Modal Analysis of Nonclassically Damped Structural Systems Using Canonical Transformation

Keywords: Seismic Analysis, Canonical Transformation, Modal Decomposition, Seismic Excitation, and Damped Structural Analysis.

Abstract: An alternate modal decomposition method for dynamic analysis of non-classically damped structural systems is presented. The resulting decoupled equations contain only real parameters. Hence, the solution can be obtained in the real field. Several procedures are outlined to solve these equations for both deterministic and nonstationary random ground excitations. Prior work has shown that the effect of nonclassical damping may be significant for the response of light equipment attached to a structure. Therefore, the proposed solution technique is applied to find the response of light equipment that is attached to a multi-degree-of-freedom structure. Numerical results obtained from deterministic and nonstationary random vibration analyses indicate that the effect of nonclassical damping on the response of tuned equipment is significant only when the mass ratio and damping ratio of the equipment are small. Under this circumstance, the approximate classically damped solution, i.e., the solution obtained using the undamped modal matrix and disregarding the off-diagonal terms of the resulting damping matrix, is usually unconservative. For detuned equipment, neglecting the effect of nonclassical damping generally results in an equipment response that is close to the exact results. However, for certain equipment detuned at high frequency, neglecting nonclassical damping results in conservative equipment responses.