jagomart
digital resources
picture1_Dynamics Of Rigid Bodies Lecture Notes Pdf 158229 | Chapt16 Lecture


 165x       Filetype PDF       File size 1.00 MB       Source: web.boun.edu.tr


File: Dynamics Of Rigid Bodies Lecture Notes Pdf 158229 | Chapt16 Lecture
seventh edition chapter vector mechanics for engineers 16dynamics ferdinand p beer plane motion of rigid bodies e russell johnston jr forces and accelerations lecture notes j walt oler texas tech ...

icon picture PDF Filetype PDF | Posted on 19 Jan 2023 | 2 years ago
Partial capture of text on file.
                                                                                           Seventh Edition
                             CHAPTER VECTOR MECHANICS FOR ENGINEERS:
                             16DYNAMICS
                                         Ferdinand P. Beer        Plane Motion of Rigid Bodies:
                                         E. Russell  Johnston, Jr.   Forces and Accelerations
                                         Lecture Notes:
                                         J. Walt Oler
                                         Texas Tech University
                                                                        © 2003 The McGraw-Hill Companies, Inc. All rights reserved.
                             EditSev
                             ioeVector Mechanics for Engineers: Dynamics
                             nnt
                              h Contents
                                  Introduction                            Sample Problem 16.3
                                  Equations of Motion of a Rigid Body     Sample Problem 16.4
                                  Angular Momentum of a Rigid Body        Sample Problem 16.5
                                    in Plane Motion                       Constrained Plane Motion
                                  Plane Motion of a Rigid Body:           Constrained Plane Motion: 
                                    d’Alembert’s Principle                  Noncentroidal Rotation
                                  Axioms of the Mechanics of Rigid        Constrained Plane Motion: 
                                    Bodies                                  Rolling Motion
                                  Problems Involving the Motion of a      Sample Problem 16.6
                                    Rigid Body                            Sample Problem 16.8
                                  Sample Problem 16.1                     Sample Problem 16.9
                                  Sample Problem 16.2                     Sample Problem 16.10
                                 © 2003 The McGraw-Hill Companies, Inc. All rights reserved.          16 - 2
                                                                                                                                 1
                                              EditSev
                                              ioe   Vector Mechanics for Engineers: Dynamics
                                              n nt
                                                h   Introduction
                                                                   • In this chapter and in Chapters 17 and 18, we will be 
                                                                      concerned with the kinetics of rigid bodies, i.e., relations 
                                                                      between the forces acting on a rigid body, the shape and mass 
                                                                      of the body, and the motion produced.
                                                                   • Results of this chapter will be restricted to:
                                                                         - plane motion of rigid bodies, and
                                                                         - rigid bodies consisting of plane slabs or bodies which 
                                                                             are symmetrical with respect to the reference plane.
                                                                   • Our approach will be to consider rigid bodies as made of 
                                                                      large numbers of particles and to use the results of Chapter 
                                                                      14 for the motion of systems of particles.  Specifically,
                                                                                  r        r                         r         r
                                                                                                                               &
                                                                              ∑F=ma                and          ∑MG=HG
                                                                   • D’Alembert’s principle is applied to prove that the external 
                                                                                                                                                      r
                                                                      forces acting on a rigid body are equivalent a vector ma
                                                                      attached to the mass center and a couple of moment Iα.
                                                      © 2003 The McGraw-Hill Companies, Inc. All rights reserved.                                                     16 - 3
                                              EditSev
                                              ioe   Vector Mechanics for Engineers: Dynamics
                                              n nt
                                                h   Equations of Motion for a Rigid Body
                                                                                                                          • Consider a rigid body acted upon 
                                                                                                                             by several external forces.
                                                                                                                          • Assume that the body is made of 
                                                                                                                              a large number of particles.
                                                                                                                          • For the motion of the mass center 
                                                                                                                             Gof the body with respect to the 
                                                                                                                             Newtonian frame Oxyz,
                                                                                                                                               r       r
                                                                                                                                          ∑F=ma
                                                                                                                          • For the motion of the body with 
                                                                                                                             respect to the centroidal frame 
                                                                                                                             Gx’y’z’,          r         r
                                                                                                                                                         &
                                                                                                                                          ∑MG=HG
                                                                                                                          • System of external forces is 
                                                                                                                             equipollent to the system 
                                                                                                                                                    r         r
                                                                                                                                                              &
                                                                                                                             consisting of ma and HG .
                                                      © 2003 The McGraw-Hill Companies, Inc. All rights reserved.                                                     16 - 4
                                                                                                                                                                                                                   2
                            EditSev
                            ioeVector Mechanics for Engineers: Dynamics
                            nnt
                             h Angular Momentum of a Rigid Body in Plane Motion
                                                            • Angular momentum of the slab may be 
                                                              computed by
                                                                   r    n  r′ r′
                                                                          ()
                                                                  H =∑ r ×v∆m
                                                                    G      i   i  i
                                                                        i=1
                                                                        n  r′  r r′
                                                                          []()
                                                                      =∑r×ω×r ∆m
                                                                           i      i   i
                                                                        i=1
                                                                        r    ′2
                                                                           ()
                                                                      =ω∑r ∆m
                                                                         r   i   i
                                                                      = Iω
                                                            • After differentiation,
                                                                   r     r    r
                                                                   &     &
                                                                  HG =Iω = Iα
                                                            • Results are also valid for plane motion of bodies 
                                 • Consider a rigid slab in   which are symmetrical with respect to the 
                                   plane motion.              reference plane.
                                                            • Results are not valid for asymmetrical bodies or 
                                                              three-dimensional motion.
                                © 2003 The McGraw-Hill Companies, Inc. All rights reserved.       16 - 5
                            EditSev
                            ioeVector Mechanics for Engineers: Dynamics
                            nnt
                             h Plane Motion of a Rigid Body: D’Alembert’s Principle
                                                           • Motion of a rigid body in plane motion is 
                                                             completely defined by the resultant and moment 
                                                             resultant about G of the external forces.
                                                               ∑F =ma       ∑F =ma      ∑M =Iα
                                                                   x     x     y     y       G
                                                           • The external forces and the collective effective 
                                                             forces of the slab particles are equipollent (reduce 
                                                             to the same resultant and moment resultant) and 
                                                             equivalent (have the same effect on the body).
                                                           • d’Alembert’s Principle:  The external forces 
                                                             acting on a rigid body are equivalent to the 
                                                             effective forces of the various particles forming 
                                                             the body.
                                                           • The most general motion of a rigid body that is 
                                                             symmetrical with respect to the reference plane 
                                                             can be replaced by the sum of a translation and a 
                                                             centroidal rotation.
                                © 2003 The McGraw-Hill Companies, Inc. All rights reserved.       16 - 6
                                                                                                                             3
                              EditSev
                              ioe Vector Mechanics for Engineers: Dynamics
                              n nt
                                h Axioms of the Mechanics of Rigid Bodies
                                                                  • The forces r       r′act at different points on 
                                                                               F and F
                                                                    a rigid body but but have the same magnitude, 
                                                                    direction, and line of action. 
                                                                  • The forces produce the same moment about 
                                                                    any point and are therefore, equipollent 
                                                                    external forces.
                                                                  • This proves the principle of transmissibility 
                                                                    whereas it was previously stated as an axiom.
                                   © 2003 The McGraw-Hill Companies, Inc. All rights reserved.              16 - 7
                              EditSev
                              ioe Vector Mechanics for Engineers: Dynamics
                              n nt
                                h Problems Involving the Motion of a Rigid Body
                                                                     • The fundamental relation between the forces 
                                                                       acting on a rigid body in plane motion and 
                                                                       the acceleration of its mass center and the 
                                                                       angular acceleration of the body is illustrated 
                                                                       in a free-body-diagram equation.
                                                                     • The techniques for solving problems of 
                                                                       static equilibrium may be applied to solve 
                                                                       problems of plane motion by utilizing
                                                                         - d’Alembert’s principle, or
                                                                         - principle of dynamic equilibrium
                                                                     • These techniques may also be applied to 
                                                                       problems involving plane motion of 
                                                                       connected rigid bodies by drawing a free-
                                                                       body-diagram equation for each body and 
                                                                       solving the corresponding equations of 
                                                                       motion simultaneously.
                                   © 2003 The McGraw-Hill Companies, Inc. All rights reserved.              16 - 8
                                                                                                                                         4
The words contained in this file might help you see if this file matches what you are looking for:

...Seventh edition chapter vector mechanics for engineers dynamics ferdinand p beer plane motion of rigid bodies e russell johnston jr forces and accelerations lecture notes j walt oler texas tech university the mcgraw hill companies inc all rights reserved editsev ioevector nnt h contents introduction sample problem equations a body angular momentum in constrained d alembert s principle noncentroidal rotation axioms rolling problems involving ioe n nt this chapters we will be concerned with kinetics i relations between acting on shape mass produced results restricted to consisting slabs or which are symmetrical respect reference our approach consider as made large numbers particles use systems specifically r f ma mg hg is applied prove that external equivalent attached center couple moment acted upon by several assume number gof newtonian frame oxyz centroidal gx y z system equipollent slab may computed vm g m...

no reviews yet
Please Login to review.