Modal Analysis of Transient Vibration Problems in Linearly Viscoelastic Solids

摘要

Transient vibration problems in linear viscoelasticity may be solved by means of the Sturm-Liouville theory provided the homogeneous boundary conditions for the free vibrations can be combined to give a characteristic equation with real roots. This characteristic equation will depend on the geometric and inertial characteristics of the system, and not on the viscoelastic properties of the solid. If all the conditions above are not satisfied, it is still generally possible to reduce the homogeneous boundary conditions to a complex frequency equation by assuming separable solutions with exp (st) as the time dependent factor. The associated modes of deflection will generally be nonorthogonal. Transient vibration problems of this type may be solved by contour integrals, which may be evaluated by residue theory or reduced to a Fourier integral by a change of variable. (Author)