1) principal parametric resonance
主参激共振
1.
According to the nonlinear dynamic equations of motion for slender cantilever beams axially excited by narrow-band random processes of the base,a set of nonlinear modulation equations for the principal parametric resonances is developed based on the method of multiple scales.
以轴向基础窄带随机激励悬臂梁非线性动力学方程组为分析对象,采用多尺度法,获得了系统主参激共振的非线性调谐方程组。
2.
The method of multiple scales was used to solve directly the nonlinear differential equations and to derive the nonlinear modulation equation for the principal parametric resonance.
采用多尺度法,对所得方程进行一次近似展开,着重计算了窄带随机主参激共振时系统平凡响应的最大Lyapunov指数及随机稳定性问题,并通过直接数值积分验证了所得稳定区域的有效性。
3.
The method of multiple scales combined with the Cartesian transformation is used solve to the nonlinear differential equations and derive a set of nonlinear modulation equations for the principal parametric resonance of the first mode and 3:1 internal resonance between the first two modes.
采用多尺度法并结合笛卡尔坐标变换 ,导出了系统受前两阶模态间 3∶ 1内共振及第二阶模态主参激共振时的非线性调制方程组 ,数值求解了该方程组的定常解及相应的稳定性问题。
2) primary parametric resonance
主参数共振
1.
In order to study the primary parametric resonance of a externally excited thin circular plate on nonlinear foundation,nonlinear dynamical equation of the system is established with the application of elastic theory.
应用非线性振动的多尺度法求得系统主参数共振的近似解,并进行数值计算。
2.
By means of the method of multiple scales for nonlinear oscillations, the first approximate primary parametric resonance of the system is acquired.
应用非线性振动的多尺度法求得系统满足主参数共振条件的一次近似解,并进行数值计算,分析定常解的稳定性。
3.
Applying the method of multiple scales for nonlinear vibration, the first approximation solution of primary parametric resonance an.
根据非线性振动的多尺度法求得系统主参数共振-主共振情况的一次近似解,并进行数值计算。
3) principal resonance
参数主共振
1.
The principal resonance of a Duffing oscillator to combined deterministic and narrow band random parametric excitations is investigated.
研究了Ｄｕｆｉｎｇ振子在谐和与窄带随机噪声联合激励下的参数主共振响应和稳定性问题。
2.
The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated.
研究了VanderPol_Duffing振子在谐和与随机噪声联合激励下的参数主共振响应和稳定性问题· 用多尺度法分离了系统的快变项 ,并求出了系统的最大Liapunov指数和稳态概率密度函数 ,还分析了失稳、分叉和跳跃现象 ,讨论了系统的阻尼项、非线性项、随机项和确定性参激强度等参数对系统响应的影响· 数值模拟表明所提出的方法是有效的·
4) principal parametric resonance
主参数共振
1.
By means of the method of averaging together with truncation of Taylor expansions, two slow_flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance.
研究了Duffing_VanderPol振子的主参数共振响应及其时滞反馈控制问题·依平均法和对时滞反馈控制项Taylor展开的截断得到的平均方程表明,除参数激励的幅值和频率外,零解的稳定性只与原方程中线性项的系数和线性反馈有关,但周期解的稳定性还与原方程中非线性项的系数和非线性反馈有关·通过调整反馈增益和时滞,可以使不稳定的零解变得稳定·非零周期解可能通过鞍结分岔和Hopf分岔失去稳定性,但选择合适的反馈增益和时滞,可以避免鞍结分岔和Hopf分岔的发生·数值仿真的结果验证了理论分析的正确性
5) primary parametric resonance and primary resonance
主参数共振-主共振
1.
In order to study primary parametric resonance and primary resonance of a thin circular plate subjected to harmonic excitation on nonlinear foundation by applying elastic theory, nonlinear dynamical equation of the system is established.
应用非线性振动的多尺度法求得系统主参数共振-主共振条件的一次近似解,并进行数值计算。
6) Primary resonance and primary parametric resonance
主共振-主参数共振
1.
The primary resonance and primary parametric resonance of a thin rectangular plate on nonlinear foundation in temperature field,are discussed.
为了研究温度场中非线性地基上矩形薄板受简谐激励的主共振-主参数共振问题,应用弹性力学理论建立其动力学方程,应用Galerkin方法将其转化为非线性振动方程。
补充资料：电子自旋共振(见电子回旋共振)
电子自旋共振(见电子回旋共振)
electron spin resonance
电子自旋共振eleetron spin resonanee见电子回旋共振。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条