结构动力学ppt课件

1、CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION171 INTRODUCTION172 BEAM FLEXURE: ELEMENTARY CASECHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTIONsumming moments about point Aequilibrium relationship for vertical forcesCHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION173 BEAM FLEXURE: INCL

2、UDING AXIALFORCE EFFECTSCHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION173 BEAM FLEXURE: INCLUDING AXIALFORCE EFFECTSmomentequilibrium equation now becomesRotation of beam axisCHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION174 BEAM FLEXURE: INCLUDING VISCOUS DAMPINGMaterial dampingDistribu

3、ted dampingCHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION176 AXIAL DEFORMATIONS: UNDAMPEDCHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTIONCHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONFirst, constant EI and m181 BEAM FLEXURE: ELEMENTARY CASEone form of solution of this equation can be obta

4、ined easily by separation of variables usingCHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONCHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONThese real constants must be evaluated so as to satisfy the known boundary conditions (displacement, slope, moment, or shear) at the ends of the beam. Taking this

5、 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 Beamfrom which one obtainsCHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONCHAPTER

6、18. ANALYSIS OF UNDAMPED FREE VIBRATIONCHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONExample E182. Cantilever BeamCHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONCHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONCHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONCHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRAT

7、IONExample E183. Cantilever Beam with Rigid Mass at Free Endthe translational and rotary inertial force componentsCHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONforce and moment equilibrium of the rigid mass requires that boundary conditions182 BEAM FLEXURE: INCLUDING AXIALFORCE EFFECTSCHAPTER 18. A

8、NALYSIS OF UNDAMPED FREE VIBRATIONIn fact, it is evident that when the axial force P equals zero, so that g = 0, then CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION183 BEAM FLEXURE: WITH DISTRIBUTED ELASTIC SUPPORTSeparating variables as beforegiving two independent equationsCHAPTER 18. ANALYSIS OF

9、 UNDAMPED FREE VIBRATION184 BEAM FLEXURE: ORTHOGONALITY OF VIBRATION MODE SHAPESCHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONThe second orthogonality condition,For a nonuniform beam, the equation of motion in free vibrationsCHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION185 FREE VIBRATIONS IN AXIAL DEFORMATIONUsing the solutionCHAPTER 18. ANALYSIS OF