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

• Published in: Mechanical systems and signal processing 2023-03, Vol.187, p.109858, Article 109858
• Main Authors: Ling, Mingxiang, Yuan, Lei, Zhou, Hao, Ning, Minliang
• Format: Article
• Language: English
• Subjects: Beam frames with rigid body; Dynamic stiffness matrix; Multi-body dynamics; Transfer matrix method
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2022.109858

[Display omitted] •Transfer matrix method is improved for beam structures with branches and rigid bodies.•Transfer matrix of beams with rigid bodies, tree branches and parallel sub-chains are derived.•Dynamic stiffness and transfer matrix methods are combined for analyzing beam structures.•Vibration analysis of beams carrying spring-mass systems is concisely achieved.•Vibration analysis of multi-body systems consisting of rigid bodies and beams is concisely achieved. Beam frames can be found in many application scenarios, ranging from big-scale structure engineering of buildings, bridges to small systems of micromachines, sensors, robotics and metamaterials. 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.