Modern Engineering and Physical Sciences are strongly dependent on computational power. Mathematical models are becoming increasingly more sophisticated and high order, able to characterize complex dynamical interactions with high precision. However, this growing dependence on computational power has a high cost. It is of great importance to work on the simplification of high-fidelity, high-order complex models, allowing us to characterize the most important dynamical behaviours with feasible computational resources.

Mathematical modelling and control of nonlinear dynamical phenomena in structural systems and other complex multibody mechanisms, including the dimensionality of the nonlinear systems, can be considered as a measure of complexity. Additionally, nonlinear systems with memory are characterized by long transients which strongly influence the dynamics identification control procedure. This memory effect is frequently observed as a hysteretic behaviour, appearing as additional degrees of freedom, and is frequently modelled with fractional derivatives. On the other hand, material, structural, and multibody interaction nonlinearities can lead to localized effects which increase the system complexity, but the particular response of the dynamical system can be described by a size reduced model.

In this context, the aim of this Special Issue is to discuss the general problem of model size reduction for describing nonlinear vibration of structural elements and systems. The aim is also to provide and analyse tools that allow accurate capturing of nonlinear dynamic behaviour using a minimal number of degrees of freedom. Papers describing original theoretical research as well as new experimental results are desired. Original research and review articles are welcome.

Potential topics include but are not limited to the following:

• Nonlinear dynamical phenomena in structural systems
• Nonlinear systems with memory (fractional order model)
• Nonlinear mode interaction
• Nonlinear vibration of structural elements and systems
• Synchronization phenomenon
• Dynamics identification control procedure
• Nonlinear normal modes
• Energy transfer
• Stability of slender structures in the main resonance regions
• Experimental results
• Data acquisition and actuator response time-delays in the design process of the reduced-order controller
• Wavelet spectrum
• Multiple-model predictive controller (mMPC)