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.

Influence of Mullins and hardening effects of seismic isolation rubber bearings on the seismic response

2021 ◽  
Author(s):  
Hiroshi Shimmyo ◽  
Tolga Onal ◽  
Shozo Nakamura ◽  
Kazuya Tokunaga
Keyword(s):  
Seismic Response ◽  
Seismic Isolation ◽  
Hysteresis Loops ◽  
Highway Bridges ◽  
Restoring Force ◽  
Two Factors ◽  
Product Test ◽  
Rubber Bearings ◽  
Isolated Bridges ◽  
Force Displacement

<p>In the current Specifications for Highway Bridges of the Japan Road Association, a bilinear force- displacement relationship is recommended as the hysteresis loops of the seismic isolation rubber bearings for the dynamic structural analysis of seismically isolated bridges. However, it has been confirmed that the restoring force characteristics of the actual devices are different from the bilinear model due to the Mullins effect and the hardening phenomenon of the rubber under large shear strains. In this study, the effect of these two factors on the seismic response of a bridge is investigated through the dynamic analysis with the tri-linear double target model considering the factors. The parameters of the model are obtained from product test results of lead-plugged laminated rubber bearings and high-damping laminated rubber bearings.</p>

Periodic and Nonperiodic Thermomechanical Responses of Shape-Memory Oscillators

2001 ◽  
Author(s):  
Walter Lacarbonara ◽  
Davide Bernardini ◽  
Fabrizio Vestroni
Keyword(s):  
Shape Memory ◽  
Numerical Procedure ◽  
Period Doubling ◽  
Hysteresis Loops ◽  
Response Curves ◽  
Restoring Force ◽  
Codimension One ◽  
Nonlinear Responses ◽  
Gradient Based ◽  
The Stability

Abstract Nonlinear responses of shape-memory oscillators are investigated systematically using a numerical procedure and a modified Ivshin-Pence model for the restoring force. Due to the discontinuities in the tangent stiffness, classical gradient-based shooting techniques for determining periodic responses are not applicable. Herein the implemented algorithm searches the periodic solutions as fixed points of the Poincaré map. The Jacobian of the map is calculated via a central finite-difference scheme and its eigenvalues are computed to ascertain the stability of the solutions and the associated codimension-one bifurcations. A number of frequency-response curves are constructed for some meaningful shape-memory oscillators (characterized by different hysteresis loops) and for various excitation levels in the primary and superharmonic frequency ranges. The investigations are conducted both in isothermal and non-isothermal conditions. A rich class of solutions and bifurcations — including jump phenomena, pitchfork, period doubling, complete or incomplete bubble structures with a variety of nonperiodic responses — is found and discussed.

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.

An M-Shaped Asymmetric Nonlinear Oscillator for Broadband Energy Harvesting

2013 ◽  
Author(s):  
S. Leadenham ◽  
A. Erturk
Keyword(s):  
Energy Harvesting ◽  
Nonlinear Oscillator ◽  
Mechanical Load ◽  
Nonlinear Behavior ◽  
Base Excitation ◽  
Lumped Mass ◽  
Response Curves ◽  
Restoring Force ◽  
Bandwidth Enhancement ◽  
Shaped Beam

Nonlinear oscillators have been given growing attention due to their ability to enhance the performance of energy harvesting devices by increasing the frequency bandwidth. Duffing oscillators are a typical type of nonlinear oscillator characterized by a symmetric hardening or softening cubic restoring force. In order to realize the cubic nonlinearity in a cantilever at reasonable excitation levels, often an external magnetic field or mechanical load is imposed, since the inherent geometric nonlinearity would otherwise require impractically high excitation levels to be pronounced. As an alternative to magnetoelastic structures and other forms of symmetric Duffing oscillators, in this paper, an M-shaped bent beam with clamped end conditions is investigated for bandwidth enhancement under base excitation. The M-shaped beam geometry can exhibit significantly asymmetric spring behavior: hardening in one direction and softening in the other. A particular advantage of the M-shaped structure is its well-pronounced nonlinear characteristics without needing an external component to create hardening or softening. The force-displacement relationship of the M-shaped beam with a central lumped mass attachment is experimentally identified and asymmetric nonlinear behavior is verified. The purely elastic system parameters (such as the linear and nonlinear stiffness components) identified from the experiments are used in numerical simulations and compared with the experimental results. A quadratic damping term is included to account for nonlinear dissipative effects. Bandwidth enhancement with increasing base excitation is investigated experimentally and numerically. Very good agreement is observed between the simulated frequency response curves and experimental measurements.

Analysis of Maximum Elasto-Plastic Response of Multi-Degree-of-Freedom Oscillators Based on a Modal Combination of Equivalently Linearized Response of Each Mode

2016 ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Hiroki Nishiraku ◽  
Yusuke Ono
Keyword(s):  
Analytical Method ◽  
Degree Of Freedom ◽  
Base Excitation ◽  
Plastic Response ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linearized System ◽  
Plastic Displacement ◽  
Relationship Of ◽  
Force Displacement

This study develops a new analytical method for evaluating maximum elasto-plastic displacement of multi-degree-of-freedom (MDOF) oscillators under the action of base excitation based on a modal combination. The essence is that modal frequencies, shapes and damping during yielding of any member of the MDOF oscillators are readily specified by the modal analysis with the secondary stiffness of the members being yielded. In addition, assuming that a bilinear hysteresis may describe the force-displacement relationship of each mode, an equivalently linearized system consisting of a single-degree-of-freedom (SDOF) oscillator is introduced to approximate maximum elsato-plastic displacement of each mode. Employing the SRSS-rule, the maximum elasto-plastic displacement of the MDOF oscillator subjected to Kobe-NS accelerogram is calculated and compared with that computed by the commercial software. Applicability of the proposed method to evaluating maximum elasto-plastic displacement of the MDOF oscillator is thoroughly discussed.

Harmonic Oscillations of Nonlinear Two-Degree-of-Freedom Systems

1955 ◽  
Vol 22 (1) ◽  
pp. 107-110
Author(s):  
T. C. Huang
Keyword(s):  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Viscous Damping ◽  
Free Oscillations ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Two Degree Of Freedom

Abstract In this paper an investigation is made of equations governing the oscillations of a nonlinear system in two degrees of freedom. Analyses of harmonic oscillations are illustrated for the cases of (1) the forced oscillations with nonlinear restoring force, damping neglected; (2) the free oscillations with nonlinear restoring force, damping neglected; and (3) the forced oscillations with nonlinear restoring force, small viscous damping considered. Amplitudes of oscillations and frequency equations are derived based on the mathematically justified perturbation method. Response curves are then plotted.

scholarly journals Strength Effect of Different U-Shaped HDR Thicknesses in Hook-End Precast Beam-Column Joint: A Nonlinear FE Analysis

2018 ◽  
Vol 65 ◽  
pp. 08009
Author(s):  
Kai Siong Woon ◽  
Farzad Hejazi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hysteresis Loops ◽  
Fe Analysis ◽  
Reinforced Concrete Frame ◽  
Concrete Frame ◽  
Similar Shape ◽  
Column Joint ◽  
Force Displacement ◽  
Strength Effect

A precast reinforced concrete frame constructed with new hook-end joint at both beam-column connections was numerical modelled and analysed using Finite Element Method, for its overall strength attainment under the action of horizontal cyclic loading. Five different thicknesses of U-shaped HDR, ranging from 15 to 35 mm thick in 5-mm intervals, were assigned in the numerical model as the vibrational absorber component in between the hook-end beam-column joints. The numerical force-displacement curves showed that precast frame with various thicknesses of U-shaped HDR had similar shape of hysteresis loops among each other. However, the precast frame with 25 mm thick of U-shaped HDR at its hook-end beam-column joint demonstrated the capacity to fulfil the highest force and displacement demands when compared with other thicknesses of HDR.

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