Modified transfer matrix method for vibration analysis of beam structures including branches and rigid bodies

Beam frames can be found in many application scenarios, ranging from big-scale structure en-gineering of buildings, bridges to small systems of micromachines, sensors, robotics and meta-materials. However, several challenging issues, e.g. serial-parallel configurations, beam and rigid body coupling along with inconsistent dimension of state variables, often lead to a complicated dynamic modeling. In this paper, we show that the free vibration analysis of a class of beam structures with serial-parallel branches and rigid bodies can be significantly streamlined by modifying the transfer matrix method in a graphic manner. Treating general beam structures as a topological graph with standard building blocks enables a modular modeling process and hence offers a new way to divide the complex modeling issue into much easier steps. The transfer matrix of typical building blocks, such as a beam connected to rigid bodies, tree branches and parallel clamped sub-chains, are derived and standardized providing new perspectives and distinct forms in contrast to previous studies. The transfer matrix method exhibits several advantages of easy programming, accurate solution and small degrees-of-freedom for serial structures. The presented approach extends these characteristics to a range of multi-body systems consisting of rigid bodies and beams. Comparative validation with four application case studies confirms these advantages.

Automated summary

This paper presents a method to simplify the free vibration analysis of beam structures by modifying the transfer matrix method. Treating beam structures as topological graphs and deriving and standardizing the transfer matrix of typical building blocks makes the complex modeling problem easier to solve. Comparative validation with practical case studies confirms the advantages of this method.