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# video_lecture - V-36 Chapter V: Applications and...

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V-36 Chapter V: Applications and approximate methods An iterative approach for determining the lowest natural frequency - the power method The Rayleigh and Dunkerley approaches provide us with upper and lower bounds, respectively, on the lowest natural frequency of a system. The lower bound from Dunkerley is set by the on- diagonal terms of the dynamical matrix [ D ]=[ K ] 1 [ M ] – the method does not provide a means to improve on this bound. With the Rayleigh method, some improvement is possible by choosing any number of di f erent trial vectors ° v from which the square root of the Rayleigh quotient is found, ° Q ( ° v )= ° ° v T [ K ] ° v/ ° v T [ M ] ° v . One chooses the lowest of the values of ° Q ( ° v ) as the best estimate for the lowest natural frequency from among these trial vectors. In this section, we will pursue a method that allows us to systematically improve on our estimates for both the lowest natural frequency and the corresponding modal vector. This method, known

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video_lecture - V-36 Chapter V: Applications and...

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