Simplified expressions for modelling rigid rocking structures on two-spring foundations

2012 ◽  
Vol 45 (1) ◽  
pp. 31-39 ◽  
Author(s):  
Quincy T. Ma ◽  
John W. Butterworth
Keyword(s):  
Pushover Analysis ◽  
Restoring Force ◽  
Single Degree Of Freedom ◽  
System A ◽  
Prototype Structure ◽  
Time Histories ◽  
Nonlinear Force ◽  
A New Technique ◽  
Force Displacement ◽  
System Geometry

This paper presents a new technique for modelling the dynamic response of uplifting rigid structures subjected to base excitation. The proposed technique exploits the use of a two spring foundation, and subsequently an equivalent single-degree-of-freedom procedure is established to model the dynamics of the system. A set of simplified closed-form expressions have been developed to estimate the system’s restoring force-displacement characteristics. The simplified expressions only require details of the system geometry and are shown to predict the nonlinear force-displacement characteristics of a rocking structure as closely as those determined from a complicated pushover analysis. This paper presents two additional numerical examples to demonstrate the use of the proposed technique to simulate the displacement time-histories of a prototype structure under free-vibration-decay or when subjected to earthquake excitations.

Dynamic Response of Nonlinear Oscillators With Hysteresis

2015 ◽  
Author(s):  
Biagio Carboni ◽  
Walter Lacarbonara
Keyword(s):  
Hysteresis Loops ◽  
Base Excitation ◽  
Response Curves ◽  
Restoring Force ◽  
Single Degree Of Freedom ◽  
Wire Ropes ◽  
Dynamical Behaviors ◽  
Nonlinear Features ◽  
Restoring Forces ◽  
Force Displacement

The nonlinear features of the steady-state periodic response of hysteretic oscillators are investigated. Frequency-response curves of base-excited single-degree-of-freedom (SDOF) systems possessing different hysteretic restoring forces are numerically obtained employing a continuation procedure based on the Jacobian of the Poincaré map. The memory-dependent restoring forces are expressed as a direct summation of linear and cubic elastic components and a hysteretic part described by a modified version of the Bouc-Wen law. The resulting force-displacement curves feature a pinching around the origin. Depending on the hysteresis material parameters (which regulate the shapes of the hysteresis loops), the oscillator exhibits hardening, softening and softening-hardening behaviors in which the switching from softening to hardening takes place above certain base excitation amplitudes. A comprehensive analysis in the parameters space is performed to identify the thresholds of these different behaviors. The restoring force features here considered have been experimentally obtained by means of an original rheological device comprising assemblies of steel and shape memory wire ropes. This study is carried out also with the aim of designing the restoring forces which give rise to dynamical behaviors useful for a variety of applications.

Simulation Method of Soil Resistance on the Pushover Model of Group Pile Foundations

2012 ◽  
Vol 204-208 ◽  
pp. 981-985
Author(s):  
Yong Liang Zhang ◽  
Tian Bao Li
Keyword(s):  
Pile Foundation ◽  
Pushover Analysis ◽  
Simulation Method ◽  
Small Displacement ◽  
Advantages And Disadvantages ◽  
Elasto Plasticity ◽  
Nonlinear Force ◽  
Relationship Of ◽  
Force Displacement ◽  
Group Pile

Soil is a strong non-linear media and show obvious nonlinear under the small displacement of the foundation. Under the strong earthquake, the seismic performance of group pile foundation is closely related to the nonlinear force-displacement relationship of soil around the pile foundation and the elasto-plasticity o fpile. This paper introduces the nonlinear static pushover analysis of group pile foundation , summarizes the commonly used simulation method of soil around the pile foundation and compares the advantages and disadvantages of various simulation method.

Self-Regulating Variable Oil Damper for Structural Response Control

1997 ◽  
Author(s):  
Haruhiko Kurino ◽  
Takuji Kobori
Keyword(s):  
Structural Response ◽  
Maxwell Model ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Structure Model ◽  
Story Structure ◽  
Single Degree Of Freedom ◽  
Random Disturbances ◽  
Nonlinear Force ◽  
Force Displacement

Abstract This paper proposes a simple semi-active control algorithm adopted for a variable damper whose damping coefficient is non-linearly controllable according to the signal. The physical constraint inherently associated with the variable damper expressed in a Maxwell model is taken into consideration for the study. We study a single-degree-of-freedom system under a harmonic excitation by paying attention to the nonlinear force-displacement relation of the device. It is concluded that the variable damper with the proposed algorithm can achieve twice as much damping augmentation as is expected from an ordinary passive damper under non-stationary random disturbances as well as a harmonic excitation. We also study a multi-degree-of-freedom system with the same algorithm and certify its control performance. The effectiveness of the proposed device is clearly seen from the numerical analyses using a 5-story structure model. Because of the nature of the algorithm, it is possible to replace all the complicated signal processor by an auto regulating valve controller housed on the device.

Wave Devouring Propulsion System: From Concept to Trans-Pacific Voyage

2009 ◽  
Author(s):  
Yutaka Terao
Keyword(s):  
Propulsion System ◽  
Roll Motion ◽  
Wave Forces ◽  
Restoring Force ◽  
Hull Form ◽  
System A

In the spring of 2008, the Mermaid II began her historic voyage from Hawaii to Japan. According to the log of the vessel, the journey took 110 days and covered about 7800 km. The successful conclusion of the voyage demonstrated the possibility that Wave Devouring Propulsion System (WDPS) could be adapted to practical use. In order to capitalize on the success of this voyage, the author intended to design and tested a new WDPS hull within a year to build it. A WDPS is a thrust generator for a vessel that converts wave forces directly into forward thrust. Additionally it efficiently reduces hull pitch and roll motion, while also performing as a motion stabilizer. The Mermaid II, which is equipped with a WDPS, incorporates a specially designed catamaran hull form and twin hydrofoil system. A solid hydrofoil system that captures wave forces is set on the underside of the bow of the vessel. Those hydrofoils are connected to the hull with pin joints and are supported by soft springs that provide foil pitch restoring force.

Dynamics of Compliant Risers

1990 ◽  
Vol 34 (02) ◽  
pp. 123-135
Author(s):  
N. M. Patrikalakis ◽  
G. A. Kriezis ◽  
H. N. Gursoy ◽  
T. Maekawa
Keyword(s):  
Three Dimensional ◽  
Small Scale ◽  
Nonlinear Boundary Value Problems ◽  
Restoring Force ◽  
Numerical Solution Method ◽  
Quadratic Drag ◽  
Theoretical Predictions ◽  
Nonlinear Force ◽  
Nonlinear Static ◽  
Three Dimensional Configuration

The objective of this paper is first to formulate the three-dimensional dynamic equations of a compliant riser, idealized as a rotationally nonuniform rod, around a nonlinear static configuration with linearized restoring force and inertial components in the presence of general current and monochromatic wave excitation. Next, to harmonically linearize nonlinear forces such as quadratic drag for the general three-dimensional problem by minimizing the mean square error between the linear approximation and the nonlinear force. Finally, to present an efficient numerical solution method appropriate for nonlinear boundary-value problems with sharp boundary layers such as the problem at hand. Numerical examples and comparisons with time-domain solutions for a catenary riser with a three-dimensional configuration and a steep-wave riser are included. Comparisons of our theoretical predictions with experimental results obtained from a small-scale riser model are also summarized to evaluate our theoretical ability to predict the response of compliant riser systems.

Analysis of a Nonlinear Dynamic Vibration Absorber

1953 ◽  
Vol 20 (4) ◽  
pp. 515-518
Author(s):  
L. A. Pipes
Keyword(s):  
Forced Oscillations ◽  
Vibration Absorber ◽  
Dynamic Vibration Absorber ◽  
Nonlinear Characteristics ◽  
Disturbing Force ◽  
Main Mass ◽  
Dynamic Vibration ◽  
Nonlinear Force ◽  
Linear Spring ◽  
Force Displacement

Abstract This paper presents a mathematical analysis of the action of a dynamic vibration absorber. The system analyzed consists of a main mass attached to a rigid foundation by a linear spring coupled to the absorber mass by a spring of nonlinear characteristics. The forced oscillations of the system produced by a harmonic disturbing force acting on the main mass are studied analytically. It is assumed that the coupling absorber spring has nonlinear force-displacement characteristics of the hyperbolic sine type. Expressions for the amplitudes of the vibrations of the two masses as functions of the frequency of the disturbing force are obtained.

scholarly journals Predicting Maximum and Cumulative Response of A Base-isolated Building Using Pushover Analysis

Buildings ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 91
Author(s):  
Kenji Fujii ◽  
Yoshiyuki Mogi ◽  
Takumi Noguchi
Keyword(s):  
Seismic Design ◽  
Pushover Analysis ◽  
Analysis Method ◽  
Single Degree Of Freedom ◽  
Local Responses ◽  
Single Degree ◽  
Cumulative Response ◽  
Cumulative Strain ◽  
Lead Rubber Bearings ◽  
Rubber Bearings

The evaluation of the maximum and cumulative response is an important issue for the seismic design of new base-isolated buildings. This study predicts the maximum and cumulative response of a 14-story reinforced concrete base-isolated building using a set of pushover analyses. In the proposed pushover analysis method, the maximum and cumulative responses of the first and higher modes are evaluated from the nonlinear analysis of equivalent single-degree-of-freedom (SDOF) models. Then, the maximum local responses are predicted by enveloping the two pushover analysis results by referring to the contribution of the first and higher modal responses, while the cumulative strain energies of the lead-rubber bearings and steel dampers are predicted from the cumulative response of the first mode. The results reveal that the responses predicted by the proposed set of pushover analyses have satisfactory accuracy.

An Approximate Method for the Dynamic Analysis of Elastic Linkages

1977 ◽  
Vol 99 (2) ◽  
pp. 449-455 ◽  
Author(s):  
A. Midha ◽  
A. G. Erdman ◽  
D. A. Frohrib
Keyword(s):  
Exact Analytical Solution ◽  
Equations Of Motion ◽  
Numerical Procedure ◽  
Degree Of Freedom ◽  
Suggested Approach ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
System A ◽  
Suggested Technique ◽  
Particular Solution

A new numerical procedure based on an iterative technique is progressively developed in this paper for obtaining an approximate particular solution from the equations of motion of an elastic linkage with small damping and at subresonant speeds. The method is introduced by employing a simple vibrating system, a single degree-of-freedom mass-dashpot-spring model under both harmonic forcing and periodic forcing. A harmonically excited two degree-of-freedom model is also solved by the suggested approach. Error functions are developed for each case to give an estimation of the order of error between the exact analytical solution and the approximate technique. The suggested technique is then extended to solve an elastic linkage problem where the uncoupled equations of motion are treated as a series of single degree-of-freedom problems and solved. These are retransformed into the physical coordinate system to obtain the particular solution. The first and second derivatives of the forcing functions (involving rigid-body inertia) are approximated utilizing the finite difference method.

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