SlideShare uma empresa Scribd logo
1 de 21
Baixar para ler offline
GROUND EXCITED SYSTEMS Prof. A. Meher Prasad Department of Civil Engineering Indian Institute of Technology Madras email: prasadam@iitm.ac.in
Dynamic Equations of Motion Force excited system Ground excited system where   is the relative displacement of the  structure w.r.t  ground. Non-moving reference Ground Acceleration vector where, are the ground accelerations in x,y,z  directions respectively. are null vectors except that those elements are equal to 1, which corresponds to x,y,z translational DOF.
Let  System equations reduce to following uncoupled equations where  participation factors, Note: a j  = b j  = 0 since initial conditions are zero  i.e Modal Superposition applied to GES
Solution  to uncoupled equation of motion can be expressed as,  In general , for design the response quantities of interest are: R = maximum values of (u , f s ,  Δ, V, M) Equivalent lateral loads Storey shears Storey Moments Storey drifts Relative displacements
[object Object],[object Object],max deformation of spring Modal Frequency Response Analysis Damping m k
Ground Excited MDOF System =  relative displacement of the  structure w r t ground  = Ground acceleration vector : where, are ground accelerations in x, y & z directions respectively Reference base x y z
1)  SRSS 2)  CQC 3)  Double Sum 4)  Grouping Serious errors for closely spaced frequencies and for 3-D structures ,which include torsional contribution. SRSS   : Square Root of Sum of Squares .It gives most probable maximum response. Modal combination rules ** Since the maximum response in each mode would not necessarily occur at the same instant of time, over conservative to add separate modal maximum responses.
CQC : Complete Quadratic Combination Rule (Wilson, Der Kiureghion & Baya 1981). It is based on random vibration theory. Note: All cross modal terms included very good agreement with full modal superposition extra computation minimal.
[object Object],[object Object],Finite Element Method In Structural Dynamics ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Time Domain Methods
[object Object],[object Object],[object Object],[object Object],[object Object],Desirable attributes:
[object Object],[object Object],[object Object],[object Object],Time Domain Methods
[object Object],Frequency Domain Methods ,[object Object],[object Object],[object Object],Direct Frequency Response Analysis
Multiple support Excitation Super structure free Dof Support Dof
Decompose {u f } into pseudo static and dynamic parts {u f }= {u s } + {u d }  Considering only static response ( i.e. stiffness matrix alone) Influence matrix Describes influence of support displacement on structural displacement j th  column of [ i ]=structural displacements due to unit support displacement u rl  only ( l  th  base displacement)
(By definition ) and i.e.
If assume light damping Uncoupled equations of motion are,
A big mass (much bigger than the total mass of the structure ( ~10 6  total mass ) is added to each degree of freedom at moving bases. As more big masses are applied, more low frequency modes have to be extracted.
The desired base motion is obtained by applying a point force to each degree of freedom at moving bases by Where  M big =big mass and  is the applied acceleration prescribed for degree of freedom N associated with moving supports The combined equation of motion is  with Where  is the diagonal matrix containing the big masses for moving base ‘i’ and  is the base motion applied to this base
The mass matrix [M] now contains the mass of the structure as well as the big masses associated with the secondary base. The modal equations with
1.000 1.000 6.7662 52.2836 0.0 4.7876 5.2909 10 8 0.9999 1.000 6.7661 52.2836 0.0 4.7876 5.2909 10 6 0.9995 1.0003 6.7641 52.2823 10 -10 4.7871 5.2910 10 4 0.9524 1.0335 6.5531 52.0552 10 -9 4.8011 5.3025 10 2 Response peaks (m/s 2 ) X 1  max  X 2  max  X 3  max  X 4  max Natural frequency Ratio of large mass to structure

Mais conteúdo relacionado

Mais procurados

Response spectra
Response spectraResponse spectra
Response spectra321nilesh
 
Modelling and Simulations Minor Project
Modelling and Simulations Minor ProjectModelling and Simulations Minor Project
Modelling and Simulations Minor ProjectMinjie Lu
 
Seismic Analysis of Structures - II
Seismic Analysis of Structures - IISeismic Analysis of Structures - II
Seismic Analysis of Structures - IItushardatta
 
Basic concepts on structural dynamics
Basic concepts on structural dynamicsBasic concepts on structural dynamics
Basic concepts on structural dynamicsPrasad Raju
 
Structural dynamics and earthquake engineering
Structural dynamics and earthquake engineeringStructural dynamics and earthquake engineering
Structural dynamics and earthquake engineeringBharat Khadka
 
Dynamics of multiple degree of freedom linear systems
Dynamics of multiple degree of freedom linear systemsDynamics of multiple degree of freedom linear systems
Dynamics of multiple degree of freedom linear systemsUniversity of Glasgow
 
Castigliano’s Method
Castigliano’s MethodCastigliano’s Method
Castigliano’s Methodaapx
 
[Review] contact model fusion
[Review] contact model fusion[Review] contact model fusion
[Review] contact model fusionHancheol Choi
 
Seismic Analysis of Structures - III
Seismic Analysis of Structures - IIISeismic Analysis of Structures - III
Seismic Analysis of Structures - IIItushardatta
 
205 wikarta-kuliah i mektek ti
205 wikarta-kuliah i mektek ti205 wikarta-kuliah i mektek ti
205 wikarta-kuliah i mektek tiAri Indrajaya
 
A High Order Continuation Based On Time Power Series Expansion And Time Ratio...
A High Order Continuation Based On Time Power Series Expansion And Time Ratio...A High Order Continuation Based On Time Power Series Expansion And Time Ratio...
A High Order Continuation Based On Time Power Series Expansion And Time Ratio...IJRES Journal
 

Mais procurados (19)

Response spectra
Response spectraResponse spectra
Response spectra
 
Modelling and Simulations Minor Project
Modelling and Simulations Minor ProjectModelling and Simulations Minor Project
Modelling and Simulations Minor Project
 
Seismic Analysis of Structures - II
Seismic Analysis of Structures - IISeismic Analysis of Structures - II
Seismic Analysis of Structures - II
 
Multi degree of freedom systems
Multi degree of freedom systemsMulti degree of freedom systems
Multi degree of freedom systems
 
Basic concepts on structural dynamics
Basic concepts on structural dynamicsBasic concepts on structural dynamics
Basic concepts on structural dynamics
 
Structural dynamics and earthquake engineering
Structural dynamics and earthquake engineeringStructural dynamics and earthquake engineering
Structural dynamics and earthquake engineering
 
Dynamics of multiple degree of freedom linear systems
Dynamics of multiple degree of freedom linear systemsDynamics of multiple degree of freedom linear systems
Dynamics of multiple degree of freedom linear systems
 
PART I.2 - Physical Mathematics
PART I.2 - Physical MathematicsPART I.2 - Physical Mathematics
PART I.2 - Physical Mathematics
 
Lecture7 (37)
Lecture7 (37)Lecture7 (37)
Lecture7 (37)
 
Lecture 5 (46)
Lecture 5 (46)Lecture 5 (46)
Lecture 5 (46)
 
PART I.3 - Physical Mathematics
PART I.3 - Physical MathematicsPART I.3 - Physical Mathematics
PART I.3 - Physical Mathematics
 
Castigliano’s Method
Castigliano’s MethodCastigliano’s Method
Castigliano’s Method
 
Module 8
Module 8 Module 8
Module 8
 
[Review] contact model fusion
[Review] contact model fusion[Review] contact model fusion
[Review] contact model fusion
 
Seismic Analysis of Structures - III
Seismic Analysis of Structures - IIISeismic Analysis of Structures - III
Seismic Analysis of Structures - III
 
Lecture 2(57)
Lecture 2(57)Lecture 2(57)
Lecture 2(57)
 
PART I.4 - Physical Mathematics
PART I.4 - Physical MathematicsPART I.4 - Physical Mathematics
PART I.4 - Physical Mathematics
 
205 wikarta-kuliah i mektek ti
205 wikarta-kuliah i mektek ti205 wikarta-kuliah i mektek ti
205 wikarta-kuliah i mektek ti
 
A High Order Continuation Based On Time Power Series Expansion And Time Ratio...
A High Order Continuation Based On Time Power Series Expansion And Time Ratio...A High Order Continuation Based On Time Power Series Expansion And Time Ratio...
A High Order Continuation Based On Time Power Series Expansion And Time Ratio...
 

Semelhante a Ground Excited Systems

Structural Dynamics
Structural DynamicsStructural Dynamics
Structural DynamicsAbdul Majid
 
Dynamic Response Of A Vibrating Structure To Sinusoidal Excitation
Dynamic Response Of A Vibrating Structure To Sinusoidal ExcitationDynamic Response Of A Vibrating Structure To Sinusoidal Excitation
Dynamic Response Of A Vibrating Structure To Sinusoidal Excitationtapoore
 
DOMV No 4 PHYSICAL DYNAMIC MODEL TYPES (1).pdf
DOMV No 4  PHYSICAL DYNAMIC MODEL TYPES (1).pdfDOMV No 4  PHYSICAL DYNAMIC MODEL TYPES (1).pdf
DOMV No 4 PHYSICAL DYNAMIC MODEL TYPES (1).pdfahmedelsharkawy98
 
Straus r7-Software Dynamics Analysis
Straus r7-Software Dynamics AnalysisStraus r7-Software Dynamics Analysis
Straus r7-Software Dynamics Analysisgulilero
 
SANU BISWAS (9102) 704A.pdf
SANU BISWAS (9102) 704A.pdfSANU BISWAS (9102) 704A.pdf
SANU BISWAS (9102) 704A.pdfSanuBiswas9102
 
4 forced vibration of damped
4 forced vibration of damped4 forced vibration of damped
4 forced vibration of dampedJayesh Chopade
 
Lecture1 NPTEL for Basics of Vibrations for Simple Mechanical Systems
Lecture1 NPTEL for Basics of Vibrations for Simple Mechanical SystemsLecture1 NPTEL for Basics of Vibrations for Simple Mechanical Systems
Lecture1 NPTEL for Basics of Vibrations for Simple Mechanical SystemsNaushad Ahamed
 
Suppressing undesired vibration of 3 r robot arms using impact dampers
Suppressing undesired vibration of 3 r robot arms using impact dampersSuppressing undesired vibration of 3 r robot arms using impact dampers
Suppressing undesired vibration of 3 r robot arms using impact dampersijmech
 
somnath roy roll 26301320047.pdf
somnath roy roll 26301320047.pdfsomnath roy roll 26301320047.pdf
somnath roy roll 26301320047.pdfSanuBiswas9102
 
Ravi jabi harsh
Ravi jabi harshRavi jabi harsh
Ravi jabi harshjabi khan
 
A Modal Pushover Analysis on Multi-Span Bridge to Estimate Inelastic Seismic ...
A Modal Pushover Analysis on Multi-Span Bridge to Estimate Inelastic Seismic ...A Modal Pushover Analysis on Multi-Span Bridge to Estimate Inelastic Seismic ...
A Modal Pushover Analysis on Multi-Span Bridge to Estimate Inelastic Seismic ...IOSR Journals
 
Modelling of flexible link manipulator dynamics using rigid link theory with
Modelling of flexible link manipulator dynamics using rigid link theory withModelling of flexible link manipulator dynamics using rigid link theory with
Modelling of flexible link manipulator dynamics using rigid link theory withIAEME Publication
 
Identification of coulomb, viscous and particle damping parameters from the r...
Identification of coulomb, viscous and particle damping parameters from the r...Identification of coulomb, viscous and particle damping parameters from the r...
Identification of coulomb, viscous and particle damping parameters from the r...ijiert bestjournal
 
Chapter 2 lecture 1 mechanical vibration
Chapter 2  lecture 1 mechanical vibrationChapter 2  lecture 1 mechanical vibration
Chapter 2 lecture 1 mechanical vibrationBahr Alyafei
 

Semelhante a Ground Excited Systems (20)

Structural Dynamics
Structural DynamicsStructural Dynamics
Structural Dynamics
 
Dynamic Response Of A Vibrating Structure To Sinusoidal Excitation
Dynamic Response Of A Vibrating Structure To Sinusoidal ExcitationDynamic Response Of A Vibrating Structure To Sinusoidal Excitation
Dynamic Response Of A Vibrating Structure To Sinusoidal Excitation
 
Mode shap
Mode shapMode shap
Mode shap
 
DOMV No 4 PHYSICAL DYNAMIC MODEL TYPES (1).pdf
DOMV No 4  PHYSICAL DYNAMIC MODEL TYPES (1).pdfDOMV No 4  PHYSICAL DYNAMIC MODEL TYPES (1).pdf
DOMV No 4 PHYSICAL DYNAMIC MODEL TYPES (1).pdf
 
Straus r7-Software Dynamics Analysis
Straus r7-Software Dynamics AnalysisStraus r7-Software Dynamics Analysis
Straus r7-Software Dynamics Analysis
 
Linear non linear
Linear non linearLinear non linear
Linear non linear
 
SANU BISWAS (9102) 704A.pdf
SANU BISWAS (9102) 704A.pdfSANU BISWAS (9102) 704A.pdf
SANU BISWAS (9102) 704A.pdf
 
4 forced vibration of damped
4 forced vibration of damped4 forced vibration of damped
4 forced vibration of damped
 
Lecture1 NPTEL for Basics of Vibrations for Simple Mechanical Systems
Lecture1 NPTEL for Basics of Vibrations for Simple Mechanical SystemsLecture1 NPTEL for Basics of Vibrations for Simple Mechanical Systems
Lecture1 NPTEL for Basics of Vibrations for Simple Mechanical Systems
 
Suppressing undesired vibration of 3 r robot arms using impact dampers
Suppressing undesired vibration of 3 r robot arms using impact dampersSuppressing undesired vibration of 3 r robot arms using impact dampers
Suppressing undesired vibration of 3 r robot arms using impact dampers
 
somnath roy roll 26301320047.pdf
somnath roy roll 26301320047.pdfsomnath roy roll 26301320047.pdf
somnath roy roll 26301320047.pdf
 
Ravi jabi harsh
Ravi jabi harshRavi jabi harsh
Ravi jabi harsh
 
C012131116
C012131116C012131116
C012131116
 
A Modal Pushover Analysis on Multi-Span Bridge to Estimate Inelastic Seismic ...
A Modal Pushover Analysis on Multi-Span Bridge to Estimate Inelastic Seismic ...A Modal Pushover Analysis on Multi-Span Bridge to Estimate Inelastic Seismic ...
A Modal Pushover Analysis on Multi-Span Bridge to Estimate Inelastic Seismic ...
 
Modelling of flexible link manipulator dynamics using rigid link theory with
Modelling of flexible link manipulator dynamics using rigid link theory withModelling of flexible link manipulator dynamics using rigid link theory with
Modelling of flexible link manipulator dynamics using rigid link theory with
 
M0746274
M0746274M0746274
M0746274
 
Identification of coulomb, viscous and particle damping parameters from the r...
Identification of coulomb, viscous and particle damping parameters from the r...Identification of coulomb, viscous and particle damping parameters from the r...
Identification of coulomb, viscous and particle damping parameters from the r...
 
Chapter 2 lecture 1 mechanical vibration
Chapter 2  lecture 1 mechanical vibrationChapter 2  lecture 1 mechanical vibration
Chapter 2 lecture 1 mechanical vibration
 
Respose surface methods
Respose surface methodsRespose surface methods
Respose surface methods
 
12 l1-harmonic methodology
12 l1-harmonic methodology12 l1-harmonic methodology
12 l1-harmonic methodology
 

Mais de Teja Ande

Numerical Methods
Numerical MethodsNumerical Methods
Numerical MethodsTeja Ande
 
Response Spectrum
Response SpectrumResponse Spectrum
Response SpectrumTeja Ande
 
Lesson14 Exmpl
Lesson14 ExmplLesson14 Exmpl
Lesson14 ExmplTeja Ande
 
Lesson9 2nd Part
Lesson9 2nd PartLesson9 2nd Part
Lesson9 2nd PartTeja Ande
 
Lecture 13 Building Populations
Lecture 13 Building PopulationsLecture 13 Building Populations
Lecture 13 Building PopulationsTeja Ande
 
Lecture 11 Performance Based Evaluation
Lecture 11 Performance Based EvaluationLecture 11 Performance Based Evaluation
Lecture 11 Performance Based EvaluationTeja Ande
 
Lecture 6 7 Rm Shear Walls
Lecture 6 7 Rm Shear WallsLecture 6 7 Rm Shear Walls
Lecture 6 7 Rm Shear WallsTeja Ande
 
Lecture 10 Urm Out Of Plane Walls Part 2
Lecture 10 Urm Out Of Plane Walls Part 2Lecture 10 Urm Out Of Plane Walls Part 2
Lecture 10 Urm Out Of Plane Walls Part 2Teja Ande
 
Lecture 6 7 Rm Shear Walls
Lecture 6 7 Rm Shear WallsLecture 6 7 Rm Shear Walls
Lecture 6 7 Rm Shear WallsTeja Ande
 
Lecture 4 5 Urm Shear Walls
Lecture 4 5 Urm Shear WallsLecture 4 5 Urm Shear Walls
Lecture 4 5 Urm Shear WallsTeja Ande
 
Lecture 2 3 Compression, Condition Assess
Lecture 2 3 Compression, Condition AssessLecture 2 3 Compression, Condition Assess
Lecture 2 3 Compression, Condition AssessTeja Ande
 
Lecture 4 5 Urm Shear Walls
Lecture 4 5 Urm Shear WallsLecture 4 5 Urm Shear Walls
Lecture 4 5 Urm Shear WallsTeja Ande
 
Lecture 2 3 Compression, Condition Assess
Lecture 2 3 Compression, Condition AssessLecture 2 3 Compression, Condition Assess
Lecture 2 3 Compression, Condition AssessTeja Ande
 

Mais de Teja Ande (20)

Numerical Methods
Numerical MethodsNumerical Methods
Numerical Methods
 
Sdof
SdofSdof
Sdof
 
Response Spectrum
Response SpectrumResponse Spectrum
Response Spectrum
 
Sam Session
Sam SessionSam Session
Sam Session
 
Lesson14 Exmpl
Lesson14 ExmplLesson14 Exmpl
Lesson14 Exmpl
 
Lesson14
Lesson14Lesson14
Lesson14
 
Lesson10
Lesson10Lesson10
Lesson10
 
Lesson9 2nd Part
Lesson9 2nd PartLesson9 2nd Part
Lesson9 2nd Part
 
Lesson8
Lesson8Lesson8
Lesson8
 
Lesson9
Lesson9Lesson9
Lesson9
 
Lecture 13 Building Populations
Lecture 13 Building PopulationsLecture 13 Building Populations
Lecture 13 Building Populations
 
Lesson1
Lesson1Lesson1
Lesson1
 
Lecture 11 Performance Based Evaluation
Lecture 11 Performance Based EvaluationLecture 11 Performance Based Evaluation
Lecture 11 Performance Based Evaluation
 
Lecture 6 7 Rm Shear Walls
Lecture 6 7 Rm Shear WallsLecture 6 7 Rm Shear Walls
Lecture 6 7 Rm Shear Walls
 
Lecture 10 Urm Out Of Plane Walls Part 2
Lecture 10 Urm Out Of Plane Walls Part 2Lecture 10 Urm Out Of Plane Walls Part 2
Lecture 10 Urm Out Of Plane Walls Part 2
 
Lecture 6 7 Rm Shear Walls
Lecture 6 7 Rm Shear WallsLecture 6 7 Rm Shear Walls
Lecture 6 7 Rm Shear Walls
 
Lecture 4 5 Urm Shear Walls
Lecture 4 5 Urm Shear WallsLecture 4 5 Urm Shear Walls
Lecture 4 5 Urm Shear Walls
 
Lecture 2 3 Compression, Condition Assess
Lecture 2 3 Compression, Condition AssessLecture 2 3 Compression, Condition Assess
Lecture 2 3 Compression, Condition Assess
 
Lecture 4 5 Urm Shear Walls
Lecture 4 5 Urm Shear WallsLecture 4 5 Urm Shear Walls
Lecture 4 5 Urm Shear Walls
 
Lecture 2 3 Compression, Condition Assess
Lecture 2 3 Compression, Condition AssessLecture 2 3 Compression, Condition Assess
Lecture 2 3 Compression, Condition Assess
 

Último

Meet the new FSP 3000 M-Flex800™
Meet the new FSP 3000 M-Flex800™Meet the new FSP 3000 M-Flex800™
Meet the new FSP 3000 M-Flex800™Adtran
 
Spring24-Release Overview - Wellingtion User Group-1.pdf
Spring24-Release Overview - Wellingtion User Group-1.pdfSpring24-Release Overview - Wellingtion User Group-1.pdf
Spring24-Release Overview - Wellingtion User Group-1.pdfAnna Loughnan Colquhoun
 
Introduction to Matsuo Laboratory (ENG).pptx
Introduction to Matsuo Laboratory (ENG).pptxIntroduction to Matsuo Laboratory (ENG).pptx
Introduction to Matsuo Laboratory (ENG).pptxMatsuo Lab
 
Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...
Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...
Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...DianaGray10
 
Do we need a new standard for visualizing the invisible?
Do we need a new standard for visualizing the invisible?Do we need a new standard for visualizing the invisible?
Do we need a new standard for visualizing the invisible?SANGHEE SHIN
 
AI Fame Rush Review – Virtual Influencer Creation In Just Minutes
AI Fame Rush Review – Virtual Influencer Creation In Just MinutesAI Fame Rush Review – Virtual Influencer Creation In Just Minutes
AI Fame Rush Review – Virtual Influencer Creation In Just MinutesMd Hossain Ali
 
UiPath Solutions Management Preview - Northern CA Chapter - March 22.pdf
UiPath Solutions Management Preview - Northern CA Chapter - March 22.pdfUiPath Solutions Management Preview - Northern CA Chapter - March 22.pdf
UiPath Solutions Management Preview - Northern CA Chapter - March 22.pdfDianaGray10
 
UWB Technology for Enhanced Indoor and Outdoor Positioning in Physiological M...
UWB Technology for Enhanced Indoor and Outdoor Positioning in Physiological M...UWB Technology for Enhanced Indoor and Outdoor Positioning in Physiological M...
UWB Technology for Enhanced Indoor and Outdoor Positioning in Physiological M...UbiTrack UK
 
9 Steps For Building Winning Founding Team
9 Steps For Building Winning Founding Team9 Steps For Building Winning Founding Team
9 Steps For Building Winning Founding TeamAdam Moalla
 
Things you didn't know you can use in your Salesforce
Things you didn't know you can use in your SalesforceThings you didn't know you can use in your Salesforce
Things you didn't know you can use in your SalesforceMartin Humpolec
 
Using IESVE for Loads, Sizing and Heat Pump Modeling to Achieve Decarbonization
Using IESVE for Loads, Sizing and Heat Pump Modeling to Achieve DecarbonizationUsing IESVE for Loads, Sizing and Heat Pump Modeling to Achieve Decarbonization
Using IESVE for Loads, Sizing and Heat Pump Modeling to Achieve DecarbonizationIES VE
 
Cloud Revolution: Exploring the New Wave of Serverless Spatial Data
Cloud Revolution: Exploring the New Wave of Serverless Spatial DataCloud Revolution: Exploring the New Wave of Serverless Spatial Data
Cloud Revolution: Exploring the New Wave of Serverless Spatial DataSafe Software
 
Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...
Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...
Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...Will Schroeder
 
Cybersecurity Workshop #1.pptx
Cybersecurity Workshop #1.pptxCybersecurity Workshop #1.pptx
Cybersecurity Workshop #1.pptxGDSC PJATK
 
COMPUTER 10: Lesson 7 - File Storage and Online Collaboration
COMPUTER 10: Lesson 7 - File Storage and Online CollaborationCOMPUTER 10: Lesson 7 - File Storage and Online Collaboration
COMPUTER 10: Lesson 7 - File Storage and Online Collaborationbruanjhuli
 
OpenShift Commons Paris - Choose Your Own Observability Adventure
OpenShift Commons Paris - Choose Your Own Observability AdventureOpenShift Commons Paris - Choose Your Own Observability Adventure
OpenShift Commons Paris - Choose Your Own Observability AdventureEric D. Schabell
 
KubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCost
KubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCostKubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCost
KubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCostMatt Ray
 
IESVE Software for Florida Code Compliance Using ASHRAE 90.1-2019
IESVE Software for Florida Code Compliance Using ASHRAE 90.1-2019IESVE Software for Florida Code Compliance Using ASHRAE 90.1-2019
IESVE Software for Florida Code Compliance Using ASHRAE 90.1-2019IES VE
 
Bird eye's view on Camunda open source ecosystem
Bird eye's view on Camunda open source ecosystemBird eye's view on Camunda open source ecosystem
Bird eye's view on Camunda open source ecosystemAsko Soukka
 
COMPUTER 10 Lesson 8 - Building a Website
COMPUTER 10 Lesson 8 - Building a WebsiteCOMPUTER 10 Lesson 8 - Building a Website
COMPUTER 10 Lesson 8 - Building a Websitedgelyza
 

Último (20)

Meet the new FSP 3000 M-Flex800™
Meet the new FSP 3000 M-Flex800™Meet the new FSP 3000 M-Flex800™
Meet the new FSP 3000 M-Flex800™
 
Spring24-Release Overview - Wellingtion User Group-1.pdf
Spring24-Release Overview - Wellingtion User Group-1.pdfSpring24-Release Overview - Wellingtion User Group-1.pdf
Spring24-Release Overview - Wellingtion User Group-1.pdf
 
Introduction to Matsuo Laboratory (ENG).pptx
Introduction to Matsuo Laboratory (ENG).pptxIntroduction to Matsuo Laboratory (ENG).pptx
Introduction to Matsuo Laboratory (ENG).pptx
 
Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...
Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...
Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...
 
Do we need a new standard for visualizing the invisible?
Do we need a new standard for visualizing the invisible?Do we need a new standard for visualizing the invisible?
Do we need a new standard for visualizing the invisible?
 
AI Fame Rush Review – Virtual Influencer Creation In Just Minutes
AI Fame Rush Review – Virtual Influencer Creation In Just MinutesAI Fame Rush Review – Virtual Influencer Creation In Just Minutes
AI Fame Rush Review – Virtual Influencer Creation In Just Minutes
 
UiPath Solutions Management Preview - Northern CA Chapter - March 22.pdf
UiPath Solutions Management Preview - Northern CA Chapter - March 22.pdfUiPath Solutions Management Preview - Northern CA Chapter - March 22.pdf
UiPath Solutions Management Preview - Northern CA Chapter - March 22.pdf
 
UWB Technology for Enhanced Indoor and Outdoor Positioning in Physiological M...
UWB Technology for Enhanced Indoor and Outdoor Positioning in Physiological M...UWB Technology for Enhanced Indoor and Outdoor Positioning in Physiological M...
UWB Technology for Enhanced Indoor and Outdoor Positioning in Physiological M...
 
9 Steps For Building Winning Founding Team
9 Steps For Building Winning Founding Team9 Steps For Building Winning Founding Team
9 Steps For Building Winning Founding Team
 
Things you didn't know you can use in your Salesforce
Things you didn't know you can use in your SalesforceThings you didn't know you can use in your Salesforce
Things you didn't know you can use in your Salesforce
 
Using IESVE for Loads, Sizing and Heat Pump Modeling to Achieve Decarbonization
Using IESVE for Loads, Sizing and Heat Pump Modeling to Achieve DecarbonizationUsing IESVE for Loads, Sizing and Heat Pump Modeling to Achieve Decarbonization
Using IESVE for Loads, Sizing and Heat Pump Modeling to Achieve Decarbonization
 
Cloud Revolution: Exploring the New Wave of Serverless Spatial Data
Cloud Revolution: Exploring the New Wave of Serverless Spatial DataCloud Revolution: Exploring the New Wave of Serverless Spatial Data
Cloud Revolution: Exploring the New Wave of Serverless Spatial Data
 
Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...
Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...
Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...
 
Cybersecurity Workshop #1.pptx
Cybersecurity Workshop #1.pptxCybersecurity Workshop #1.pptx
Cybersecurity Workshop #1.pptx
 
COMPUTER 10: Lesson 7 - File Storage and Online Collaboration
COMPUTER 10: Lesson 7 - File Storage and Online CollaborationCOMPUTER 10: Lesson 7 - File Storage and Online Collaboration
COMPUTER 10: Lesson 7 - File Storage and Online Collaboration
 
OpenShift Commons Paris - Choose Your Own Observability Adventure
OpenShift Commons Paris - Choose Your Own Observability AdventureOpenShift Commons Paris - Choose Your Own Observability Adventure
OpenShift Commons Paris - Choose Your Own Observability Adventure
 
KubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCost
KubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCostKubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCost
KubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCost
 
IESVE Software for Florida Code Compliance Using ASHRAE 90.1-2019
IESVE Software for Florida Code Compliance Using ASHRAE 90.1-2019IESVE Software for Florida Code Compliance Using ASHRAE 90.1-2019
IESVE Software for Florida Code Compliance Using ASHRAE 90.1-2019
 
Bird eye's view on Camunda open source ecosystem
Bird eye's view on Camunda open source ecosystemBird eye's view on Camunda open source ecosystem
Bird eye's view on Camunda open source ecosystem
 
COMPUTER 10 Lesson 8 - Building a Website
COMPUTER 10 Lesson 8 - Building a WebsiteCOMPUTER 10 Lesson 8 - Building a Website
COMPUTER 10 Lesson 8 - Building a Website
 

Ground Excited Systems

  • 1. GROUND EXCITED SYSTEMS Prof. A. Meher Prasad Department of Civil Engineering Indian Institute of Technology Madras email: prasadam@iitm.ac.in
  • 2. Dynamic Equations of Motion Force excited system Ground excited system where is the relative displacement of the structure w.r.t ground. Non-moving reference Ground Acceleration vector where, are the ground accelerations in x,y,z directions respectively. are null vectors except that those elements are equal to 1, which corresponds to x,y,z translational DOF.
  • 3. Let System equations reduce to following uncoupled equations where participation factors, Note: a j = b j = 0 since initial conditions are zero i.e Modal Superposition applied to GES
  • 4. Solution to uncoupled equation of motion can be expressed as, In general , for design the response quantities of interest are: R = maximum values of (u , f s , Δ, V, M) Equivalent lateral loads Storey shears Storey Moments Storey drifts Relative displacements
  • 5.
  • 6. Ground Excited MDOF System = relative displacement of the structure w r t ground = Ground acceleration vector : where, are ground accelerations in x, y & z directions respectively Reference base x y z
  • 7. 1) SRSS 2) CQC 3) Double Sum 4) Grouping Serious errors for closely spaced frequencies and for 3-D structures ,which include torsional contribution. SRSS : Square Root of Sum of Squares .It gives most probable maximum response. Modal combination rules ** Since the maximum response in each mode would not necessarily occur at the same instant of time, over conservative to add separate modal maximum responses.
  • 8. CQC : Complete Quadratic Combination Rule (Wilson, Der Kiureghion & Baya 1981). It is based on random vibration theory. Note: All cross modal terms included very good agreement with full modal superposition extra computation minimal.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14. Multiple support Excitation Super structure free Dof Support Dof
  • 15. Decompose {u f } into pseudo static and dynamic parts {u f }= {u s } + {u d } Considering only static response ( i.e. stiffness matrix alone) Influence matrix Describes influence of support displacement on structural displacement j th column of [ i ]=structural displacements due to unit support displacement u rl only ( l th base displacement)
  • 16. (By definition ) and i.e.
  • 17. If assume light damping Uncoupled equations of motion are,
  • 18. A big mass (much bigger than the total mass of the structure ( ~10 6  total mass ) is added to each degree of freedom at moving bases. As more big masses are applied, more low frequency modes have to be extracted.
  • 19. The desired base motion is obtained by applying a point force to each degree of freedom at moving bases by Where M big =big mass and is the applied acceleration prescribed for degree of freedom N associated with moving supports The combined equation of motion is with Where is the diagonal matrix containing the big masses for moving base ‘i’ and is the base motion applied to this base
  • 20. The mass matrix [M] now contains the mass of the structure as well as the big masses associated with the secondary base. The modal equations with
  • 21. 1.000 1.000 6.7662 52.2836 0.0 4.7876 5.2909 10 8 0.9999 1.000 6.7661 52.2836 0.0 4.7876 5.2909 10 6 0.9995 1.0003 6.7641 52.2823 10 -10 4.7871 5.2910 10 4 0.9524 1.0335 6.5531 52.0552 10 -9 4.8011 5.3025 10 2 Response peaks (m/s 2 ) X 1 max X 2 max X 3 max X 4 max Natural frequency Ratio of large mass to structure