来的。无粘流体的无旋性表示为波动方程。这两个方程是耦合的。应变-位移关系和应力-应变关系被引入运动方程中，以获得具有位移和旋转函数的微分方程。通过假设函数可分离形式，在一个变量中得到一个常微分方程组。采用三阶样条函数来近似位移和旋转函数，并结合边界条件，得到一个广义特征值问题。对样条系数的特征频率参数和特征向量进行特征值问题求解。通过不同边界条件下的厚度比、长度比、角铺设、材料性质和层数等参数，分析了频率参数的研究。
