结构动力学课件—dyanmicsofstructures-ch1718

1、,CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION,171 INTRODUCTION,172 BEAM FLEXURE: ELEMENTARY CASE,CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION,summing moments about point A,equilibrium relationship for vertical forces,CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION,173 BEAM FLEXU

2、RE: INCLUDING AXIALFORCE EFFECTS,CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION,173 BEAM FLEXURE: INCLUDING AXIALFORCE EFFECTS,momentequilibrium equation now becomes,Rotation of beam axis,CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION,174 BEAM FLEXURE: INCLUDING VISCOUS DAMPING,Material

3、damping,Distributed damping,CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION,176 AXIAL DEFORMATIONS: UNDAMPED,CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,First, constant EI and m,181 BEAM FLEXURE: ELEMENTARY CASE,one form of solution of th

4、is equation can be obtained easily by separation of variables using,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,These real constants must be evaluated so as to satisfy the known boundary conditions (displacement, slope, moment, or shear) at the end

5、s of the beam. Taking this action, any three of the four constants can be expressed in terms of the fourth and an expression (called the frequency equation) can be obtained from which the frequency parameter a is determined.,Example E181. Simple Beam,from which one obtains,CHAPTER 18. ANALYSIS OF UN

6、DAMPED FREE VIBRATION,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,Example E182. Cantilever Beam,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,CHAPTER

7、18. ANALYSIS OF UNDAMPED FREE VIBRATION,Example E183. Cantilever Beam with Rigid Mass at Free End,the translational and rotary inertial force components,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,force and moment equilibrium of the rigid mass requires that boundary conditions,182 BEAM FLEXURE:

8、INCLUDING AXIALFORCE EFFECTS,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,In fact, it is evident that when the axial force P equals zero, so that g = 0, then,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,183 BEAM FLEXURE: WITH DISTRIBUTED ELASTIC SUPPORT,Separating variables as before,giving tw

9、o independent equations,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,184 BEAM FLEXURE: ORTHOGONALITY OF VIBRATION MODE SHAPES,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,The second orthogonality condition,For a nonuniform beam, the equation of motion in free vibrations,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,185 FREE VIBRATIONS IN AXIAL DEFORMATION,Using the solution,CHAPTER 18. ANALYSIS OF UN