Examine the concept of dynamic response analysis in structural engineering, particularly focusing on its significance in assessing the seismic vulnerability of infrastructure. Investigate the fundamental principles underlying dynamic response analysis methods, including finite element analysis, modal analysis, and response spectrum analysis. Delve into the intricate interplay between structural dynamics and seismic forces, elucidating how structural properties such as stiffness, damping, and mass distribution influence a structure's behavior during seismic events. Furthermore, explore advanced computational techniques utilized in dynamic response analysis, such as time$-$history analysis and nonlinear modeling, to capture the complex nonlinear behavior of structures subjected to seismic loading. Critically evaluate the strengths and limitations of dynamic response analysis methodologies in predicting structural responses under seismic excitation, considering factors like model fidelity, computational efficiency, and practical applicability. Finally, discuss emerging trends and future directions in dynamic response analysis research aimed at enhancing the seismic resilience of civil infrastructure.