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F franklin j d powell a emami naeini feedback control

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Unformatted text preview: igenvalue calculations. Although the problem appears rather simplistic in nature, it is a severe test for linear irregular shaped elements where accurate bending mode frequencies are required. 2. Since the beam is free of any constraints, only one-half of the beam is required for modeling. Symmetry constraints are applied at the mid-length of the models. To obtain the desired bending mode (in the XY plane) all nodes at Z = 0 are constrained in the Z direction. Additionally, for the axial mode only, all nodes at Y = 0 are constrained in the Y direction. 3. For the axial mode case, Householder extraction is used with all UX degrees of freedom chosen as MDOFs. For the bending mode case, subspace extraction is used with shifted subspace to circumvent zero energy modes. 4. All load cases show good agreement in the prediction of the first axial natural frequency. This mode is simply linearly-varying longitudinal motion which is easily handled by both linear and quadratic elements. Irregular element shapes have only a minor effect on solution accuracy since axial motion is pre...
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