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An extended harmonic balance method based on incremental nonlinear control parameters

机译：基于增量非线性控制参数的扩展谐波平衡方法

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摘要

A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parame-terised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.
机译：提出了一种新的计算谐波激励引起的多自由度非线性动态系统稳态响应的公式。目的是使用线性方程式求解多维非线性系统。非线性由一组“非线性控制参数”参数化，因此动态系统对于这些参数的零值实际上是线性的，非线性随着这些参数的值的增加而增加。开发了由一阶截断的泰勒级数展开形成的两组线性方程。第一组线性方程式提供了线性系统响应相对于非线性控制参数的灵敏度的总和，第二组是使用先前响应来更新灵敏度的递归方程式。然后，将获得的稳态响应的灵敏度用于在迭代过程中计算非线性动态系统的稳态响应。使用非线性微机电系统（MEMS）进行基本谐波激励来说明该方法的应用和验证。这些示例中的非线性控制参数是施加到MEMS器件的电极上的DC电压。

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