Poincaré非线性振动理论在连续介质力学中的推广(Ⅱ)——若干应用
Extension of Poincare’s Nonlinear Oscillation Theory to Continuum Mechanics(Ⅱ)——Applications
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摘要: 文本是文[1]的继续.文[1]中,提出和建议使用非线性偏微分方程直接摄动与加权积分方程法,计算连续介质系统的共振与非共振周期解.本文中,应用该方法计算了定跨度弹性梁在各种常见边界条件下强迫振动的共振与非共振周期解,方板在集中周期荷载作用下的共振周期解.指出了,非主振型对非线性振动周期解的影响及静荷载对幅频特性曲线的影响.Abstract: This is a continuation of [1]. In [1] we suggested a method of direct perturbation of partial differential equation and weighted integration to calculate the periodic solution for continuum mechanics. In this paper, by using the above method we calculate the resonant and nonresonant periodic solutions of beam with fixed span and different boundary conditions and the resonant periodic solution of square plate under the action of concentrated periodic load. Besides, the influences of non-principal mode upon periodic solution and of static load upon amplitude-frequency curve are given.
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[1] 霍麟春、李骊,Poincaré非线性振动理论在连续介质力学中的推广(Ⅰ)——基本理论与方法,应用数学和力学,8,1(1987). [2] Keller,3.B.and L.Ting,Periodic vibrations of systems governAd by nonlinear partial differential equations,Comm,Pure Appd,Math,,19(1966). [3] 钱伟长,《奇异摄动理论及其在力学的应用》,科学出版社(1981). [4] Каудерер Г.,Нелинейная Механика,ИИЛ Москва(1961) [5] Волъмир А.С.,Нелинейная Динамцка Пласмцнок ц Оболочек,Москва(1972) -
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