In this book, regular structures are de ned as periodic structures consisting of repeated elements (translational symmetry) as well as structures with a geom- ric symmetry. Regular structures have for a long time been attracting the attention of scientists by the extraordinary beauty of their forms. They have been studied in many areas of science: chemistry, physics, biology, etc. Systems with geometric symmetry are used widely in many areas of engineering. The various kinds of bases under machines, cyclically repeated forms of stators, reduction gears, rotors with blades mounted on them, etc. represent regular structures. The study of real-life engineering structures faces considerable dif culties because they comprise a great number of working mechanisms that, in turn, consist of many different elastic subsystems and elements. The computational models of such systems represent a hierarchical structure and contain hundreds and thousands of parameters. The main problems in the analysis of such systems are the dim- sion reduction of model and revealing the dominant parameters that determine its dynamics and form its energy nucleus. The two most widely used approaches to the simulation of such systems are as follows: 1. Methods using lumped parameters models, i.e., a discretization of the original system and its representation as a system with lumped parameters [including nite-element method (FEM)]. 2. The use of idealized elements with distributed parameters and known analytical solutions for both the local elements and the subsystems.

In this book, regular structures are de ned as periodic structures consisting of repeated elements (translational symmetry) as well as structures with a geom- ric symmetry. Regular structures have for a long time been attracting the attention of scientists by the extraordinary beauty of their forms. They have been studied in many areas of science: chemistry, physics, biology, etc. Systems with geometric symmetry are used widely in many areas of engineering. The various kinds of bases under machines, cyclically repeated forms of stators, reduction gears, rotors with blades mounted on them, etc. represent regular structures. The study of real-life engineering structures faces considerable dif culties because they comprise a great number of working mechanisms that, in turn, consist of many different elastic subsystems and elements. The computational models of such systems represent a hierarchical structure and contain hundreds and thousands of parameters. The main problems in the analysis of such systems are the dim- sion reduction of model and revealing the dominant parameters that determine its dynamics and form its energy nucleus. The two most widely used approaches to the simulation of such systems are as follows: 1. Methods using lumped parameters models, i.e., a discretization of the original system and its representation as a system with lumped parameters [including nite-element method (FEM)]. 2. The use of idealized elements with distributed parameters and known analytical solutions for both the local elements and the subsystems.

This black comedy marks the debut feature of television director Ben Wheatley. When they are released from jail after doing time for an unspecified crime, gangster father and son, Bill (Robert Hill) and Karl (Robin Hill), become obsessed with identifying the police informant whom they are convinced is in their midst. Meanwhile, the family business looks set to implode as suspicions grow between the various shady characters operating out of Down Terrace.