Wuhan University of Technology1.1 Methods of discretizationGeneralizeddisplacementsv(x)b,sinx2元xb,sinL3元xbysinLSine-seriesrepresentationofsimplebeamdeflection2-11
2-11 Wuhan University of Technology 1.1 Methods of discretization – Generalized displacements Sine-series representation of simple beam deflection
Wuhan University of Technology1.1 Methods of discretization-GeneralizeddisplacementsIn cases where the mass of the system is quite uniformlydistributedthroughout,analternativeapproachto limitingthenumber of degrees of freedom may be preferable;Asimpleexampleofthisapproachisthetrigonometric-seriesrepresentation of thedeflection ofa simple beam.Inthiscase,thedeflectionshapemaybeexpressedasthesumof independentsine-wavecontributions,asshowninnextFig.,orinmathematical form:n元x>v(x)=b.sinLn=l2-12
2-12 Wuhan University of Technology 1.1 Methods of discretization – Generalized displacements In cases where the mass of the system is quite uniformly distributed throughout, an alternative approach to limiting the number of degrees of freedom may be preferable; A simple example of this approach is the trigonometric-series representation of the deflection of a simple beam. In this case, the deflection shape may be expressed as the sum of independent sine-wave contributions, as shown in next Fig., or in mathematical form: 1 ( ) sin n n n x vx b L