Homology design of vibration mode shape under uncertain boundary conditions
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A methodology is proposed for homology design to realize such a vibration mode shape that satisfies a certain geometrical relation before and during vibration. The formulation is based on the finite element eigenvalue and sensitivity analyses so that a governing equation for the design variables is derived under the condition that the homology constraint holds while the eigenvalue problem is satisfied.
The nonlinear effect of uncertain boundary conditions on the homologous mode shape is examined through convex model of the uncertainties. The worst case of the disturbed mode shape due to the uncertainties is estimated employing the Lagrange multiplier method.
The numerical example of out-of-plane vibration of a planar lattice frame displays the validity of the proposed method for homology design. The worst case of the disturbed mode shape is discussed when rotational stiffness of the boundary fluctuates.
KeywordsVibration mode shape homology design finite element sensitivity analysis Moore-Penrose generalized inverse uncertain boundary condition convex model
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