Impact Damper With Granular Materials for Multibody System

1996 ◽  
Vol 118 (1) ◽  
pp. 95-103 ◽  
Author(s):  
I. Yokomichi ◽  
Y. Araki ◽  
Y. Jinnouchi ◽  
J. Inoue
Keyword(s):  
Granular Materials ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Maximum Displacement ◽  
Impact Damper ◽  
Particle Bed ◽  
Modal Mass ◽  
Three Degree Of Freedom ◽  
The Impact

An efficient impact damper consists of a bed of granular materials moving in a container mounted on a multibody vibrating system. This paper deals with the damping characteristics of a multidegree-of-freedom (MDOF) system that is provided with the impact damper when the damper may be applied to any point of the system. In the theoretical analysis, the particle bed is assumed to be a mass which moves unidirectionally in a container, and collides plastically with its end. Equations of motion are developed for an equivalent single-degree-of-freedom (SDOF) system and attached damper mass with use made of the normal mode approach. The modal mass is estimated such that it represents the equivalent mass on the point of maximum displacement in each of the vibrating modes. The mass ratio is modified with the modal vector to include the effect of impact interactions. Results of the analysis are applied to the special case of a three-degree-of-freedom (3DOF) system, and the effects of the damper parameteres including mode shapes and damper locations are determined. A digital model is also formulated to simulate the damped motion of the physical system.

scholarly journals Particle Damping with Granular Materials for Multi Degree of Freedom System

2011 ◽  
Vol 18 (1-2) ◽  
pp. 245-256 ◽  
Author(s):  
Masanobu Inoue ◽  
Isao Yokomichi ◽  
Koju Hiraki
Keyword(s):  
Granular Materials ◽  
Equations Of Motion ◽  
Experimental Studies ◽  
Wide Frequency Range ◽  
Vertical Vibration ◽  
Degree Of Freedom ◽  
Particle Damping ◽  
Single Mass ◽  
Particle Dampers ◽  
Particle Bed

A particle damper consists of a bed of granular materials moving in cavities within a multi degree-of-freedom (MDOF) structure. This paper deals with the damping effects on forced vibrations of a MDOF structure provided with the vertical particle dampers. In the analysis, the particle bed is assumed to be a single mass, and the collisions between the granules and the cavities are completely inelastic, i.e., all energy dissipation mechanisms are wrapped into zero coefficient of restitution. To predict the particle damping effect, equations of motion are developed in terms of equivalent single degree-of-freedom (SDOF) system and damper mass with use made of modal approach. In this report, the periodic vibration model comprising sustained contact on or separation of the damper mass from vibrating structure is developed. A digital model is also formulated to simulate the damped motion of the physical system, taking account of all vibration modes. Numerical and experimental studies are made of the damping performance of plural dampers located at selected positions throughout a 3MDOF system. The experimental results confirm numerical prediction that collision between granules and structures is completely inelastic as the contributing mechanism of damping in the vertical vibration. It is found that particle dampers with properly selected mass ratios and clearances effectively suppress the resonance peaks over a wide frequency range.

Dynamic Modelling of a Three Degree-of-Freedom Planar Platform-Type Manipulator

1997 ◽  
Author(s):  
Hazem A. Attia ◽  
Maher G. Mohamed
Keyword(s):  
Differential Equations ◽  
Efficient Solution ◽  
Equations Of Motion ◽  
Translational Motion ◽  
Dynamic Modelling ◽  
Degree Of Freedom ◽  
Constraint Forces ◽  
Dynamic Formulation ◽  
System Of Particles ◽  
Three Degree Of Freedom

Abstract In this paper, the dynamic modelling of a planar three degree-of-freedom platform-type manipulator is presented. A kinematic analysis is carried out initially to evaluate the initial coordinates and velocities. The dynamic model of the manipulator is formulated using a two-step transformation. Initially, the dynamic formulation is written in terms of the Cartesian coordinates of a dynamically equivalent system of particles. Since there is no rotational motion associated with a particle, then the differential equations of motion are derived by applying Newton’s second law to study the translational motion of the particles. The constraint forces between the particles are expressed in terms of Lagrange multipliers. Then, the differential equations of motion are written in terms of the relative joint variables. This leads to an efficient solution and integration of the equations of motion. A numerical example is presented and a computer program is developed.

Nonlinear Dynamic of Cantilever Functionally Graded Plates Under the Thermalmechanical Loads

2009 ◽  
Author(s):  
Yu-xin Hao ◽  
Wei Zhang ◽  
Jian-hua Wang
Keyword(s):  
Nonlinear System ◽  
Functionally Graded Materials ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Governing Equations ◽  
Graded Materials ◽  
Two Degree Of Freedom

An analysis on nonlinear dynamic of a cantilevered functionally graded materials (FGM) plate which subjected to the transverse excitation in the uniform thermal environment is presented for the first time. Materials properties of the constituents are graded in the thickness direction according to a power-law distribution and assumed to be temperature dependent. In the framework of the Third-order shear deformation plate theory, the nonlinear governing equations of motion for the functionally graded materials plate are derived by using the Hamilton’s principle. For cantilever rectangular plate, the first two vibration mode shapes that satisfy the boundary conditions is given. The Galerkin’s method is utilized to discretize the governing equations of motion to a two-degree-of-freedom nonlinear system under combined thermal and external excitations. By using the numerical method, the two-degree-of-freedom nonlinear system is analyzed to find the nonlinear responses of the cantilever FGMs plate. The influences of the thermal environments on the nonlinear dynamic response of the cantilevered FGM plate are discussed in detail through a parametric study.

Passive Multi-Degree-of-Freedom Structural Control Using LPC Impact Dampers

2015 ◽  
Author(s):  
Mohamed Gharib ◽  
Mansour Karkoub
Keyword(s):  
Structural Control ◽  
Flexible Structures ◽  
Tall Buildings ◽  
Degree Of Freedom ◽  
Frame Structure ◽  
Linear Arrangement ◽  
Impact Damper ◽  
Particle Chain ◽  
The Impact ◽  
Partial Damage

Excessive vibration is one of the main reasons leading to partial damage and in some cases collapse of tall buildings and structures. Impact dampers provide an effective, economical, and easy to install solution to the vibration problem in several applications. The latest developed type in the impact dampers family is the Linear Particle Chain (LPC) impact damper. It consists of a linear arrangement of two sizes of freely moving masses, constrained by two stops. This paper presents the results of an experimental investigation on the effectiveness of the LPC impact damper in damping the vibrations of a multi-degree-of-freedom system under different types of excitations. A prototype of the LPC impact dampers is fabricated and tested in our lab using a three-story frame structure. The experimental outcomes clearly show that the LPC impact damper can effectively attenuate the free and forced vibrations of flexible structures.

Development of Seated Human Model With Uncertain Parameters and Estimation of the Ride Comfort

2018 ◽  
Author(s):  
Jong-Jin Bae ◽  
Namcheol Kang
Keyword(s):  
Ride Comfort ◽  
Probability Distributions ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Human Model ◽  
Whole Body ◽  
Mode Shapes ◽  
Comfort Index ◽  
Parametric Studies ◽  
Nonlinear Equations Of Motion

This study deals with the biodynamic responses of the 5-degree-of-freedom mathematical human model to whole-body vibrations in a vehicle. The nonlinear equations of motion of the human model were derived, and the spring constants and damping coefficients were extracted from the experimental data in the literature using optimization process. The natural frequencies and mode shapes were also calculated using linearized human model. In order to examine the effects of the variations of the human parameters, the parametric studies with respect to the stiffness values were performed. The mode veering phenomenon was observed between fourth and fifth mode of the linearized human model. In addition, the frequency responses of the nonlinear 5-degree-of-freedom model were also obtained, and the frequency shift and jump phenomena were observed. Furthermore, the estimation of the ride comfort was performed using CarSim and Matlab/Simulink with several road profiles according to ISO classification. Besides, we also calculated the ride comfort index using BS 6841 standard. In order to calculate the statistical responses of human model, the Monte-Carlo simulation applied to the nonlinear human model having uncertain stiffness assuming Gaussian distribution. These stochastic approaches enable the proposed human model to estimate probability distributions of the ride comfort index.

scholarly journals Remarks on optimization of impact damping for a non-ideal and nonlinear structural system

2020 ◽  
pp. 146134842094007
Author(s):  
Marcelo A Silva ◽  
Alexandre M Wahrhaftig ◽  
Reyolando MLRF Brasil
Keyword(s):  
Dynamic Response ◽  
Optimization Problems ◽  
Augmented Lagrangian Method ◽  
Equations Of Motion ◽  
Maximum Amplitude ◽  
Power Source ◽  
Structural System ◽  
Impact Damper ◽  
Design Variables ◽  
The Impact

It is intended, in this work, to present some research results on the optimization of an impact damper for a structural system excited by a non-ideal power source. In the model, the impact vibration absorber is, basically, a small free mass inside a box carved in the structure that undergoes undamped linear motions colliding against the walls of the box. Whenever the mass shocks against the walls of the box, an exchange of kinetic energy between the mass and the structure may be used to control the amplitude of the dynamic response of the structure. In this work, the structure is excited by a non-ideal power source, a DC electric motor installed on it, which may present the Sommerfeld effect. A non-ideal power source is one that interacts with the motion of the structure as opposed to an ideal source whose amplitude and frequency are fixed, independent of the displacements of the structure. Here, the dynamic response of the system is computed using step-by-step numerical integration of the equations of motion derived via a Lagrangian formulation. The optimization problem is defined considering as the objective function the maximum amplitude of the structure displacement, while the design variables are the weight of the free mass and the width of the carved box. Using the augmented Lagrangian method, several optimization problems are formulated, and, solving them, the best design to maximize the efficiency of the impact damper is obtained.

Dynamics of Multibody Tracked Vehicles Using Experimentally Identified Modal Parameters

1996 ◽  
Vol 118 (3) ◽  
pp. 499-507 ◽  
Author(s):  
Toshikazu Nakanishi ◽  
Xuegang Yin ◽  
A. A. Shabana
Keyword(s):  
Equations Of Motion ◽  
Kinematic Chain ◽  
General Purpose ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Tracked Vehicles ◽  
Revolute Joints ◽  
Modal Damping ◽  
Modal Mass ◽  
The Individual

The mode shapes, frequencies, and modal mass and stiffness coefficients of multibody systems such as tracked vehicles can be determined using experimental identification techniques. In multibody simulations, however, knowledge of the modal parameters of the individual components is required, and consequently, a procedure for extracting the component modes from the mode shapes of the assembled system must be used if experimental modal analysis techniques are to be used with general purpose multibody computer codes. In this investigation, modal parameters (modal mass, modal stiffness, modal damping, and mode shapes), which are determined experimentally, are employed to simulate the nonlinear dynamic behavior of a multibody tracked vehicle which consists of interconnected rigid and flexible components. The equations of motion of the vehicle are formulated in terms of a set of modal and reference generalized coordinates, and the theoretical basis for extracting the component modal parameters of the chassis from the modal parameters of the assembled vehicle is described. In this investigation, the track of the vehicle is modeled as a closed kinematic chain that consists of rigid links connected by revolute joints, and the effect of the chassis flexibility on the motion singularities of the track is examined numerically. These singularities which are encountered as the result of the change in the track configuration are avoided by using a deformable secondary joint instead of using the loop-closure equations.

Frictional Impact-Contacts in Multiple Flexible Links

2021 ◽  
pp. 2150075
Author(s):  
M. Ahmadizadeh ◽  
A. M. Shafei ◽  
R. Jafari
Keyword(s):  
Differential Equations ◽  
Recursive Algorithm ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Open Loop ◽  
Mode Shapes ◽  
Special Treatment ◽  
Exact Moment ◽  
Impact Phase ◽  
The Impact

Multiple impacts of 2D (planar) open-loop robotic systems composed of [Formula: see text] elastic links and revolute joints are studied in this paper. The dynamic equations of motion for such systems are derived by the Gibbs-Appell recursive algorithm, while the regularized method is employed to model the impact-contact mechanism. The Timoshenko beam theory is used to model the transverse vibrations of the links. Also, both the structural damping and air damping are considered to enhance the modeling accuracy. The system joints are assumed to be frictionless and slack-free, but friction force is included for the links colliding with the ground. The [Formula: see text]-flexible-link system considered goes through a flight phase and an impact phase during its motion. In the impact phase, new equations of motion are derived by including the terms caused by the viscoelastic forces in the system’s differential equations. Owing to the extremely short acting time of the impact force, the related differential equations can be solved only via special treatment, i.e. by detecting the exact moment of impact. To this end, entering or leaving the impact phase is analyzed and controlled with high precision by a special computational algorithm presented in this work. To demonstrate the efficacy and precision of the algorithm developed, computer simulations are conducted to study the dynamic behavior of a 3-link robotic mechanism. To investigate the effect of mode shape on the elastic deformation of links, four different mode shapes are used in the simulations and their results are compared.

scholarly journals Optimum Allocation of MR Dampers within Semi-Active Control Strategies of Three-Degree-of-Freedom Systems

2016 ◽  
Vol 4 (4) ◽  
pp. 45
Author(s):  
Omar Mahmoud Elmeligy ◽  
M. H. M. Hassan
Keyword(s):  
Fuzzy Logic ◽  
Active Control ◽  
Structural Control ◽  
Control Strategies ◽  
Structural Response ◽  
Degree Of Freedom ◽  
Maximum Displacement ◽  
Maximum Acceleration ◽  
Mr Dampers ◽  
Three Degree Of Freedom

Smart structural control is now emerging as an alternative to conventional earthquake resistant design and traditional structural control techniques. Fuzzy logic based control is one of the promising smart control strategies that could be used for this function. Magneto Rheological (MR) dampers are considered one of the promising semi-active control devices that can be used to control the structural response of buildings under earthquake excitation. The properties of MR dampers can be controlled using several smart techniques such as Fuzzy Logic. In this paper, a comparative analysis is conducted to investigate the most optimum location for placing MR dampers, which are controlled by Fuzzy Logic, in a three-degree-of-freedom benchmark problem. The study explores three potential schemes for allocating and operating MR dampers within the system under consideration. Two main structural response parameters are considered in this study, maximum displacement and maximum acceleration. In addition, the study investigates the lowest number of fuzzy-controlled MR dampers that are required in order to produce the required structural behaviour. This is an initial step towards the development of a generic allocation algorithm that is capable of identifying the required number of MR dampers, and their location, for controlling any multi-degree-of-freedom system.

scholarly journals Modeling and Simulation Methods for MDOF Structures and Rotating Machinery With Impact Dampers

1995 ◽  
Author(s):  
John M. McElhaney ◽  
A. Palazzolo ◽  
A. Kascak
Keyword(s):  
Complex Dynamics ◽  
Space Shuttle ◽  
Primary Objective ◽  
Dynamics Simulation ◽  
Mode Shapes ◽  
Impeller Blade ◽  
Impact Damper ◽  
Mdof Systems ◽  
The Impact ◽  
Very High

Previously published work on applied impact damping typically relates to SDOF models or simple MDOF models such as the classical cantilever beam. Structural models often require an extremely large number of DOF with mode shapes that are generally very complex. Dynamics simulation of these typically becomes both complicated and time consuming as well. The non-linear behavior of impact dampers further complicates such simulation in that standard linear solutions are not possible. The primary objective in this research extends previous work by applying impact dampers to MDOF structures that are modeled with general 3-D ‘beam’ finite elements. Modal based models of the MDOF systems and efficient impact damper tracking algorithms were also developed which significantly reduced CPU time for simulation. Significant among the objectives was obtaining an impact damper design for the MDOF casing structure of the Space Shuttle Main Engine (SSME), High Pressure Oxygen Turbo-Pump (HPOTP), subject to pump rotor shaft unbalance. Impact damper performance is based on suppression of vibration at casing critical frequencies for rotor speed ranges, at rotor full speed, and very high unbalance to simulate a defect such as loosing an impeller blade fragment or a cracked bearing[6]. Simulations show significant reductions in vibration at the casing critical frequencies and very high unbalance levels while little or no improvement was observed off resonance. Additionally, the previous work with an experimental rotor bearing system (RBS) and impact damper was modeled using the developed modal based methods. Simulation of the resulting model response shows remarkable agreement with the experimental. Finally, both the RBS and the HPOTP were modeled and simulated as unstable systems with attached impact dampers. The simulations predict that the impact damper is an excellent stabilizing mechanism for a range of instability driver values. Simulation of the models in this research with the developed modal based algorithms were accomplished with excellent efficiency, and accurate results.

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