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• W148643544 endingPage "979" @default.
• W148643544 startingPage "973" @default.
• W148643544 abstract "We propose two methods for determining the change [ΔK] in the linear stiffness properties of a structure through measurement of several of the lower modes of free vibration. The problem we consider is the following: assumed given is a baseline undamped N degree of freedom linear structural dynamics model for which the system mass matrix, stiffness matrix, natural frequencies, and mode shapes are known. It is assumed that due to aging, damage or other mechanisms, the stiffness properties are altered in a localized manner, and that the location of this property change is known. The objective is to determine the change [ΔK] in the stiffness matrix by measuring m of the lower modes at some number n > m coordinates. Two methods are proposed for this purpose. The first method utilizes damage Ritz vectors or DRV's to obtain estimates for the expanded (N-dimensional) measured mode shapes. The DRV is defined in such a way that it is directly related to the localized damage. Expressing the expanded measured mode shapes of the altered system as linear combinations of the undamaged mode shapes and the DRV turns out to provide a simple yet accurate way to do mode shape expansion. The DRV mode shape expansion is combined with an iterative, residual - based scheme for estimating the stiffness change [ΔK] and for updating the expanded mode shapes. An example showing quick, accurate convergence is presented for an eight degree of freedom spring mass model. The second updating method uses a reduced system model of the same dimension m as the measured modes, so that mode shape expansions are obviated. An updating procedure is proposed in which two quantities are determined iteratively: 1) the stiffness property change [ΔK] of the full, N-DOF model and 2) the slave/master coordinate transformation needed to do the model reduction for the altered system. The method converges quickly and accurately for the example case presented." @default.
• W148643544 created "2016-06-24" @default.
• W148643544 creator A5059448707 @default.
• W148643544 creator A5071875769 @default.
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• W148643544 date "1998-02-01" @default.
• W148643544 modified "2023-09-22" @default.
• W148643544 title "Two Methods for Model Updating Using Damage Ritz Vectors" @default.
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