An Energy-Preserving Description of Nonlinear Beam Vibrations in Modal Coordinates
An Energy-Preserving Description of Nonlinear Beam Vibrations in Modal Coordinates
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模态坐标下非线性梁振动的能量守恒描述
DOI：
10.1016/j.jsv.2013.05.021
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发表时间：
2013
影响因子：
4.7
通讯作者：
P. Goulart
中科院分区：
文献类型：
--
作者：
A. Wynn;Yinan Wang;R. Palacios;P. Goulart
守恒量被确定在方程中描述梁的大振幅自由振动投影到其线性正常模式。这是通过在模态变换之前将几何精确的运动方程写成其固有形式或哈密顿形式来实现的。对于非线性自由振动的零力平衡，它表明，有限维运动方程的模态坐标是能量守恒的，即使他们只近似的总能量的无限维系统。对于具有恒定随动力的梁，通过Casimir函数，在有限维运动方程中也得到了类能量守恒量。内在描述中的空间和时间变量之间的对偶性最终被转移到空间守恒量的定义中，这被确定为局部截面功率。数值例子来说明主要结果。
Conserved quantities are identified in the equations describing large-amplitude free vibrations of beams projected onto their linear normal modes. This is achieved by writing the geometrically exact equations of motion in their intrinsic, or Hamiltonian, form before the modal transformation. For nonlinear free vibrations about a zero-force equilibrium, it is shown that the finite-dimensional equations of motion in modal coordinates are energy preserving, even though they only approximate the total energy of the infinite-dimensional system. For beams with constant follower forces, energy-like conserved quantities are also obtained in the finite-dimensional equations of motion via Casimir functions. The duality between space and time variables in the intrinsic description is finally carried over to the definition of a conserved quantity in space, which is identified as the local cross-sectional power. Numerical examples are used to illustrate the main results.