In structural dynamics, the inertia of accelerated masses and the cornucopia of phenomena that contribute to damping have a significant influence on the internal forces and deformation of building structures. Typical problems of structural dynamics are the prediction of the vibration response of dynamically excited structures, for instance, induced by earthquakes, the identification of structural parameters based on the dynamic response, and the design of vibration-mitigating measures from the fundamental study to the implementation. Many traditional methods of structural dynamics and earthquake engineering are based on empirical approaches rather than rigorous application of fundamental mechanical principles. However, dramatic advances in mechanics now make it increasingly possible not only to model but also to solve and predict complex phenomena in dynamics. We are very pleased that, in response to these advances, this special issue of Acta Mechanica provides an insight into the latest mechanics-based developments in various branches of structural dynamics and earthquake engineering. It contains 20 contributions that we selected based on the reactions and feedback we received to our invitation.The first four papers deal with complex dynamic vehicle-bridge interaction (VBI). In the first paper, Homaei et al. [1] investigate the effect of VBI and highlight its similarities and differences to the effect of vibration dampers under earthquake excitation. Based on knowledge of recent experimental studies, König and Adam [2] present a new modeling approach for railway bridges under high-speed traffic, which takes into account both the horizontal and vertical interaction between track and structure. Hirzinger and Nackenhorst [3] apply a model-correction-based strategy for efficient reliability analysis of the uncertain VBI system, where a low-fidelity model is calibrated to the corresponding high-fidelity model close to the most probable point. The paper of Lei et al. [4] proposes a two-step bridge damage detection method based on wavelet transform analysis of the residual contact response of the moving front and rear vehicle wheels to reduce the impact of road surface roughness.Suitably, the next paper by Yang et al.[5] uses a numerical model based on the wave finite element method of wave propagation and attenuation in periodic supported rail, capturing the complex cross-section deformation of the waves. Changing topics away from railways, Amendola et al. [6] also seek a waveform solution but of nonlocal nanobeams dissipating thermal energy by radiation, employing an extension of Type II Green-Naghdi theory. The paper by Abdelnour and Zabel [7] is devoted to the identification of the modal information of complex three-dimensional space truss structures characterized by closely spaced modes as well as global and local vibration mechanisms. Pirrotta and Russotto [8], on the other hand, develop a new
