Development of a new analytical tool to design hierarchical truss beams for natural frequency

A set of recursive equations are introduced for optimum design of a wide range of hierarchical truss beams to satisfy a minimum required natural frequency. The design equations are based on a general analytical solution, which are derived based on a critical dimensional analysis. A practical example is examined in both 2D and 3D spaces, which promises substantial mass reduction, as much as 99%, when using high order hierarchical truss beams. The results are verified by numerical evaluation of three case studies. The approach looks also very promising to design nanostructures when it comes to the problems associated with vibration.