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Directional algorithms for the frequency isolation problem in undamped vibrational systems

机译:无阻尼振动系统中频率隔离问题的定向算法

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摘要

A new algorithm is presented to solve the frequency isolation problem for vibrational systems with no damping: given an undamped mass-spring system with resonant eigenvalues, the system must be re-designed, finding some close-by non-resonant system at a reasonable cost. Our approach relies on modifying masses and stiffnesses along directions in parameter space which produce a maximal variation in the resonant eigenvalues, provided the non-resonant ones do not undergo large variations. The algorithm is derived from first principles, implemented, and numerically tested. The numerical experiments show that the new algorithms are considerably faster and more robust than previous algorithms solving the same problem.
机译:提出了一种新的算法来解决无阻尼振动系统的频率隔离问题:给定具有共振特征值的无阻尼质量弹簧系统,必须重新设计系统,以合理的成本找到一些邻近的非共振系统。我们的方法依赖于沿参数空间中的方向修改质量和刚度,只要非共振的特征值不发生大的变化,这些特征和刚度将在共振特征值上产生最大的变化。该算法源自第一原理,已实现并经过了数值测试。数值实验表明,新算法比解决相同问题的先前算法快得多,并且更健壮。

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