Adjustable vertical vibration isolator with a variable ellipse curve mechanism

This paper presents a passive vertical quasi‐zero‐stiffness vibration isolator intended for relatively small objects. The present isolator has features of compactness, long stroke, and adjustability to various load capabilities. To realize these features, we use constant‐force springs, which sustain constant load regardless of their elongation, and propose a variable ellipse curve mechanism that is inspired by the principle of ellipsographs. The variable ellipse curve mechanism can convert the restoring force of the horizontally placed constant‐force springs to the vertical restoring force of the vibration isolator. At the same time as converting the direction, the vertical restoring force can be adjusted by changing the ratio of the semi‐minor axis to the semi‐major one of the ellipse. In this study, a prototype of a class of quasi‐zero‐stiffness vibration isolator with the proposed variable ellipse curve mechanism is created. Shaking table tests are performed to demonstrate the efficacy of the present mechanism, where the prototype is subjected to various sinusoidal and earthquake ground motions. It is demonstrated through the shaking table tests that the prototype can reduce the response acceleration within the same specified tolerance even when the mass of the vibration isolated object is changed. Copyright © 2017 John Wiley & Sons, Ltd.     

Criteria for assessing dynamic collapse of elastoplastic structural systems

Criteria are presented for assessing the propensity for dynamic collapse of elastoplastic structural systems. To detect the onset of dynamic collapse, three key concepts are introduced. First, the equations of motion are linearized and time shifted relative to a reference time in a dynamic process. Second, we study the free vibration of the system after the reference time. Third, we use a modal decomposition of the response. We suggest that dynamic collapse is likely if (1) there exist negative eigenvalues of the Hessian of the total potential energy and (2) the direction of motion is consistent with the loading direction of the elastoplastic material. The direction of motion is determined by using the gradient of total potential energy and the eigenmodes corresponding to the negative eigenvalues. The fidelity of the present criteria is demonstrated through numerical examples for which the non‐linear equations of motion can be integrated exactly. With the present approach, it becomes apparent that p‐delta effects, the tangent stiffness, the internal resistance, and the direction of unloading all play key roles in the dynamic collapse of structures. Copyright © 2000 John Wiley & Sons, Ltd.