结构动力学课件dyanmicsofstructures-ch19

1、chapter 19. partial differential equations of motion191 uncoupled flexural equations of motion: undamped casechapter 19. partial differential equations of motionwhen the two orthogonality relationships are applied to the rst two terms, it is evident that all terms in the series expansions, except th

2、e nth, vanish; thus,multiplying by and integrating yieldschapter 19. partial differential equations of motionchapter 19. partial differential equations of motionexample e192.(a) arrangement of beam and load;(b) applied step-function loading.chapter 19. partial differential equations of motiondetermi

3、ne mode shapes and frequencies:results were found in example e181 to becompute generalized mass and loading:chapter 19. partial differential equations of motionsolve the normalcoordinate response equation:the duhamel solution of this equation isevaluate displacement, moment and shear response:chapte

4、r 19. partial differential equations of motion192 uncoupled flexural equations of motion: damped casechapter 19. partial differential equations of motionmultiplying by , integrating, and applying the two orthogonality relationships together with the denitions of generalized mass and generalized load

5、ing leads tostiffnessproportional dampingzero, except for the term i = nchapter 19. partial differential equations of motionfinally, introducing the damping ratio for the nth mode194 uncoupled axial equations of motion: undamped casechapter 19. partial differential equations of motionmultiplying eac

6、h term by and applying the orthogonality relationshipschapter 19. partial differential equations of motionexample e194.pile subjected to end loading:(a) geometric configuration;(b) stepfunction loading.chapter 19. partial differential equations of motiondetermine mode shapes and frequencies(see example e185):compute generalized mass and loading:solve the generalizedcoordinate response (see example e192):chapter 19. partial differential equations of motionevaluate displacement and axialforce response:chapter 19. partial differential equations of motiondis