| 1. | State - vector equation with damping and vibration analysis of laminates
考虑阻尼的状态向量方程和层合板的振动分析 |
| 2. | Newton ' s law of motion as applied to the point mass is the well - known vector equation : f = ma
牛顿运动定律应用于质点时就得到这样一个著名的向量方程式： f ma |
| 3. | Vector equations is one of non - linearity equations , and we can solve it by inherit arithmetic or homotopy arithmetic
矢量方程组属于非线性方程组，可以采用遗传算法或同伦算法进行求解。 |
| 4. | There are several ways of estimating direction of arrival in use of the vector hydrophone : acoustic intensity detection , beam revolving and vector equations
利用矢量水听器进行方位估计的方法主要有声强检测、旋转波束和矢量方程组等。 |
| 5. | The vector equations are set up for four loop of one kind of nine - link barranov truss by complex number vector method , and the four equations are changed into complex exponential number form
摘要使用复数向量法对9杆巴氏桁架4个回路建立几何关系，列出矢量方程组并转化成为复指数形式。 |
| 6. | Acoustic intensity detection can efficiently estimate objective direction , and frequence partition , beam revolving and vector equations can differentiate multi - object
声强检测可以有效地进行目标方位估计，利用频带划分、旋转波束、矢量方程组可以在一定程度上有效地解决多目标干扰的问题。 |
| 7. | Simply supported and multilayered magneto - electro - elastic plates : the state vector equation of transversely isotropic magneto - electro - elastic solid is established from its governing equations in a cartesian coordinate system
对于简支压电压磁弹性层合板问题，从它的基本方程出发，建立了压电压磁弹性层合板的状态变量方程。 |
| 8. | Non - axisymmetric problem : two independent sets of the state vector equations are derived from its governing equations in a cylindrical coordinate system by introducing a set of auxiliary variables
层状压电压磁弹性材料的空间非轴对称问题：在柱坐标下，通过引入一组辅助变量，从它的控制方程推导出两组相互独立的状态变量方程。 |
| 9. | Using the fourier transform due to boundary conditions of simply support , solutions of a single magneto - electro - elastic layer in the form of initial state vector and transfer matrix are obtained in fourier transform space from the state vector equations
对状态变量方程进行fourier变换，得到了状态变量表示的单层压电压磁弹性层合板在fourier变换空间中的解，导出了多层压电压磁弹性层合板的表达式。 |
| 10. | Using the hankel transform , the state vector equations are reduced to a set of ordinary differential equations . according to the theory of ordinary differential equations and the cayley - hamilton theorem , an analytical solution of the problem is presented in the form of the product of initial state vector and transfer matrix , which is given for the four distinct eigenvalues each . applications of the solutions are discussed
利用hankel变换，将状态变量方程转化为一组常微分方程组；进而根据常微分方程组解的理论和cayley - hamilton定理，得到了以状态变量和传递矩阵乘积表示的单层压电压磁弹性材料的解析解；并讨论了4种不同特征根的情况以及解的应用。 |
