Estimation of Hysteretic Energy of MDOF Structures Based on Equivalent SDOF Systems

2007 ◽  
Vol 340-341 ◽  
pp. 435-440
Author(s):  
Hong Nan Li ◽  
Feng Wang ◽  
Zhao Hui Lu
Keyword(s):  
Ground Motions ◽  
Estimation Method ◽  
Degree Of Freedom ◽  
Energy Relation ◽  
Energy Estimation ◽  
Single Degree Of Freedom ◽  
Hysteretic Energy ◽  
Single Degree ◽  
Energy Demands ◽  
The Relationship

It is important for obtaining the relationship between seismic energies of single degree-of-freedom (SDOF) systems and multiple degree-of-freedom (MDOF) structures in engineering. In this paper, the formula of hysteretic energy between the MDOF structures and equivalent SDOF systems is developed. Here is also presented the procedure for estimating hysteretic energy of MDOF structures subjected to severe ground motions employing the energy relation equation based on equivalent SDOF systems. Eight examples for two regular and six irregular MDOF structures show that the procedure to obtain the hysteretic energy demands of MDOF structures may be used as a simple and effective energy estimation method.

The Research on Hysteretic Energy in the Equivalent System Schemes between Multi Degree of Freedom System and Single Degree of Freedom System

2012 ◽  
Vol 166-169 ◽  
pp. 2177-2181
Author(s):  
Ming Qiang Sheng ◽  
Ying Liu
Keyword(s):  
Seismic Design ◽  
Seismic Waves ◽  
Good Alternative ◽  
Cumulative Damage ◽  
Degree Of Freedom ◽  
Equivalent System ◽  
Single Degree Of Freedom ◽  
Hysteretic Energy ◽  
Single Degree ◽  
Comparison And Analysis

The cumulative damage produced by severe earthquake is significant to the structural dilapidation and collapse. Most design methods based on force or displacement can’t reflect the effect of cumulative damage. Energy-based seismic design is known as a good alternative design. At present the research on the hysteretic energy of single-degree of freedom system(SDOF) is abundant, but real buildings can only be simplified as multi-degree of freedom systems(MDOF) mostly. Therefore how to acquire suitable equivalent single-degree of freedom system(ESDOF) is a key program. In this paper 12 equivalent system schemes(ESS) have been put forward, then the ratio of hysteretic energy(RH) of 6-floors framework was calculated with 30 typical seismic waves. Based on the comparison and analysis between calculations of 3 typical ESS, by the way of envelope fitting, the expression of RH related to earthquake characteristic value a/v was established.

scholarly journals Simulation Analysis of One Degree of Freedom Motion of Electromagnetic Spherical Joint based on Maxwell

2021 ◽  
Vol 2085 (1) ◽  
pp. 012014
Author(s):  
Haoran Wang ◽  
Fucong Liu ◽  
Sai Lou
Keyword(s):  
Mathematical Model ◽  
Simulation Analysis ◽  
Lagrange Equation ◽  
Degree Of Freedom ◽  
Spherical Joint ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Structure And Motion ◽  
The Mathematical Model ◽  
The Relationship

Abstract In order to improve the stiffness of the spherical joint of the robot, reduce the difficulty of manufacturing and the complexity of the control system, this paper proposed a method of spherical joint and digital drive of the robot based on the electromagnetic principle. Firstly, introduces the structure and motion principle of the spherical joint of the robot, establishes the mathematical model of the spherical joint and establishes the dynamic model according to the second Lagrange equation. after that, the relationship between the number of ampire-turns of the electromagnet on the spherical joint, the attitude Angle of the rotor and the force of the rotor was obtained by simulating the single degree of freedom of the joint based on Ansys maxwell and Matlab, which provided a basis for the realization of the digital drive of the spherical joint.

scholarly journals Hysteretic Energy Demands in Multi-Degree-of-Freedom Systems Subjected to Earthquakes

Buildings ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 220
Author(s):  
Emrah Erduran
Keyword(s):  
Ground Motion ◽  
Energy Demand ◽  
Relative Strength ◽  
Degree Of Freedom ◽  
Special Focus ◽  
Hysteretic Energy ◽  
Demand Distribution ◽  
Single Degree ◽  
Energy Demands ◽  
Energy Based Design

Reliable estimation of energy demands imposed on a structure by a design ground motion is a key component of energy-based design. Although several studies have been conducted to quantify the energy demands in single-degree-of-freedoms systems, few have focused on multi-degree-of-freedom systems. This study aims to build on the knowledge from previous studies on multi-degree-of-freedom systems with special focus on the distribution of hysteretic energy demands among the components of the structure. Nonlinear response history analyses conducted under ground motion sets representing three different hazard levels show that the total input and hysteretic energy demands of multi-degree-of-freedom systems can be accurately estimated from equivalent single-degree-of-freedom systems for low- and medium-rise buildings. The distribution of hysteretic energy demands over the height of the multistory structures has been shown to vary significantly from ground motion to ground motion. Analyses results also show that the relative strength of adjoining beams and columns has a significant influence on the hysteretic energy demand distribution. On the other hand, the energy distribution is relatively insensitive to the damping model used in the analysis of the multi-degree-of-freedom system.

Tunable-with-energy intense modal interactions induced by geometric nonlinearity

2020 ◽  
pp. 095440622090862
Author(s):  
Alireza Mojahed ◽  
Lawrence A Bergman ◽  
Alexander F Vakakis
Keyword(s):  
Geometric Nonlinearity ◽  
Degree Of Freedom ◽  
Primary System ◽  
Energy Relation ◽  
Initial Angle ◽  
Modal Interactions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Energy Transfers ◽  
Wave Tailoring

Modal interactions are distinct features of nonlinear systems that can be exploited in applications such as vibration and shock mitigation, targeted (irreversible) energy transfers (TET), and acoustic/stress wave tailoring. For such applications, different types of nonlinearities, e.g. hardening, softening, smooth, non-smooth, material or geometric, have been considered. In this work, we examine the geometric nonlinearity resulting from an initially inclined element consisting of a linear spring and a viscous damper connected in parallel, having an initial angle of inclination, [Formula: see text]. Because of its inclined configuration, this element possesses strong (and doubly tunable with respect to [Formula: see text] and energy) geometrically nonlinear stiffness and damping effects, despite the linear constitutive laws governing its constituent components. First, we consider a single-degree-of-freedom linearly grounded oscillator attached to the nonlinear inclined element. Omitting dissipative effects, we investigate the frequency–energy relation of this system by employing the canonical action-angle transformation and show that, depending on the initial angle of inclination and the energy-level, the resulting nonlinearity can be tuned to be softening, hardening or a combination of both. Next, we explore the efficacy of the geometric nonlinearity to induce strong modal interactions by considering a three-degree-of-freedom lightly damped primary system that is weakly coupled to a single-degree-of-freedom lightly damped attachment with the inclined nonlinear element, subjected to impulsive excitation. Varying [Formula: see text] and the input energy, we demonstrate strong modal energy-exchanges between the modes of the primary system and the nonlinear attachment over broad energy-dependent spans of [Formula: see text]. We show that the passive self-adaptiveness of the nonlinear damping and the hardening–softening geometric nonlinearity can induce narrowband or broadband frequency TET, including high-to-low frequency energy transfers. Interestingly, over a definitive range of [Formula: see text], these modal interactions may be limited only between the nonlinear mode of the attachment and the highest-frequency linear mode of the primary system, inducing strong high-frequency targeted energy transfer to the primary system.

Inelastic Structural Response to Cascadia Subduction Zone Earthquakes

1995 ◽  
Vol 11 (1) ◽  
pp. 63-89 ◽  
Author(s):  
M. Lee Marsh ◽  
Christopher M. Gianotti
Keyword(s):  
Subduction Zone ◽  
Structural Response ◽  
Degree Of Freedom ◽  
Cascadia Subduction Zone ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Energy Demands ◽  
Cyclic Displacement ◽  
Energy Dissipated ◽  
Subduction Zone Earthquakes

The effects of postulated Cascadia subduction zone earthquakes on inelastic structural response are examined. The earthquakes considered ranged in size from those previously recorded to the largest plausible event, a magnitude 9.5 earthquake. Artificial acceleration records were generated and used as input for inelastic response history analyses of single-degree-of-freedom systems with bilinear or degrading stiffness hysteretic relationships. The results indicate that the maximum displacements are not significantly greater than those produced by previously recorded events. The inelastic energy dissipated and the numbers of displacement cycles are somewhat greater for the largest events, although the energy demands and the cyclic displacement demands are similar to those from the recorded events for magnitudes up to 8.5.

Spectral Variability and Its Relationship to Structural Response Estimated from Scaled and Spectrum-Matched Ground Motions

2016 ◽  
Vol 32 (4) ◽  
pp. 2191-2205 ◽  
Author(s):  
A. E. Seifried ◽  
J. W. Baker
Keyword(s):  
Response Spectrum ◽  
Ground Motions ◽  
Structural Response ◽  
Degree Of Freedom ◽  
Structural Systems ◽  
Spectral Variability ◽  
Single Degree Of Freedom ◽  
Inelastic Response ◽  
Single Degree ◽  
Spectral Dispersion

Conditional spectral dispersion ( CSD) is a measure of response spectrum variability that implicitly characterizes the variety of spectral shapes within a suite of ground motions. It is used here to explain the discrepancy between median structural demands estimated from different suites of scaled and spectrum-matched ground motions. Performing response history analyses with spectrum-matched ground motions is known to result in unconservatively biased median demand estimates in some cases. Herein, several suites of scaled ground motions with equivalent median intensities and varying levels of CSD are selected. A single suite of spectrum-matched ground motions is also created. These records are used to analyze the responses of inelastic single-degree-of-freedom and first-mode-dominated multiple-degree-of-freedom structural systems. Collapse capacities are also examined. A consistent trend between CSD and resulting median responses indicates that the bias phenomenon can be fully explained by an asymmetric relationship between conditional spectral ordinates at periods affecting inelastic response.

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