Hoang Pham
Jerry H. Ginsberg
School of Mech. Eng., Georgia Inst. of Technol., GA 30332
Various aspects associated with eigenvalue veering, such as extreme parameter sensitivity and localization of response, are of paramount importance for predicting the dynamic response of lightly coupled systems having nearly periodic components. This paper presents a perturbation solution that simplifies analysis of forced response of continuous systems whose free vibration eigensolutions display eigenvalue veering and mode localization. In this investigation, the classic two-span beam with a strong torsional restraint at the intermediate pin support provides a prototype for developing the perturbation solution. Offset of the pin from the center position destroys periodicity of the two-span system, whereas the strength of the torsional spring relates the extent of interspan decoupling. A study by Chen and Ginsberg [J. Vib. Acoust. 114, 141 (1992)] established a relationship between the eigenfunctions and the eigenvalues for different values of the pin offset. The previous findings are merged with a Ritz expansion to formulate the forced response. The adequacy of the solution is determined by comparisons to results of baseline ``Sturm--Liouville-type'' analyses. Flexibility of the perturbation solution is assessed in various case studies of lightly coupled two-span systems.