Wuhan University of TechnologyChapter1Overview of Structural Dynamics2-1
2-1 Wuhan University of Technology Chapter 1 Overview of Structural Dynamics
Wuhan University of TechnologyContents1.1Methods of discretizationLumped-mass procedureGeneralizeddisplacementsThe finite element concept1.2 Formulation of the equations of motionDirect equilibration using d'Alembert's principlePrinciple of virtual displacementsVariational approach2-2
2-2 Wuhan University of Technology 1.1 Methods of discretization Lumped-mass procedure Generalized displacements The finite element concept 1.2 Formulation of the equations of motion Direct equilibration using d’Alembert’s principle Principle of virtual displacements Variational approach Contents
Wuhan University of Technology1.1 Methods of discretization-Lumped-massprocedurep(t)Inertialforces2-3
2-3 Wuhan University of Technology 1.1 Methods of discretization – Lumped-mass procedure
Wuhan University of Technology1.1 Methods of discretization-Lumped-massprocedureBecause the mass of the beam is distributed continuously alongits length, the displacements and accelerations must be defined foreach point along the axis if the inertial forces are to be completelydefined;In this case, theanalysis must be formulated in terms of partialdifferential equations because position alongthe spanas well astimemustbetakenasindependentvariables2-4
2-4 Wuhan University of Technology Because the mass of the beam is distributed continuously along its length, the displacements and accelerations must be defined for each point along the axis if the inertial forces are to be completely defined; In this case, the analysis must be formulated in terms of partial differential equations because position along the span as well as time must be taken as independent variables. 1.1 Methods of discretization – Lumped-mass procedure
Wuhan University of Technology1.1 Methods of discretization-Lumped-massprocedurep(t)m,m2m3Lumped-massidealizationof asimplebeam2-5
2-5 Wuhan University of Technology 1.1 Methods of discretization – Lumped-mass procedure Lumped-mass idealization of a simple beam