Dynamics 70 M1 Intro
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Transcript of Dynamics 70 M1 Intro
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Introduction to Dynamics
Module 1
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DNMC70
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Int roduct ion
Welcome!
Welcome to the DynamicsTraining Course!
This training course covers the ANSYS procedures required to
perform dynamic analyses.
It is intended for novice and experienced users interested in
solving dynamic problems using ANSYS.
Several other advanced training courses are available on specific
topics. See the training course schedule on the ANSYS
homepage: www.ansys.com under Training Services.
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Int roduct ionCourse Object ives
By the end of this course, you will be able to use ANSYS to:
Preprocess, solve, and postprocess a modal, harmonic, transient, and
spectrum analysis.
Use a Restart Analysis to either add time points to an existing load
history or recover from an unconverged solution.
Use the Mode Superposition method to reduce the solution time of
either a transient or harmonic analysis.
Use ANSYSs advanced modal analysis capabilities. These include
prestressed modal, cyclic symmetry, and large deflection analyses.
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Int roduct ionCou rse Material
The Training Manualyou have is an exact copy of the slides.
Workshop descriptions and instructions are included in the
Workshop Supp lement.
Copies of the workshop files are available (upon request) from the
instructor.
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Module 1
In t roduct ion to Dynam ics
A. Define dynamic analysis and its purpose.
B. Discuss different types of dynamic analysis.
C. Cover some basic concepts and terminology.
D. Introduce the Variable Viewer in the Time-History Postprocessor.
E. Do a sample dynamic analysis exercise.
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Dynamics
A. Def in i t ion & Purpose
What is dynamic analysis?
A technique used to determine the dynamicbehavior of a
structure or component, where the structures inert ia(mass
effects) and dampingplay an important role.
Dynamic behavior may be one or more of the following: Vibration characteristics - how the structure vibrates and at what
frequencies.
Effect of time varying loads (on the structures displacements and
stresses, for example).
Effect of periodic (a.k.a. oscillating or random) loads.
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Dynamics
Definition & Purpose
A static analysis might ensure that
the design will withstand steady-
state loading conditions, but it
may not be sufficient, especially if
the load varies with time.
The famous Tacoma Narrows
bridge (Galloping Gert ie) collapsedunder steady wind loads during a
42-mph wind storm on November
7, 1940, just four months after
construction.
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Dynamics
Definition & Purpose
A dynamic analysis usually takes into account one or more of the
following:
Vibrations - due to rotating machinery, for example.
Impact - car crash, hammer blow.
Alternating forces - crank shafts, other rotating machinery.
Seismic loads - earthquake, blast.
Random vibrations - rocket launch, road transport.
Each situation is handled by a specific type of dynamic analysis.
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Dynamics
B. Types of Dynam ic Analys is
Consider the following examples:
An automobile tailpipe assembly could shake apart if its natural
frequency matched that of the engine. How can you avoid this?
A turbine blade under stress (centrifugal forces) shows different
dynamic behavior. How can you account for it?
Answer - do a modal analysisto determine a structures vibration
characteristics.
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Dynamics
Types of Dynamic Analysis
An automobile fender should be able to withstand low-speed impact,
but deform under higher-speed impact.
A tennis racket frame should be designed to resist the impact of a
tennis ball and yet flex somewhat.
Solution - do a transient dynamic analysisto calculate a structures
response to time varying loads.
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Dynamics
Types of Dynamic Analysis
Rotating machines exert steady,
alternating forces on bearings andsupport structures. These forces
cause different deflections and
stresses depending on the speed of
rotation.
Solution - do a harmonic analysis todetermine a structures response to
steady, harmonic loads.
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Building frames and bridge structures in an
earthquake prone region should be designed to
withstand earthquakes.
Solution - do a spectrum analysis to determine a
structures response to seismic loading.
Courtesy: U.S. Geological Survey
Dynamics
Types of Dynamic Analysis
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Spacecraft and aircraft components must withstand random loading
of varying frequencies for a sustained time period.
Solution - do a random vibration analysis to determine how a
component responds to random vibrations.
Courtesy:
NASA
Dynamics
Types of Dynamic Analysis
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Dynamics
C. Basic Concepts and Term ino logy
Topics discussed:
General equation of motion
Solution methods
Modeling considerations
Mass matrix
Damping
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Dynamics - Basic Concepts & Termino logy
Equat ion of Mot ion
The general equation of motion is as follows.
tFuKuCuM
Different analysis types solve different forms of this equation.
Modal analysis: F(t) is set to zero, and [C] is usually ignored.
Harmonic analysis: F(t) and u(t) are both assumed to be harmonic in
nature, i.e, Xsin(wt), where X is the amplitude and w is the frequencyin radians/sec.
Transient dynamic analysis: The above form is maintained.
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Dynamics - Basic Concepts & Termino logy
Solut ion Method s
How do we solve the general equation of motion?
Two main techniques:
Mode superposition
Direct integration
Mode superposition
The frequency modes of the structure are predicted, multiplied by
generalized coordinates, and then summed to calculate the
displacement solution.
Can be used for transient and harmonic analyses.
Covered in Module 6.
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Dynamics - Basic Concepts & Termino logy
Solution Methods
Direct integration
Equation of motion is solved directly, without the use of
generalized coordinates.
For harmonic analyses, since both loads and response are
assumed to be harmonic, the equation is written and solved as afunction of forcing frequency instead of time.
For transient analyses, the equation remains a function of time
and can be solved using either an explicit or implicit method.
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Dynamics - Basic Concepts & Termino logy
Solution Methods
Explicit Method
No matrix inversion
Can handle nonlinearities easily
(no convergence issues)
Integration time step Dt must besmall (1e-6 second is typical)
Useful for short duration transients
such as wave propagation, shock
loading, and highly nonlinear
problems such as metal forming.
ANSYS-LS/DYNA uses this method.
Not covered in this seminar.
Implicit Method
Matrix inversion is required
Nonlinearities require equilibrium
iterations (convergence problems)
Integration time step Dt can be largebut may be restricted by
convergence issues
Efficient for most problems except
where Dt needs to be very small.
This is the topic covered in thisseminar
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Dynamics - Basic Concepts & Termino logy
Model ing Considerat ions
Geometry and Mesh:
Generally same considerations as a static analysis.
Include as many details as necessary to sufficiently represent the
model mass distribution.
A fine mesh will be needed in areas where stress results are of
interest. If you are only interested in displacement results, a
coarse mesh may be sufficient.
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Dynamics - Basic Concepts & Termino logy
Modeling Considerations
Material properties:
Both Youngs modulus and density are required.
Remember to use consistent units.
For density, specify mass densi tyinstead ofweight d ensi tywhen usingBritish units:
[Mass density] = [weight density]/[g] = [lbf/in3] / [in/sec2] = [lbf-sec2/in4]
Density of steel = 0.283/386 = 7.3 x 10-4 lbf-sec2/in4
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Dynamics - Basic Concepts & Termino logy
Modeling Considerations
Nonlinearities (large deflections, contact, plasticity, etc.):
Allowed only in a full transient dynamic analysis.
Ignored in all other dynamic analysis types - modal, harmonic,
spectrum, and reduced or mode superposition transient. That is,
the initial state of the nonlinearity will be maintained throughout
the solution.
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[M]Consistent
xx0xx0xx0xx0
00x00x
xx0xx0
xx0xx000x00x
ROTZUY
UX
ROTZ
UYUX
2
2
2
1
1
1
[M]Lumped
0000000000
00000
00000
0000000000
x
x
x
x
x
x
Dynamics - Basic Concepts & Termino logy
Mass Matrix
Mass matrix [M] is required for a dynamic analysis and is
calculated for each element from its density.
Two types of [M]: consis tentand lumped. Shown below for
BEAM3, the 2-D beam element.
1 2
BEAM3BEAM3
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Dynamics - Basic Concepts & Termino logy
Mass Matrix
Consistent mass matrix
Calculated from element shape functions.
Default for most elements.
Some elements have a special form called the reducedmass
matrix, which has rotational terms zeroed out.
Lumped mass matrix
Mass is divided among the elements nodes. Off-diagonal terms
are zero.
Activated as an analysis option (LUMPM command).
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Dynamics - Basic Concepts & Termino logy
Mass Matrix
Which mass matrix should you use?
Consistent mass matrix (default setting) for most applications.
Reduced mass matrix (if available) or lumped [M] for structures
that are small in one dimension compared to the other two
dimensions, e.g, slender beams or very thin shells.
Lumped mass matrix for wave propagation problems.
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Dynamics - Basic Concepts & Termino logy
Damping
What is damping?
The energy dissipation mechanism that causes
vibrations to diminish over time and eventually
stop.
Amount of damping mainly depends on the
material, velocity of motion, and frequency of
vibration.
Can be classified as:
Viscous damping
Hysteresis or solid damping
Coulomb or dry-friction damping
Dampening of
a Response
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Dynamics - Basic Concepts & Termino logy
Damping
Viscous damping
Occurs when a body moves through a fluid.
Should be considered in a dynamic analysis since the damping
force is proportional to velocity.
The proportionality constant c is called the damping constant.
Usually quantified as damping rat iox (ratio of damping constant cto critical damping constant cc*). Critical damping is defined as the threshold between oscillatory
and non-oscillatory behavior, where damping ratio = 1.0.
*For a single-DOF spring mass system of mass m and frequency w, cc = 2mw.
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Dynamics - Basic Concepts & Termino logy
Damping
Hysteresis or solid damping
Inherently present in a material.
Should be considered in a dynamic analysis.
Not well understood and therefore difficult to quantify.
Coulomb or dry-friction damping
Occurs when a body slides on a dry surface.
Damping force is proportional to the force normal to the surface.
Proportionality constant m is the coefficient of friction. Generally not considered in a dynamic analysis.
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Dynamics - Basic Concepts & Termino logy
Damping
ANSYS allows all three forms of damping.
Viscous damping can be included by specifying the damping ratiox, Rayleigh damping constant a (discussed later), or by definingelements with damping matrices.
Hysteresis or solid damping can be included by specifying
another Rayleigh damping constant, b (discussed later). Coulomb damping can be included by defining contact surface
elements and gap elements with friction capability (not discussed
in this seminar; see the ANSYS Structural Analysis Guid efor
information).
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In ANSYS damping is defined as
Dynamics - Basic Concepts & Termino logy
Damping
]C[C]K[]K)[(]M[]C[NEL
1k
k
NMAT
1j
jjc x
bbba [C]
aM
b
bcK
bj
[Ck]
Cx
structure damping matrix
constant mass matrix multiplier (ALPHAD)structure mass matrix
constant stiffness matrix multiplier (BETAD)
variable stiffness matrix multiplier (DMPRAT)
structure stiffness matrix
constant stiffness matrix multiplier for material j (MP,DAMP)
element damping matrix (element real constants)
frequency-dependent damping matrix (DMPRAT and MP,DAMP)
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Damping is specified in various forms:
Viscous damping factor or damping ratio x Quality factor or simply Q
Loss factor or Structural damping factorh Log decrement D Spectral damping factor D
Most of these are related to DAMPING RATIO x used in ANSYS Conversion factors are shown next
Dynamics - Basic Concepts & Termino logy
Damping
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Conversion between various damping specifications:
Dynamics - Basic Concepts & Termino logy
Damping
MeasureDamping
ratioLoss Factor
Log
Decrement
Quality
Factor
Spectral
Damping
Amplification
Factor
Damping
Ratio x h D 1/(2Q) D/(4U) 1/2A
Loss Factor x h D Q D/(2U) 1/A
Log
Decrement x h D Q D/(2U)
Quality
Factor x h D Q U/D
Spectral
Damping Ux Uh 2UD U/Q D U
Amplification
Factor x h D Q U/D
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Dynamics - Basic Concepts & Termino logy
Damping
Alpha Damping
Also known as mass damping.
Specified only if viscous damping is
dominant, such as in underwater
applications, shock absorbers, or
objects facing wind resistance.
If beta damping is ignored, a can becalculated from a known value ofx(damping ratio) and a known
frequency w:a = 2xw
Only one value of alpha is allowed, sopick the most dominant response
frequency to calculate a. Input using the ALPHAD command.
Frequency
DampingRatio
a3
1
2
0.5
Effect of Alpha Damping on Damping
Ratio (Beta Damping Ignored)
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Dynamics - Basic Concepts & Termino logy
Damping
Beta Damping
Also known as structuralorst i f fness
damping.
Inherent property of most materials.
Specified per material or as a single,
global value.
If alpha damping is ignored, b can becalculated from a known value ofx(damping ratio) and a known frequencyw:
b = 2x/w Pick the most dominant response
frequency to calculate b. Input using MP,DAMP or BETAD
command.
Frequency
DampingRatio
b0.0040.003
0.001
0.002
Effect of Beta Damping on Damping
Ratio (Alpha Damping Ignored)
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Dynamics - Basic Concepts & Termino logy
Damping
Rayleigh damping constants a and b Used as multipliers of [M] and [K] to calculate [C]:
[C] = a[M] + b[K]a/2w+ bw/2 = x
where w is the frequency, and x is the damping ratio.
Needed in situations where damping ratio x cannot be specified. Alpha is the viscous damping component, and Beta is the
hysteresis (a.k.a. solid orst i f fness)damping component.
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Dynamics - Basic Concepts & Termino logy
Damping
To specify both a and b damping: Use the relation
a/2w+ bw/2 = x Since there are two unknowns,
assume that the sum of alpha and
beta damping gives a constant
damping ratio x over the frequencyrange w1 to w2. This gives twosimultaneous equations from which
you can solve fora and b.x = a/2w1 + bw1/2x = a/2w2 + bw2/2 Frequency
DampingRatio ab
ba
w1 w2
How to Approximate Rayleigh
Damping Constants
Rayleigh Equation: the sumof the a and b terms is nearlyconstant over the range of
frequencies
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Dynamics - PostProcessin g
D. Variable Viewer
The Variable Viewer is a
specialized tool allowing one topostprocess results with respect
to time or frequency.
The Variable Viewer can be
started by:
Main Menu > TimeHist Postpro >Variable Viewer
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1 2 3 4 5 6 7 8
13 14
17
Add variable button1Delete variable button2
Graph variable button3
List variable button4
Properties button5
Import data button6
Export data button7
Export data type8
Real/Imaginary Components
Variable list
Variable name input area
11
Expression input area
12
Defined APDL variables
13
Defined Post26 variables
14
15
Calculator
Dynamics - PostProcessin g
Variable Viewer
15 16
9
11
10
9 Clear Time-History Data
10 Refresh Time-History Data
12
16
17
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100kg
25kg
k = 36kN/m
F
0,0
0,4000
t
tNF
k = 36kN/m
x
y
Dynamics - PostProcessin g
Variable Viewer
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Dynamics
E. Introductory Workshop
In this workshop, you will run a
sample dynamic analysis of theGalloping Gertie (Tacoma
Narrows bridge).
Follow the instructions in your
Dynamics Workshopsupplement
(Int rodu ctory Dynamics -Gallopin g Gertie, Page W-5).
The idea is to introduce you to
the steps involved in a typical
dynamic analysis. Details of
what each step means will be
covered in the rest of thisseminar.
Failure of Tacoma Narrows Bridge
http://localhost/var/www/apps/conversion/tmp/scratch_6/Dynamics_70_workshops.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_6/Dynamics_70_workshops.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_6/Dynamics_70_workshops.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_6/Dynamics_70_workshops.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_6/Dynamics_70_workshops.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_6/Dynamics_70_workshops.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_6/Dynamics_70_workshops.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_6/Dynamics_70_workshops.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_6/Dynamics_70_workshops.ppt -
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