Nonlinear normal modes in an intrinsic theory of anisotropic beams
Nonlinear normal modes in an intrinsic theory of anisotropic beams
复制标题
各向异性梁固有理论中的非线性简正模
DOI：
10.1016/j.jsv.2010.10.023
复制
发表时间：
2011
影响因子：
4.7
通讯作者：
R. Palacios
中科院分区：
文献类型：
--
作者：
R. Palacios
梁的非线性振动中的非线性简正模是由固有方程导出的，即以速度和应变为主要自由度。因此，位移和转动不是系统状态，而是使用局部梁材料参考系的传播获得的，如在刚体动力学中。结果表明，内变量足以描述梁的自由振动。该方法不需要材料性质的假设，即它对一般的各向异性行为有效，也不需要梁的运动学假设，即它基于Cosserat对变形曲线的精确几何描述。此外，通过仅涉及振型和已知系数的乘积的积分，得到了固有坐标下的非线性振型方程。利用这种描述，通过对在固有模式坐标空间中定义非线性简正模的不变流形的渐近逼近来寻找非线性简正模。最后用均质各向同性悬臂梁和组合悬臂梁的具体算例说明了该方法的有效性。
Nonlinear normal modes in nonlinear oscillations of beams are derived from intrinsic equations, that is, using velocities and strains as primary degrees of freedom. Displacements and rotations are thus not system states but are instead obtained using the propagation of the local beam material reference frames, as in rigid-body dynamics. It is shown that the intrinsic variables suffice to describe the free vibrations of the beam. The approach does not need assumptions in the material properties, i.e., it is valid for general anisotropic behavior, or the beam kinematics, i.e., it is based on Cosserat's exact geometrical description of the deformable curve. Furthermore, the nonlinear modal equations in intrinsic coordinates are obtained from integrals involving only products of the mode shapes and known coefficients. Using this description, the nonlinear normal modes are sought through an asymptotic approximation to the invariant manifolds that define them in the space of intrinsic modal coordinates. Particular cases of homogeneous isotropic and composite cantilever beams are finally used to exemplify the approach.