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首页> 外文期刊>Shock and vibration >Nonlinear Normal Modes in a Two-Stage Isolator Using a Modified Finite-Element Galerkin Method
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Nonlinear Normal Modes in a Two-Stage Isolator Using a Modified Finite-Element Galerkin Method

机译：使用改进的有限元Galerkin方法的两级隔离器中的非线性正常模式

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A modified Galerkin method is proposed to approximate the nonlinear normal modes in a new type of a two-stage isolator. Besides the displacement of payload and the force transmissibility of this typical nonlinear dynamic system, the nonlinear normal modes defined as invariant manifolds can provide more information about the nonlinear coupling between the system components when periodic motions corresponding to the normal modes of the system occur. The presented approach applies a combination of finite-element discretization and Fourier series expansion for the approximate invariant manifolds. A Galerkin projection of the governing equations for the approximate invariant manifolds yields a set of nonlinear algebraic equations in expansion coefficients, which can be solved numerically with a general choice of zero as initial guess for the cases in this work. The resultant approximate solutions for the invariant manifolds can accurately describe the nonlinear interactions between system components in periodic motions of the specific nonlinear normal modes. In addition, one can solve the invariant manifolds for an annular domain of interest directly by this method, without considering other domain that includes the origin of phase space.
机译：提出了一种修改的Galerkin方法，以近似于新型的两级隔离器中的非线性正常模式。除了有效载荷的位移和该典型非线性动态系统的力传递性之外，定义为不变歧管的非线性正常模式可以在对应于系统的正常模式的周期运动时提供有关系统组件之间的非线性耦合的更多信息。本方法适用于近似不变歧管的有限元离散化和傅立叶串联扩展的组合。用于近似不变歧管的控制方程的Galerkin投影产生了一组膨胀系数中的一组非线性代数方程，其可以用数量的零选择来解决这项工作中的案例的初始猜测。因此，不变歧管的所得到的近似解可以准确地描述特定非线性正常模式的周期运动中系统组件之间的非线性相互作用。另外，通过该方法可以通过这种方法解决环状域的不变歧管，而不考虑包括相空间起源的其他域。

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