300 M. Misawa and H. Kawasoe Frequency used in finding additional mass and stiffness, Hz ! Angular frequency, rad/s ˝2 Diagonal matrix with!i 2 (i D1, 2, : : : , nT) Subscripts b Boundary coordinates of component c Quantity of component id Quantity of identified model k Internal coordinates of component o Quantity of original model p Translational coordinate with additional mass and stiffness q Coordinates without additional mass and stiffness s Quantity of structure t Quantity of tested component test Measured quantity 29.1 Introduction To confirm the dynamic characteristics of a structure, it is necessary to perform a modal test of the fabricated structure. However, there is a problem in performing modal tests when the structure increases in size. For large flexible structures, such as deployed antennas and solar paddles for satellite use, gravitational considerations may prevent a fully assembled ground modal test because these structures are not strong enough to withstand the force of gravity. Component modal tests can provide a means of predicting the dynamic characteristics of the structure without testing the whole structure. There are a variety of approaches associated with experimental component modal synthesis (CMS). An experimental CMS procedure was presented to assemble a global model of the coupled structural dynamics through equivalent mass and stiffness representations of the components [1]. This procedure relies on accurate response and force measurements because mass normalized normal modes at boundary coordinates are the basis of the analytical synthesis. Doebling et al. [2] presented a method for estimating the residual flexibility from structural vibration data for experimental CMS. Morgan et al. [3] developed the forced response method with experimentally based CMS models and measured response data. An approach to CMS was presented for application in the testing of large flexible space structures [4]. This approach uses the test-based characteristics of individual components determined experimentally through modal and static tests. Chen and Cherng [5] proposed an experimental procedure to measure the generalized dynamic compliance with rotational effects. Rotational displacements at the boundary are used for the coupling of components. Komatsu et al. [6] improved the predicted dynamic characteristics of structures with rotational displacements found by introducing a polynomial approximation for the measured modes. For verifying constrained modes when fixed-base testing proves impractical, a free-boundary modal test with the residual flexibility method has been investigated [7, 8]. Martinez et al. [9] presented a method to create a combined experimental/analytical model of a structure for improving the accuracy of the analytical model. This model is assembled using a component mode synthesis technique. Free-free modes and the residual flexibility at the boundary of a tested component are measured and used in the coupling. Admire et al. [10] also used the same approach to develop a constrained model for deriving constrained modes and frequencies. Tinker [11] described the application of the free-suspension residual flexibility test method to Space Station modules. After correlation of the Pathfinder finite element model to residual flexibility test data, constrained frequencies and modes obtained with the model are compared to fixed-base test results. A practical dynamic flexibility method based on a combination of test and analysis information was also proposed [12]. This method enables the computation of the approximate value of the dynamic flexibility using the power series expansion. Under two special situations, this method has a limitation and was improved [13]. Morgan et al. [14] presented an experimentally based nonbaseband CMS method with residual flexibility for the dynamic analysis of a proportionally damped system. An alternate approach for verification of constrained models is the mass additive method. This method forces local deformation near boundaries by adding mass to the boundaries of a tested structure. By subtracting the mass from the equation of motion of the tested structure, constrained modes are estimated. Admire et al. [15] developed a mass additive
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