Dynamic Modeling And Characteristic Analysis Of Origami Structure Based On Transfer Matrix Method

Because the origami structure can be programmable,change shape,change topology,and induce ultra-conventional mechanical properties through folding changes,it has become a hot research topic in the field of physics and engineering in recent years.Origami structures and origami metamaterials have good application prospects in many fields such as robotics,aerospace,vehicle transportation,medical equipment,etc.,such as aerospace folding structures,reconfigurable folding robots,and transport vibration damping protection.Origami structures are subject to dynamic loads in engineering applications,but most of the current research focuses on the structural,kinematics and statics of origami structures,and there is less research on the dynamics of origami structures.The dynamic study of origami structures begins with the solution of how to build a dynamic model that reflects its dynamic behavior.Taking several classical origami structures as an example,this paper explains how to establish an origami structure dynamic model base on the transfer matrix method and analyze its dynamic performance,the main contents are as follows:A method for establishing a dynamic model of tubular origami structure is proposed.In order to establish a dynamic model of the tubular origami structure,according to the assumption of rigid folding,the spatial truss model of the tubular origami structure is simplified to the rod and hinge model,and the deformation of the torsional hinge equivalent crease is adopted,and the crease surface adopts the member equivalent.Based on this simplified model,the mechanical properties of tubular origami structural elements are described using a transfer matrix.According to the connection relationship of the tubular origami structure,it is regarded as a series of multiple folding units,and its transmission matrix is derived by using the equivalent model,and the transfer equation of the tubular origami structure is obtained by using the transfer matrix method,and its inherent vibration characteristics are obtained by combining the boundary conditions;the external force is incorporated into the transmission equation to obtain the dynamic response equation of the tubular origami structure under external excitation,and the simple and harmonious response of any point in the tubular origami structure can be obtained by using the boundary condition.Based on the established model,the natural frequency and frequency response of the two studies are analyzed,and through the comparative analysis with the finite element simulation,the established model can accurately reflect the dynamic performance of the tubular origami structure.In order to establish a dynamic model of the Miura origami structure,the mass of its crease surface is consolidated at its apex,the crease can be regarded as a massless spring,and the Miura origami structural unit can be regarded as a single degree of freedom spring-mass system.According to the connection form of Miura origami structural units,the Miura origami structure is divided into series and parallel types,and the transfer matrix of Miura origami structural units is derived by using the equivalent model of folding units,and the transfer matrix equation of tandem and parallel Miura origami structures is established by using the transfer matrix method.Combined with its boundary conditions to solve the natural frequency,compared with the finite element simulation,the accuracy of the established model is verified.The external excitation force is incorporated into the transmission matrix of the Miura origami unit,and the dynamic response equation of the system is obtained,and the frequency response of the Miura origami structure can be solved.In order to reflect the dynamic behavior of the origami structure more accurately,the deformation of the crease surface is considered,and the bending and torsional deformation of the crease surface is simulated during the folding process by using an elastic beam.According to the idea of the transfer matrix method,taking the accordion origami structure as an example,its elements are equivalent to elastic beams and torsional hinge structures,and its transfer matrix model is established.The results show that the model established by non-rigid folding can more accurately reflect the mechanical properties of origami structure than the model under the rigid assumption.Based on this dynamic model,the influence of accordion origami structural parameters on its dynamic performance is analyzed.The analysis results show that the initial folding angle of the origami structural unit is in the range of 0 ° to 120 °,the crease surface is almost unchanged,and the crease surface only performs folding movement around the crease;when the initial folding angle is greater than 120 °,the crease surface of the origami structure will be bent and deformed.This means that the origami structure will show different mechanical properties in different folding states.