Stability of Isolators at Large Horizontal Displacements

1997 ◽  
Vol 13 (3) ◽  
pp. 415-430 ◽  
Author(s):  
Maura Imbimbo ◽  
James M. Kelly
Keyword(s):  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Closed Form Expression ◽  
Elastic Analysis ◽  
Form Expression ◽  
Elastomeric Bearings ◽  
Post Buckling ◽  
Link Model ◽  
The Stability ◽  
Horizontal Displacements

Elastomeric bearings used as seismic isolators are susceptible to a buckling type of instability similar to that of structural columns. The buckling load and buckling behaviour can be determined from an elastic analysis of the isolator modelled as a continuous composite column with bending and shear flexibility; this analysis cannot be used, however, to assess the post-buckling behaviour or the stability of the isolator at large horizontal displacements. By using a two-spring rigid link model that considers large angles without using linear approximations, it is possible to predict the post-buckling behaviour of an isolator. Using the simple closed form expression, this paper will model three aspects of post-buckled isolator behaviour: the dependence of horizontal stiffness on vertical load, the stability at large horizontal displacements, and the increase of horizontal displacement with respect to axial load and vertical displacement.

A Generalized Hill’s Method for the Stability Analysis of Parametrically Excited Dynamic Systems

1982 ◽  
Vol 49 (1) ◽  
pp. 217-223 ◽  
Author(s):  
S. T. Noah ◽  
G. R. Hopkins
Keyword(s):  
Stability Analysis ◽  
Dynamic Systems ◽  
Absolute Convergence ◽  
General System ◽  
Closed Form Expression ◽  
Form Expression ◽  
Null Solution ◽  
Hill’S Method ◽  
The Stability ◽  
Pulsating Fluid

A method is described for investigating the stability of the null solution for a general system of linear second-order differential equations with periodic coefficients. The method is based on a generalization of Hill’s analysis and leads to a generalized Hill’s infinite determinant. Following a proof of its absolute convergence, a closed-form expression for the characteristic infinite determinant is obtained. Methods for the stability analysis utilizing different forms of the characteristic determinant are discussed. For cases where the instabilities are of the simple parametric type, a truncated form of the determinant may be used directly to locate the boundaries of the resonance regions in terms of appropriate system parameters. The present generalized Hill’s method is applied to a multidegree-of-freedom discretized system describing pipes conveying pulsating fluid. It is demonstrated that the method is a flexible and efficient computational tool for the stability analysis of general periodic systems.

Design and Prototype of a Two-Axis Acoustic Levitator

2016 ◽  
Author(s):  
Justin Clough ◽  
Michael W. Sracic ◽  
Daniel Piombino ◽  
Jonathan Braaten ◽  
Scott Connors ◽  
...  
Keyword(s):  
Water Droplet ◽  
Vertical Direction ◽  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Test Stand ◽  
Frame Structure ◽  
Particle Stability ◽  
The Stability ◽  
Adequate Power ◽  
Acoustic Levitator

The purpose of this paper is to document the process required to design and prototype a two-axis acoustic levitator and to show that the two-axis levitator improves the stability of a particle in an acoustic levitation field. The levitator design consists of the following subsystems: the transducer assemblies, which are responsible for generating the acoustic pressure field needed for levitation; the electrical system, which is responsible for providing the transducer assemblies with adequate power to maintain levitation; and the frame structure, which is responsible for locating and rigidly supporting the transducer assemblies. The two-axis levitator is designed to have four transducers that operate at 27.2 kHz, and simulated results show that the system satisfies nearly all the design criteria and objectives. A transducer test stand and prototype were constructed to verify the design. The test stand was used to characterize all four transducers, and once the assembly was constructed the prototype operating frequency was determined to be 27.5 kHz. The prototype was used to successfully levitate Styrofoam pellets, a plastic pellet, and water droplets of various sizes. The displacement of a water droplet of approximately 1 mm in diameter was measured when levitated with both one-axis (vertical) and two-axis (vertical and horizontal) levitation. Using one-axis levitation, the water droplet displaced a maximum of 1.1 mm in the horizontal direction and 0.17 mm in the vertical direction. Using two-axis levitation, the horizontal displacement was 0.07 mm and the vertical displacement was 0.05 mm. Therefore, the two-axis acoustic levitator provides significant improvements in levitated particle stability.

scholarly journals The Integration of Two Interferometric Radars for Measuring Dynamic Displacement of Bridges

2021 ◽  
Vol 13 (18) ◽  
pp. 3668
Author(s):  
Piotr Olaszek ◽  
Andrzej Świercz ◽  
Francesco Boscagli
Keyword(s):  
Longitudinal Vibration ◽  
Experimental Tests ◽  
Horizontal Displacement ◽  
Vertical Displacement ◽  
High Accuracy ◽  
Vertical Vibration ◽  
Remote Measurement ◽  
Railway Bridges ◽  
Vertical Displacements ◽  
Horizontal Displacements

Measurements of displacements of bridges under dynamic load are particularly difficult in the case of structures where access to the area under the tested structure is impossible. Then, remote measurement methods are preferred, such as interferometric radar. Interferometric radar has high accuracy when measuring displacement in the direction of its target axis. The problems appear when a bridge vibrates in two directions: horizontal (lateral or longitudinal) and vertical. The use of one radar to measure those vibrations may be impossible. This paper presents the application of a set of two interferometric radars to measure vertical vibration and horizontal longitudinal vibration with high accuracy. The method was positively verified by experimental tests on two railway bridges characterized by different levels of horizontal displacement. The accuracy of the radar measurements was tested by the direct measurement of vertical displacements using inductive gauges. In conclusion, in the case of vertical displacement measurements using one interferometric radar, the influence of horizontal displacements should be excluded. In the case of locating radars at the area of bridge supports, it is necessary to either use a set of two radars or first investigate the magnitude of possible horizontal displacements in relation to vertical displacements.

scholarly journals Parameter optimization of double side wall method for soft surrounding rock tunnel

2019 ◽  
Vol 136 ◽  
pp. 04021
Author(s):  
Zhihua Yang ◽  
Rumiao He ◽  
Ke Li ◽  
Hongyan Guo
Keyword(s):  
Side Wall ◽  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Surrounding Rock ◽  
Radius Of Curvature ◽  
Tunnel Excavation ◽  
The Stability ◽  
Rock Tunnel ◽  
Double Wall ◽  
Wall Method

When the Xiaojiazhai tunnel is constructed by the double-wall method, different curvature radii have different effects on controlling the stability of the surrounding rock and speeding up the construction progress. By numerically simulating the tunnel excavation under different radius of curvature, it is concluded that R is adopted respectively. The deformation displacement of surrounding rock is =11.6m∠520 and R=5.76m∠1060. The maximum horizontal displacement and vertical displacement are smaller when R=5.76m∠1060 is selected. According to the analysis results, when R=5.76m∠1060 is selected, the deformation of surrounding rock can be controlled to ensure the safety of construction and provide reference for future construction.

Investigation of an algorithm for analyzing deformations of geodetic points when observing horizontal displacements of hydraulic structures

2017 ◽  
Vol 925 (7) ◽  
pp. 23-30
Author(s):  
Yu.I. Markuze ◽  
Anh Cuong Le
Keyword(s):  
Personal Computer ◽  
Horizontal Displacement ◽  
Hydraulic Structures ◽  
Huge Number ◽  
Geodetic Measurements ◽  
The Stability ◽  
Horizontal Displacements

In recent years, many hydraulic structures have been modernized and built in Vietnam. Monitoring the deformations of hydraulic structures are extremely important. The results of observations of deformations to assess the stability and safety of structures help specialists make the process of construction and reconstruction of hydraulic structures more reliable and safe. At present, a personal computer is very widely used in processing the results of geodetic measurements. By using algorithms on a computer, we can simply and quickly solve problems with a huge number of calculations. The article deals with the application of a recurrent way of equalizing for the analysis of deformations of geodetic points when observing horizontal displacement of hydraulic structures in Vietnam. The use of the proposed algorithm in this article is conveniently implemented in practical calculations using a computer. The result of the calculation of the example indicates that combining the observation cycles to increase the accuracy of the observed items.

A Study on the Influence by Karst on the Stability of Surrounding Rock in Neighborhood Tunnel

2012 ◽  
Vol 446-449 ◽  
pp. 2177-2181 ◽  
Author(s):  
Cheng Wang ◽  
Xiao Qiang Pi
Keyword(s):  
Side Wall ◽  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Surrounding Rock ◽  
Tunnel Construction ◽  
Stability Of Surrounding Rock ◽  
Vertical Displacements ◽  
The Stability ◽  
Selection Of

Based on the Shuangbei tunnel, this paper studied influences on the deformation and stress of surrounding rock, regarding different Karst sizes and locations in such a neighborhood tunnel. The study indicates that variations of size and distance of the karst have prominent influence on the vertical displacements of vault and right side-wall in the tunnel near the karst, but have no influence on the horizontal displacement; while variation of karst size has prominent influence not only on the horizontal displacement, but also on the vertical displacement at the bottom of the tunnel far away from the karst; variations of size and distance of the karst have the prominent influence on the vault stress of the two tunnels. The results offer the reference to the tunnel construction and the selection of support type.

Further Results on the Stability of Viscoelastic Columns

1987 ◽  
Vol 11 (3) ◽  
pp. 179-194
Author(s):  
W. Szyszkowski ◽  
P.G. Glockner
Keyword(s):  
Element Model ◽  
Static Stability ◽  
Model Material ◽  
Constitutive Law ◽  
Time Dependent ◽  
Closed Form Expression ◽  
Solution Technique ◽  
Arbitrary Boundary ◽  
Post Buckling ◽  
The Stability

Recent results published by the authors on the stability behaviour of columns made of time-dependent materials are extended in a number of ways. Firstly, the closed-form expression obtained for the safe load limit of a simply supported column made of a linear three-element model material, is generalized for an arbitrary linearly viscoelastic constitutive law. The result, obtained by means of the static stability approach, is confirmed by an asymptotic solution of the dynamic stability equations. The same solution technique is used to generalize this expression for columns with arbitrary boundary conditions. Even though columns as structural members exhibit stable post-buckling behaviour, there are structural configurations, involving compression members, the overall load deflection behaviour of which indicate unstable post-buckling characteristics. A simple example is used to alert the designer to the possibility of encountering such configurations and the danger associated with such post-buckling behaviour in the case of structures made of time-dependent materials.

Optimization of the Control Function for a Footless Biped in a Stationary, Upright Posture

1987 ◽  
Author(s):  
M. S. Hsu ◽  
M. De Spain ◽  
J. Shaw ◽  
M. Mulder ◽  
N. Wagner
Keyword(s):  
Optimal Control ◽  
Closed Form ◽  
Sagittal Plane ◽  
Control Function ◽  
Closed Form Expression ◽  
Upright Posture ◽  
Numerical Techniques ◽  
Form Expression ◽  
Stability Range ◽  
The Stability

Abstract The stability of a footless biped in a stationary, upright posture is studied on the sagittal plane using two and three link models. Closed form expression of the stability range for the control gains is derived from Routh-Hurwitz criteria. Evaluation and optimization of the multiple gain systems are realized using statistical and numerical techniques. The optimal control gains are obtained and the gain-locus is derived. The algorithm for optimizing the control function is provided and several numerically derived examples are illustrated.

Collocated Position Control of Oscillatory System in Presence of Delay

2020 ◽  
Author(s):  
Bence Szaksz ◽  
Gabor Stepan
Keyword(s):  
Time Delay ◽  
Position Control ◽  
Critical Time ◽  
Oscillatory System ◽  
Constant Time Delay ◽  
Closed Form Expression ◽  
Pd Controller ◽  
Governing Equations ◽  
Form Expression ◽  
The Stability

Abstract The stability of the collocated position control of a mass is studied when a pendulum is attached to it. The simplest proportional-derivative (PD) controller is applied, but the relevant constant time delay is taken into account. The linearized governing equations of the system are investigated. Stability charts are constructed for different pendulum parameters. Closed form expression is derived for the critical time delay; for delay values larger than the critical one, the PD controller cannot stabilize the desired position of the mass. The frequencies of the self-excited vibrations at the stability boundaries have essential role in identifying the types of loss of stability.

Elastic Buckling and Post-Buckling of Von Mises Planar Trusses

2015 ◽  
Vol 769 ◽  
pp. 49-54
Author(s):  
Martin Kalina ◽  
Zdenek Kala ◽  
Petr Frantik
Keyword(s):  
Vertical Displacement ◽  
Mathematical Concept ◽  
Structural Deformation ◽  
Incremental Method ◽  
Critical Effect ◽  
Post Buckling ◽  
Load Action ◽  
The Stability ◽  
The Moment ◽  
Von Mises

The article deals with the computational model of an elastic von Mises planar truss. The description of a mathematical concept, which is intended for the creation of computational programmes based on a finite number of segments, is presented. The mathematical solution is suitable for the analysis of load-deflection curves. Structural deformation is evaluated by seeking the minimal potential energy. The article examines the effects of change in the vertical displacement of the top joint on strut axes. The step by step incremental method is used in combination with the Newton-Raphson method. The presented study is aimed at the evaluation of the force in the bifurcation point, which determines the moment when loading of the model causes passing from the pre-critical effect (attainment of maximum vertical load action) to the post-critical effect. Symmetric and asymmetric initial axis imperfections are considered and relevant symmetric and asymmetric shapes of buckling are identified. The stability problem of the von Mises truss is discussed in connection with the random effects of imperfections.

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