| The objective of this research is to develop two analytical and numerical techniques for time-domain transient analysis of general one-dimensional distributed parameter systems. A closed-form eigenfunction expansion realization is derived, which provides a systematic way to estimate transient response of non-self-adjoint systems with eigenvalue-dependent boundaries. The other is the Z-Prime method (ZPM) which is valid for complex distributed systems for whose orthogonality relations of eigenfunctions are difficult to find, or do not exist.;The focus of the research is on derivation and application of the 2-Prime method (ZPM). The transient motion of viscoelastic systems for whose stress-strain relations are frequency-dependent is, for the first time, treated in an exact and close form. The transient response of flexible distributed systems subject to noncolocated control with time delay elements in them is expressed in an explicit form. Time domain substructure synthesis is derived for general complex systems. The high accuracy and efficiency of the method is justified in the numerical examples.;The major thrust of this analysis is to obtain closed-form transient solutions of one-dimensional distributed systems, which otherwise might be difficult to obtain; yet the computational efforts required are much less than those of many existing modal analysis techniques. |
