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ASE 365 - Lecture Test 1 Compalation

ASE 365 - Lecture Test 1 Compalation - Welcome to...

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Click to edit Master subtitle style Welcome to Structural Dynamics! Dr. Jeffrey K. Bennighof ASE 365 Spring 2010

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Preliminaries My office data: WRW 308B, 471-4709 Email: [email protected] (or Office hours: 11-12 a.m. MWF Textbook: Fundamentals of Vibrations by L. Meirovitch Grading: 3 tests (20% each), final (30%) Homework: 10%
Reading and homework Read sections 1-8, 10 of chapter 1 Homework sets due on Mondays Assignments posted on http://courses.utexas.edu Grader: Rohan Mahadik (WRW 214)

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“How to thrive in 365” Come to class Stay engaged in class: Ask questions, participate Take notes Read the book Try to finish the homework by Friday, if it’s due on Monday
Concepts from Dynamics Newton’s laws for a particle: 1. No force → no acceleration 2. m v p

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Free-body diagrams 1. Decide: What is the “object”? 2. Draw the object separated from its surroundings (a “free body”). 3. Represent all forces and moments acting on the body. 4. “Inertia forces” do not belong on a FBD. (Maybe on a “kinetic diagram”…)
Newton’s laws for a particle (cont’d): 3. Interaction forces between two particles are equal and opposite fi j mj fj i mi text. in 67 p. 1.1, Problem : Example

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Moment of a force: Moment of momentum (a.k.a. angular momentum): m r F O m r p O
" conserved. is momentum Angular " : constant is , If O O H 0 M = text. in 69 p. 1.5, Problem at Look

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O O O M F r f F r r r r r r r H r r H O Σ = × = + × = × = × + × = × = = = = = = = = i N i i N j ij i N i i i i N i i i i N i i i i N i i i i N i i m m m m 1 1 1 1 1 1 1 so : about momentum Angular center. mass to relative position is where : center mass About C i i i N i i r r r M F r H C C - Σ = × = = 1
Work and energy : work of Increment m F dr dr F = dW : energy Kinetic dT m d d m dt dt d m dt m dt dt d m m dW = = = = = = = r r r r r r r r r r dr r 2 1 ) ( ) ( ) (

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) energy kinetic in change done work ( . have must we then , and If = - = = = = 1 2 12 2 1 T T W dT dW dW dr F dr F r r ) energy) potential in (change done work ( . and energy potential a is there ve, conservati are forces If - = - - = ) ( 1 2 12 V V W V ) conserved is energy total ( energy total where or so Then = + = + = + - = - - = V T E E E V T V T T T V V W 2 1 2 2 1 1 1 2 1 2 12 ) (
Systems of particles m1 mi mj m N : for law 2nd s Newton' i m N i m N j i i ij i , , 1 1 = = + = , a f F i N i N i i N j ij N i i m a f F = = = = = + 1 1 1 1 : system entire For : cancels so , law, 3rd s Newton' By ∑∑ = = - = N i N j ij ji ij 1 1 f f f system. on force resultant is where F a F F i N i i N i i m = = = = 1 1

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i N i i tot C N i i C N i i i N i i C m m m m m r r r r r = = = = = = 1 1 1 1 so : center mass Define . becomes law 2nd s Newton' and Then C tot C tot C N i i i N i i i N i i m m m m m a F a r r a = = = = = = = 1 1 1
O O O M F r f F r r r r r r r H r r H O Σ = × =

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