Semi-definite Programming For Optimization Of Dynamic Compliance

Semi-definite programming(SDP) is introduced to solve dynamic problem of topological design optimization of trusses structures with/without skew-symmetric damper that are subjected to time-harmonic dynamic loading with prescribed frequency and amplitude.This objective is implemented by minimizing truss's weight using cross-section of each member as design variable.When the prescribed loading frequency is smaller than the fundamental eigenfrequency of the structure without damping, the problem is formulated as SDP with prescribed upper bound of dynamic compliance. An important objective of dynamic problem is to drive the fundamental eigenfrequency of the structure as far away as possible from the prescribed loading frequency in order to avoid resonance. Introduction of prescribed upper bound of dynamic compliance ensures reduction of vibration level of the structure.When a skew-symmetric damper matrix is considered, dynamic stiffness matrix is Hermitian matrix. With application of Schur complement, the problem is formulated as SDP with prescribed upper bound of dynamic compliance after linear transformation. It is shown in the examples, that dynamic design with skew-symmetric damper differs much from that without damping.