An Equivalent Impedance Approach For Mid-frequency Vibration Of A Spot-welded Beam-plate Structure

The mid-frequency is a transition frequency band between low frequencies and high frequencies, in which the structure response exhibits both low-frequency and high-frequency vibration features. Neither deterministic methods nor statistical methods can accurately predict the structure responses in the mid-frequency band. In this thesis, an equivalent impedance approach is presented for the mid-frequency vibration analysis of a spot-welded beam-plate structure. It originates from the hybrid SEA/FEA method, but significantly simplifies the computation by assuming that the plate is highly damped. The approach can accurately predict the mid-frequency structure responses when the assumption is satisfied.The mid-frequency response of a complex vibrating system results from the interaction of the direct and reverberant fields of each participating subsystem. According to the reverberant reciprocity relationship, the interaction force is proportional to the imaginary part of the direct field dynamic stiffness matrix. In this thesis, a semi-analytical algorithm is proposed to approximate the direct field stiffness matrix using the boundary admittance of a semi-infinite plate. Computational efficiency is improved by avoiding the intensive computation in traditional methods such as the FEM and BEM.In the mid-frequency band, a complex structure can be divided into two parts, namely the flexible member and the stiff member, according to their vibration behaviors. Flexible member acts as a damper to the stiff member. The equivalent boundary impedance of the spot welded plate is derived by using the semi-analytical algorithm. Then the beam-plate structure is simplified by replacing the plate with a set of dampers representing the equivalent boundary impedance. This approach avoids complex calculations in the hybrid FEA/SEA method, thus makes engineering calculation more efficient. The new development is validated by comparing the results from the equivalent impedance approach with those from FEA and the hybrid FEA/SEA methods for a spot welded stiffened plate.