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.

Effect of Bass Bar Tension on Modal Parameters of a Violin's Top Plate

2015 ◽  
Vol 39 (1) ◽  
pp. 145-149 ◽  
Author(s):  
Ewa B. Skrodzka ◽  
Bogumił B.J. Linde ◽  
Antoni Krupa
Keyword(s):  
Modal Analysis ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Normal Value ◽  
Modal Damping

Abstract Experimental modal analysis of a violin with three different tensions of a bass bar has been performed. The bass bar tension is the only intentionally introduced modification of the instrument. The aim of the study was to find differences and similarities between top plate modal parameters determined by a bass bar perfectly fitting the shape of the top plate, the bass bar with a tension usually applied by luthiers (normal), and the tension higher than the normal value. In the modal analysis four signature modes are taken into account. Bass bar tension does not change the sequence of mode shapes. Changes in modal damping are insignificant. An increase in bass bar tension causes an increase in modal frequencies A0 and B(1+) and does not change the frequencies of modes CBR and B(1-).

Propagation of Nonlinearities in the Inertia Matrix of Tracked Vehicles

1994 ◽  
Author(s):  
J. H. Choi ◽  
A. A. Shabana ◽  
Roger A. Wehage
Keyword(s):  
Numerical Solution ◽  
Vehicle Dynamics ◽  
Equations Of Motion ◽  
Coefficient Matrix ◽  
Influence Coefficient ◽  
Dynamic Force ◽  
Tracked Vehicles ◽  
Revolute Joints ◽  
Inertia Matrix ◽  
Force Coupling

Abstract In this investigation, a procedure is presented for the numerical solution of tracked vehicle dynamics equations of motion. Tracked vehicles can be represented as two kinematically decoupled subsystems. The first is the chassis subsystem which consists of chassis, rollers, idlers, and sprockets. The second is the track subsystem which consists of track links interconnected by revolute joints. While there is dynamic force coupling between these two subsystems, there is no inertia coupling since the kinematic equations of the two subsystems are not coupled. The objective of the procedure developed in this investigation is to take advantage of the fact that in many applications, the shape of the track does not significantly change even though the track links undergo significant configurations changes. In such cases the nonlinearities propagate along the diagonals of a velocity influence coefficient matrix. This matrix is the only source of nonlinearities in the generalized inertia matrix. A permutation matrix is introduced to minimize the number of generalized inertia matrix LU factor evaluations for the track.

Structural Modification Software Development for Design Optimization

1995 ◽  
Author(s):  
Xiaoye Gu ◽  
Alison B. Flatau
Keyword(s):  
Structural Response ◽  
Acoustic Power ◽  
Modal Parameters ◽  
Constrained Layer Damping ◽  
Experimental Frequency ◽  
Modal Damping ◽  
Stiffness Matrices ◽  
Structural Responses ◽  
Damping Materials ◽  
Modal Mass

Abstract This paper presents a method for obtaining structural matrices from experimental frequency response function (FRF) data and using these structural matrices to predict the response of the structure to modifications at various locations. The approach taken is designed for subsequent use in optimizing structural modifications to efficiently reduce radiated acoustic power. A series of programs were written for identifying the structural matrices (mass matrices, stiffness matrices and damping matrices) from the measured FRF data. These matrices are used to obtain the modified response of the structure resulting from adding linear springs at different locations on the structure. Experimental results from a beam are presented to verify these programs. Work is in progress on extending this method to incorporate modifications to the structure produced by constrained-layer damping materials. The programs for obtaining the structural matrices and the structural response are composed of approaches used by several prior authors. Potter and Richardson’s [1,2] method is used for obtaining the relative modal parameters (modal mass, modal stiffness and modal damping). Luk and Mitchell’s [3,4] pseudo-inverse method is employed to obtain the structural matrices for cases when the number of modes measured is much less than the number of test points. A method for deriving the absolute value of modal parameters from the measured FRF data is also developed using modal analysis theory. Linear springs are added at various positions to modify the structure. The structural matrices are used to predict the modified structural responses scaled to displacement per unit force. A series of linear spring modifications are modeled and implemented experimentally to verify these programs.

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.

Analytical and Experimental Study of the Vibration of Bonded Beams With a Lap Joint

1990 ◽  
Vol 112 (4) ◽  
pp. 444-451 ◽  
Author(s):  
M. D. Rao ◽  
M. J. Crocker
Keyword(s):  
Equations Of Motion ◽  
Viscoelastic Behavior ◽  
Flexural Vibration ◽  
Epoxy Adhesive ◽  
Mode Shapes ◽  
Lap Joint ◽  
Joint System ◽  
Modal Damping ◽  
Element Approach ◽  
Differential Element

A theoretical model to study the flexural vibration of a bonded lap joint system is described in this paper. First, equations of motion at the joint region are derived using a differential element approach. The transverse displacements of the upper and lower beam are considered to be different. The adhesive is assumed to be linearly viscoelastic and the widely used Kelvin-Voight model is used to represent the viscoelastic behavior of the adhesive. The shear force at the interface between the adhesive and the beam is obtained from the simple bending motion equations of the two beams. The resulting equations of motion are combined with the equations of transverse vibration of the beams in the unjointed regions. These are later solved as a boundary value problem to obtain the eigenvalues and eigenvectors of the system. The model can be used to predict the natural frequencies, modal damping ratios, and mode shapes of the system for free vibration. Good agreement between numerical and experimental results was obtained for a system of graphite epoxy beams lap-jointed by an epoxy adhesive.

scholarly journals Investigation of Modal Behaviour of Resonance Spruce Wood Samples (Picea abies L.)

2017 ◽  
Vol 42 (1) ◽  
pp. 23-28 ◽  
Author(s):  
Przemysław Mania ◽  
Ewa Fabisiak ◽  
Ewa Skrodzka
Keyword(s):  
Picea Abies ◽  
Modal Analysis ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Pulse Excitation ◽  
Damping Factor ◽  
The North ◽  
Spruce Wood ◽  
Modal Damping ◽  
Resonance Wood

AbstractResults of experimental modal analysis of a resonance and non-resonance spruce wood (Picea abies L.) are presented. The resonance wood came from a tree from Poland and Bosnia and Herzegovina, while the non-resonance wood came from the vicinity of Olsztyn from the north-eastern Poland. The modal parameters (modal frequency, modal damping and mode shapes) of the wood samples were determined for the samples of 8 mm in thickness. Modal analysis was made by pulse excitation. The resonance and non-resonance wood differ in the fundamental modal parameters as well as in the number of potential modes. Additionally, calculated values of damping factor are presented. The values are much bigger for a non-resonance wood than for good quality resonance spruce.

Identification of Multi-Degree of Freedom Systems With Nonproportional Damping Using the Resonant Decay Method

2004 ◽  
Vol 126 (2) ◽  
pp. 298-306 ◽  
Author(s):  
Steven Naylor ◽  
Michael F. Platten ◽  
Jan R. Wright ◽  
Jonathan E. Cooper
Keyword(s):  
Measurement Noise ◽  
Mode Shapes ◽  
Damping Matrix ◽  
Modal Damping ◽  
Stiffness Matrices ◽  
Rigid Body Modes ◽  
Nonproportional Damping ◽  
Modal Mass ◽  
Damped Systems ◽  
Modal Space

This paper describes an extension of the force appropriation approach which permits the identification of the modal mass, damping and stiffness matrices of nonproportionally damped systems using multiple exciters. Appropriated excitation bursts are applied to the system at each natural frequency, followed by a regression analysis in modal space. The approach is illustrated on a simulated model of a plate with discrete dampers positioned to introduce significant damping nonproportionality. The influence of out-of-band flexible and rigid body modes, imperfect appropriation, measurement noise and impure mode shapes is considered. The method is shown to provide adequate estimates of the modal damping matrix.

Output-Only Modal Identification of a Nonuniform Beam by Using Decomposition Methods

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Rickey A. Caldwell ◽  
Brian F. Feeny
Keyword(s):  
Decomposition Methods ◽  
Analytical Approximation ◽  
Orthogonal Decomposition ◽  
Modal Identification ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Accelerometer Data ◽  
Pass Filter ◽  
Modal Damping ◽  
Output Only

Reduced-order mass weighted proper orthogonal decomposition (RMPOD), smooth orthogonal decomposition (SOD), and state variable modal decomposition (SVMD) are used to extract modal parameters from a nonuniform experimental beam. The beam was sensed by accelerometers. Accelerometer signals were integrated and passed through a high-pass filter to obtain velocities and displacements, all of which were used to build the necessary ensembles for the decomposition matrices. Each of these decomposition methods was used to extract mode shapes and modal coordinates. RMPOD can directly quantify modal energy, while SOD and SVMD directly produce estimates of modal frequencies. The extracted mode shapes and modal frequencies were compared to an analytical approximation of these quantities, and to frequencies estimated by applying the fast Fourier transform to accelerometer data. SVMD is also applied to estimate modal damping, which was compared to the estimate by logarithmic decrement applied to modal coordinate signals, with varying degrees of success. This paper shows that these decomposition methods are capable of extracting lower modal parameters of an actual experimental beam.

Experimental Modal Analysis of Rotating Disk Systems

1995 ◽  
Author(s):  
Horst Irretier ◽  
Frank Reuter
Keyword(s):  
Modal Analysis ◽  
Circular Disk ◽  
Rotating Disk ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Response Functions ◽  
Testing Technique ◽  
Theoretical Frequency ◽  
Modal Damping

Abstract A completely non-contact testing technique is presented to perform experimental modal analysis on rotating disk systems to identify modal parameters as eigenfrequencies, modal damping ratios and mode shapes due to rotation. Theoretical frequency response functions of rotating structures are presented which form the basis of the modal analysis. Experimental results of a rotating circular disk and a rotating radial impeller are presented and the influence of rotation on the modal parameters due to centrifugal, gyroscopic and aerodynamic effects is shown.

DYNAMIC RESPONSES OF A TWO-SPAN BEAM SUBJECTED TO HIGH SPEED 2DOF SPRUNG VEHICLES

2006 ◽  
Vol 06 (03) ◽  
pp. 413-430 ◽  
Author(s):  
PRITSATHAT SEETAPAN ◽  
SOMCHAI CHUCHEEPSAKUL
Keyword(s):  
Rough Surface ◽  
High Speed ◽  
Equations Of Motion ◽  
Bending Moment ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Passage Rate ◽  
System Equation ◽  
Modal Damping ◽  
Acceleration Time Histories

The deflection, bending moment, shear force and acceleration-time histories of a two-span beam subjected to moving sprung vehicles are presented. The vehicle model is a 2DOF system with a constant velocity. The two-span beam with a rough surface is used as structure model. The beam is defined in modal domain by natural frequencies, mode shapes and modal damping values. The rough surface is modeled by filtered white noise. The equations of motion for the coupled vehicle-structure system are formulated, for non-dimensionalized variables in the system equation. The first-order linear stochastic differential equations are solved, and the effects of the span passage rate and other important parameters are studied.

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