Fast Simulation of a Single Degree-of-Freedom System Consisting of An Iwan Element Using the Method of Averaging

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Drithi Shetty ◽  
Matthew Allen
Keyword(s):  
Equations Of Motion ◽  
Element Model ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Weakly Nonlinear ◽  
Single Degree ◽  
Integration Schemes ◽  
Current Implementation ◽  
Modal Model ◽  
Stiffness And Damping

Abstract While Iwan elements have been used to effectively model the stiffness and energy dissipation in bolted joints, integrating the equations of motion of these elements is fairly expensive since implicit schemes, such as Newmark’s methods, need to be used. This paper presents a method of simulating dynamic systems containing nonlinear Iwan elements that significantly reduce the computation cost by using closed-form expressions for stiffness and damping in the microslip regime and an averaging method for regions of time in which no external force is applied. The proposed algorithm is demonstrated on a single degree-of-freedom (SDOF) system to evaluate the range over which it retains accuracy and the improvement in performance it offers. Although the current implementation is limited to SDOF systems, it can be used to simulate the response of each mode in structures exhibiting weak nonlinearity that can be modeled using the modal Iwan approach. To verify this, the dynamic response of a finite element model of a beam assembly, integrated using the Newmark-β method, has been compared with its equivalent modal model integrated using the proposed algorithm. The results show that the algorithm accurately predicts the response in a fraction of the time taken by implicit integration schemes, so long as the modes remain uncoupled and weakly nonlinear.

A Comparison of the Effects of Nonlinear Damping on the Free Vibration of a Single-Degree-of-Freedom System

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Bin Tang ◽  
M. J. Brennan
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree ◽  
Dependent Term ◽  
Quadratic Damping

This article concerns the free vibration of a single-degree-of-freedom (SDOF) system with three types of nonlinear damping. One system considered is where the spring and the damper are connected to the mass so that they are orthogonal, and the vibration is in the direction of the spring. It is shown that, provided the displacement is small, this system behaves in a similar way to the conventional SDOF system with cubic damping, in which the spring and the damper are connected so they act in the same direction. For completeness, these systems are compared with a conventional SDOF system with quadratic damping. By transforming all the equations of motion of the systems so that the damping force is proportional to the product of a displacement dependent term and velocity, then all the systems can be directly compared. It is seen that the system with cubic damping is worse than that with quadratic damping for the attenuation of free vibration.

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.

A Probabilistic Analysis of Single-Degree-of-Freedom Blade Vibration

1993 ◽  
Author(s):  
Kenan Y. Sanliturk ◽  
Mehmet Imregun ◽  
David J. Ewins
Keyword(s):  
Natural Frequencies ◽  
Probabilistic Approach ◽  
Substantial Reduction ◽  
Forced Response ◽  
Degree Of Freedom ◽  
Cumulative Probability ◽  
Blade Vibration ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stiffness And Damping

The effects of random stiffness and damping variations on damped natural frequencies and response levels of turbomachinery blades are investigated by employing probabilistic approach using a single-degree-of-freedom (SDOF) model. An important feature of this study is the determination of the cumulative probability distributions for damped natural frequencies and receptance frequency response functions without having to compute their probability density distributions since it is shown that those of stiffness and damping can be used directly. The advantage of this approach is not only in the simplicity of problem formulation but also in the substantial reduction of computational requirements. Furthermore, results suggest that both stiffness and damping properties should be considered as random parameters in statistical analyses of forced response.

scholarly journals Shock Performance of Different Semiactive Damping Strategies

2010 ◽  
Vol 8 (02) ◽  
Author(s):  
D. F. Ledezma-Ramirez ◽  
N. Ferguson ◽  
M. Brennan
Keyword(s):  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Harmonic Vibration ◽  
Passive Stiffness ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Variable Damping ◽  
Stiffness And Damping ◽  
Shock Pulses

The problem of shock generated vibration is presented and analyzed. The fundamental background is explained based on the analysis of a single degree-of-freedom model with passive stiffness and damping. The advantages and limitations of such a shock mount are discussed. Afterwards, different semi-active strategies involving variable damping are presented. These strategies have been used for harmonic excitation but it is not clear how they will perform during a shock. This paper analyzes the different variable damping schemes already used for harmonic vibration in order to find any potential advantages or issues for theoretical shock pulses.

Tow-Cable Snap Loads

1965 ◽  
Vol 2 (01) ◽  
pp. 42-49
Author(s):  
Lewis Schneider ◽  
L. Grady Burton ◽  
Thomas Mahan
Keyword(s):  
Large Amplitude ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Ship Motions ◽  
Body Density ◽  
Dynamical Equations ◽  
Dynamic Stresses ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Tension Recovery

When towing submerged bodies such as sonar vehicles or oceanographic instrument packages, the tow cable may be subjected to severe loadings because of large-amplitude ship motions. These motions first cause the cable to become slack and subsequently subject it to impact stresses at the instant of tension recovery. A typical body, cable, and oscillating tow-point assemblage is idealized as a single-degree-of-freedom system and the dynamical equations of motion are solved over a broad range of forcing amplitudes and periods and system compliance. The effects of such parameters as body density and cable compliance in attenuating the dynamic stresses are discussed.

RESONANCE CONTROL FOR A FORCED SINGLE-DEGREE-OF-FREEDOM NONLINEAR SYSTEM

2004 ◽  
Vol 14 (04) ◽  
pp. 1423-1429 ◽  
Author(s):  
ANDREW Y. T. LEUNG ◽  
JIN CHEN JI ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Nonlinear System ◽  
Singularity Theory ◽  
Degree Of Freedom ◽  
Theory Approach ◽  
Nonlinear Feedback ◽  
Single Degree Of Freedom ◽  
Weakly Nonlinear ◽  
Single Degree ◽  
Resonance Control

The main characteristic of a forced single-degree-of-freedom weakly nonlinear system is determined by its primary, super- and sub-harmonic resonances. A nonlinear parametric feedback control is proposed to modify the steady-state resonance responses, thus to reduce the amplitude of the response and to eliminate the saddle-node bifurcations that take place in the resonance responses. The nonlinear gain of the feedback control is determined by analyzing the bifurcation diagrams associated with the corresponding frequency-response equation, from the singularity theory approach. It is shown by illustrative examples that the proposed nonlinear feedback is effective for controlling three kinds of resonance responses.

scholarly journals On the critical forcing amplitude of forced nonlinear oscillators

2013 ◽  
Vol 3 (4) ◽  
Author(s):  
Mariano Febbo ◽  
Jinchen Ji
Keyword(s):  
Primary Resonance ◽  
Nonlinear Oscillators ◽  
Analytical Form ◽  
Excitation Amplitude ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Weakly Nonlinear ◽  
Single Degree ◽  
Saddle Node ◽  
Basis Method

AbstractThe steady-state response of forced single degree-of-freedom weakly nonlinear oscillators under primary resonance conditions can exhibit saddle-node bifurcations, jump and hysteresis phenomena, if the amplitude of the excitation exceeds a certain value. This critical value of excitation amplitude or critical forcing amplitude plays an important role in determining the occurrence of saddle-node bifurcations in the frequency-response curve. This work develops an alternative method to determine the critical forcing amplitude for single degree-of-freedom nonlinear oscillators. Based on Lagrange multipliers approach, the proposed method considers the calculation of the critical forcing amplitude as an optimization problem with constraints that are imposed by the existence of locations of vertical tangency. In comparison with the Gröbner basis method, the proposed approach is more straightforward and thus easy to apply for finding the critical forcing amplitude both analytically and numerically. Three examples are given to confirm the validity of the theoretical predictions. The first two present the analytical form for the critical forcing amplitude and the third one is an example of a numerically computed solution.

scholarly journals Optimization of Multiple Tuned Mass Damper (MTMD) Parameters for a Primary System Reduced to a Single Degree of Freedom (SDOF) Through the Modal Approach

2020 ◽  
Author(s):  
Piotr Wielgos ◽  
Robert Geryło
Keyword(s):  
Degrees Of Freedom ◽  
Research Work ◽  
System Optimization ◽  
Degree Of Freedom ◽  
Primary System ◽  
Single Degree Of Freedom ◽  
Modal Approach ◽  
Single Degree ◽  
Stiffness And Damping ◽  
The Impact

The research paper presents a new approach towards constructing motion equations for structures with attached MTMDs (multiple tuned mass dampers). A primary system, with MDOF (multiple dynamic degrees of freedom) was reduced to an equivalent system with a SDOF (single degree of freedom) through the modal approach, and equations from additional MTMDs were added to a thus-created system. Optimization based on H2 and H∞ for the transfer function associated with the generalized displacement of an SDOF system. The research work utilized GA (genetic algorithms) and SA (simulated annealing method) optimization algorithms to determine the stiffness and damping parameters for individual TMDs. The effect of damping and stiffness (MTMD tuning) distribution depending on the number of TMDs was also analyzed. The paper also reviews the impact of primary system mass change on the efficiency of optimized MTMDs, as well as confirms the results of other authors involving greater MTMD effectiveness relative to a single TMD.

scholarly journals EFFECT OF GYROSCOPE PARAMETERS ON GYROSCOPIC TREMOR SUPPRESSION IN A SINGLE DEGREE OF FREEDOM

2019 ◽  
Vol 19 (04) ◽  
pp. 1950024
Author(s):  
BRENDON C. ALLEN ◽  
STEVEN K. CHARLES
Keyword(s):  
Frequency Response ◽  
Wrist Joint ◽  
Systematic Investigation ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Know How ◽  
Single Degree ◽  
Tremor Suppression ◽  
Stiffness And Damping ◽  
Input Torque

Although tremor is one of the most common movement disorders, there are few effective tremor-suppressing options available to patients. Gyrostabilization is a potential option, but we do not currently know how to optimize gyrostabilization for tremor suppression. To address this gap, we present a systematic investigation of how gyrostabilizer parameters affect tremor suppression in a single degree of freedom (DOF). A simple model with a single DOF at the wrist and a gyroscope mounted on the back of the hand was used to focus on the most basic effects. We simulated the frequency response of the system (hand + gyroscope) to a tremorogenic input torque at the wrist. Varying system parameters one at a time, we determined the effect of individual parameters on the system’s frequency response. To minimize the bandwidth without adding significant inertia, the inertia and spin speed of the flywheel should be as high as design constraints allow, whereas the distance from the wrist joint axis to the gyroscope and the precession stiffness and damping should be kept as low as possible. The results demonstrate the potential of gyroscopic tremor suppression and can serve as foundation for further investigations of gyroscopic tremor suppression in the upper limb.

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