Embed Size (px)
DESCRIPTION
Mathematical & Mechanical Method in Mechanical Engineering. Dr. Wang Xingbo Email: [email protected] QQ:168731668 Homepage: wxbstudio.home4u.china.com Fall ， 2005. Mathematical & Mechanical Method in Mechanical Engineering. Motivation of This Course. - PowerPoint PPT Presentation
Citation preview
Dr. Wang XingboDr. Wang XingboEmail: [email protected]: [email protected]
QQ:168731668QQ:168731668Homepage: wxbstudio.home4u.china.comHomepage: wxbstudio.home4u.china.com
FallFall ，， 20052005
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
1.1. Mechanical Engineering is being a subject of Mechanical Engineering is being a subject of sciencescience
2.2. Development of cross &Multi-subjects,especially Development of cross &Multi-subjects,especially Computer science
3.3. Future requirements of persons in research Future requirements of persons in research workwork
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Motivation of This CourseMotivation of This Course
1.1. To show idea of scientific methodologyTo show idea of scientific methodology
2.2. To introduce fundamental methodsTo introduce fundamental methods
3.3. To agitate the creative competenceTo agitate the creative competence
4.4. To dig out one or more elitesTo dig out one or more elites
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Purpose of the coursePurpose of the course
1.1. Experiential Method Experiential Method
2.2. Scientific Method Scientific Method
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Methodology Methodology
Originates from people’s experience and Originates from people’s experience and intuition without any logical or scientific intuition without any logical or scientific principlesprinciples
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Methodology Methodology Experiential MethodExperiential Method
1. Utility 1. Utility
2. Simple 2. Simple
3. 3. Trial Trial
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Experiential Method Experiential Method --TraitsTraits
1.1. A method but not the perfect oneA method but not the perfect one
2.2. Less cost but high efficientLess cost but high efficient
3.3. Without extension Without extension
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Experiential MethodExperiential Method - -EvaluationEvaluation
A process by which scientists, collectivelA process by which scientists, collectively and over-time, endeavor to construct ay and over-time, endeavor to construct an accurate representation of the worldn accurate representation of the world
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Scientific Method Scientific Method
1. Observation and description
2. Formulation of a hypothesis
3. Use of the hypothesis
4. Performance of experimental tests
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Scientific Method-Scientific Method-Four StepsFour Steps
1. A hypothesis is a limited statement regarding cause and effect in specific situations
2. A model is reserved when hypothesis has is valid
3. A scientific theory or law represents a hypothesis confirmed through repeated experimental tests
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Scientific Method:Scientific Method:Hypotheses, Models, Theories and Laws Hypotheses, Models, Theories and Laws
Step1. State the problem
Step 2. Research the problem
Step 3. Form a hypothesis
Step 4 . Test the hypothesis
Step 5. Draw conclusions from the data
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Scientific Method:Scientific Method:Solving Problems with Scientific Methods Solving Problems with Scientific Methods
A process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Mathematical Models Mathematical Models
Four procedures as follows
1. Building a Mathematical Model
2. Verifying and Refining a Model
3. Variables and Parameters
4. Continuous /Discrete in Time
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Mathematical Models Mathematical Models
1. Newtonian Dynamics
2. LaGrangian and Hamiltonian Dynamics
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Mechanical Models Mechanical Models
1. A body remains at rest or in a uniform state of motion if no external force acts on it.
2. A body, upon which a force acts, moves in such a way that the time rate of change of the momentum equals the force.
3. If two bodies act on one another by means of forces, these force
s have equal magnitudes and opposite directions.
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Mechanical Models :Mechanical Models :Newtonian Dynamics
The actual path of a dynamical system in configuration space extermeizes the action between two defined locations and times
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Mechanical Models :Mechanical Models :LaGrangian and Hamiltonian Dynamics
Chapter 1: Scientific methodsChapter 2 and 3: Vector and tensorChapter 4: Differential form Chapter5: Variational calculusChapter 6: Lie groupChapter 7: Manifold theoryChapter 8: Classical mechanics Chapter 9 :Finite deformation
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Contents in this course Contents in this course
Course procedure:20%
Homework & Discussion:20%
Final Exam:60%
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
About ExaminationAbout Examination
Chapter 1 is over!
Take a rest!
To be continued……
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
11:00am.,Oct.,26,200511:00am.,Oct.,26,2005
1. Identify the problem
2. Begin with a simple model.
3. Identify important variables and constants.
4. Develop the equation(s)
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Mathematical Models:Mathematical Models:Building a Mathematical Model Building a Mathematical Model
1. Is the information produced reasonable?
2. Are the assumptions made?
3. Are there any factors not considered?
4. How do the results, if available?
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Mathematical Models:Mathematical Models:Verifying and Refining a Model Verifying and Refining a Model
1. Output variables
2. Input variables
3. Parameters (constants)
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Mathematical Models:Mathematical Models:Variables and Parameters Variables and Parameters
1. Is the information produced reasonable?
2. Are the assumptions made?
3. Are there any factors not considered?
4. How do the results, if available?
Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering
Mathematical Models:Mathematical Models:Continuous /Discrete in Time
