Fundamental Categories and Physical Properties of Transmissibility Functions

This chapter lays both theoretical and practical groundwork for understanding transmissibility functions as mathematical representations of output-to-output relationships. It clarifies key categorical distinctions, such as local versus global, point-type versus high-resolution, and static versus dynamic (under moving loads), while highlighting their fundamental physical characteristics. Beginning with clear definitions and classifications, the chapter systematically explores how transmissibility functions behave across a range of operational conditions, including single excitation, ambient vibration, and moving loads. A central emphasis is placed on their input-robust nature, which allows them to reveal intrinsic structural properties while eliminating dependence on external excitations. Among the core physical insights presented are the equivalence of local transmissibility functions to modal ratios at system poles, and the convergence of vehicle-induced static local transmissibility to influence line transmissibility at low frequencies. Particularly noteworthy is the role of vehicle-induced long-gauge static strain transmissibility functions, which directly quantify ratios of local bending stiffnesses between monitored regions, demonstrate spatial localization, and support direct stiffness-based diagnostics. By connecting these theoretical principles to the identification algorithms and engineering applications discussed in subsequent chapters, this work supports a shift away from traditional input–output and output-only approaches, toward an output-to-output framework that enables robust structural identification and health monitoring while avoiding excitation measurements and restrictive assumptions regarding excitation characteristics.