Nonlinear restoring force model of a circular ring based on the beam constraint model

Subjects: Mechanics >> Other Disciplines of Mechanics submitted time 2024-06-17 Cooperative journals: 《应用力学学报》

HAN Wenju

Abstract： The circular ring vibration isolator is a nonlinear vibration isolator based on a circular ring structure.The circular ring produces a nonlinear restoring force due to the coupling of the tension and the curvature caused by stretching.The key to studying the performance of the vibration isolator is the accurate modeling of the nonlinear restoring force of the circular ring.In this paper,the circular ring structure is equally divided into several segments of curved beams.The force-displacement relationship model considering geometric nonlinearity is established for each segment of the curved beam using the beam constraint model.Combined with the force transfer relationship and geometric constraint relationship between curved beams,the nonlinear restoring force model of the whole circular ring during the compression process is established.The normal stress at all segment points during the deformation of the circular ring can be calculated via the beam constraint model.The restoring force of the circular ring structure in the compression process is measured by an electronic servo fatigue testing machine,and the modeling accuracy of the beam constraint model is verified.The research results show that the nonlinear restoring force characteristics of the circular ring can be characterized by the beam constraint model.The modeling accuracy of the beam constraint model is comparable to that of the elliptic integration method,but the model expression and solution process are simpler than those of the elliptic integration method.When the compression of the circular ring is the largest,the normal stress is the largest,and the maximum normal stress is obtained at the upper and lower end points of the circular ring.The modeling accuracy of the beam constraint model increases with the increase of the number of segments.When the number of segments is greater than 12,the restoring force calculation error of the beam constraint model is less than 2%.

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