振动的

Firstly, the function sinx that appears in the simple pendulum equation is replaced with a polynomial of degree 3 using Maclaurin series expansion and Chebyshev polynomial approximation. Subsequently, the resulting equation which is a Duffing type equation is approximately solved with combing Newton's method and the harmonic balance method.

首先，利用Maclaurin展开和Chebyshev多项式加速技术将单摆振动方程中的正弦型恢复力用三次多项式近似代替，得到一个Duffing型方程；然后，将牛顿法与谐波平衡法结合起来建立Duffing方程的解析逼近周期及周期解，从而给出单摆振动的解析逼近解。

In practice, the problems in the vibration utilization are nonlinear that is caused by various factors, and show different forms.

振动利用包括机械振动的利用、波动与波能的利用及电、磁、光振荡器在工程技术中的利用等。

Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.

利用数学分析和不动点原理，研究了具有正负系数的中立型时滞微分方程的振动性，得到了方程所有解振动的充分条件。

Through creating a differential equation whose oscillation is equivalent to the impulsive equation, or considering the relation between impulsive points and delay, we get some sufficient conditions for the oscillation of the equation.

第二章讨论了二阶自共轭脉冲微分方程，通过建立与之振动性等价的微分方程，或考虑脉冲点与时滞间的关系，我们得出方程振动的一些充分条件。

By the finite element method model, Natural frequency and vibration model of some project fin-stabilitde sabot-discarded penetrator during launching are calculated and analyzed.

利用建立的三维有限元模型，计算分析了30阶尾翼稳定脱壳穿甲弹的振动固有特性，得到了各阶振动的固有频率及响应振型。

In Laplace space, the exact element stiffness matrix of the axial, torsional and bending vibrations of cone-shaped and symmetrical closed thin-walled bars are derived. By use of variation principle, the element stiffness matrix of the coupling vibrations of an asymmetrical closed thin-walled bar is also given.

在拉氏空间中导出了锥形杆件和对称闭口薄壁杆件的轴向、扭转和弯曲振动的精确单元刚度矩阵，应用变分原理也给出了非对称闭口薄壁杆件耦联振动的单元刚度矩阵。

In the experiments, the accelerometer and the microphone are used respectively to measure the acceleration on the panel and the sound pressure in the cavity. Piezoelectric ceramics Transducer is used as the control source to control reverberant sound field transmission through a simply supported rectangular aluminium panel into a concrete cavity.

实验中采用加速度计和话筒作为传感器拾取板振动的加速度和闭空间内的声压信号，用压电陶瓷片作为振动控制源来控制混响声场通过简支矩形铝板向混凝土闭空间的声传入。

The dissertation studies the phenomena and characteristics of self-excitation, deduces those phenomena belong to nonlinear non-conservative autonomous steady-state periodic movement.

本文分析研究了轧机主传动系统自激振动的现象和特点，得出轧机主传动系统的自激振动现象属于非线性非保守自治系统的稳态周期运动。

A method of eliminating the residual vibration of redundant flexible robot manipulators is put forward. The endpoint residual vibration can be reduced easily through optimizing the joint self-motion.

继而提出了利用自身运动进行开环控制以消减冗余度柔性机器人残余振动的方法，在机器人末端运动停止后，通过选择最优的关节自运动，使末端的残余振动尽快消减下来。

It is well known that problems of vibrations of spherically isotropic(a special form of transversely isotropic)spherical shells are moredifficult to deal with than those of the isotropic ones.

由于包含五个弹性常数，球面各向同性(属横观各向同性的一种特殊形式)球壳振动的研究要比各向同性球壳振动的研究复杂。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷