PVD and Assumed Mode
2
7/23/2019 PVD and Assumed Mode http://slidepdf.com/reader/full/pvd-and-assumed-mode 1/2 Application of the Principal of Virtual Displacements to Lumped-Parameter Models • A virtual displacement is an arbitrary, infinitesimal, imaginary change of configuration of a system, consistent with all displacement constraints on the system. • Virtual displacements are not a function of time. • The virtual work is the work of the forces acting on a system as the system undergoes a virtual displacement. δW = ∑ i=1 N Q i δq i The generalized force, Q i is the quantity that multiplies the virtual displacement, δq i , in forming the virtual work term δW i • The Principle of Virtual isplacements !PV" #or any arbitrary virtual displacements of a system, the combined virtual work of real forces and inertia forces must vanish. δW ¿ =δW real forces + δW inertial forces =0 • $mportant% • raw two diagrams when solving problem using PV • &inematics of displacement • #ree body diagram.
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Transcript of PVD and Assumed Mode
7/23/2019 PVD and Assumed Mode
http://slidepdf.com/reader/full/pvd-and-assumed-mode 1/2
Application of the Principal of Virtual Displacements to Lumped-Parameter Models
• A virtual displacement is an arbitrary, infinitesimal, imaginary change of configuration
of a system, consistent with all displacement constraints on the system.
• Virtual displacements are not a function of time.
• The virtual work is the work of the forces acting on a system as the system undergoes
a virtual displacement.
δW =∑i=1
N
Qi δqi
The generalized force,
Qi
is the quantity that multiplies the virtual displacement, δqi
, in
forming the virtual work termδW i
• The Principle of Virtual isplacements !PV"
#or any arbitrary virtual displacements of a system, the combined virtual work of real forces
and inertia forces must vanish.
δW ¿=δW real
forces
+δW inertial
forces
=0
• $mportant%
• raw two diagrams when solving problem using PV
• &inematics of displacement
• #ree body diagram.
7/23/2019 PVD and Assumed Mode
http://slidepdf.com/reader/full/pvd-and-assumed-mode 2/2
Application of the Principle of Virtual Displacements to Continuous Models: Assumed-
Modes Method
• An admissible function is a function that satisfies the geometric boundary conditions
of the system under consideration and possesses derivatives of order at least equal to
that appearing in the strain energy e'pression.
• An assumed mode¿Ψ ¿ '" is an admissible function that is selected by the user for
the purpose of appro'imating the deformation of a continuous system.
v ( x , t )=Ψ ( x )qv (t )
• Any admissible function may be employed as t he shape function but a shape that can
be e'pected to be similar to the shape of deformation should be chosen.
δW realforces
=δW cons+δW nc=0
δW cons−δV [change∈ potential energy ]
(y P.V.δW real+δW inertial ) *
δW ¿
=δW nc−δV +δW inertialforces =0
• The strain energy in a bar undergoing a'ial deformation or bending is
V axial=1
2∫0
L
AE(u' )2 dx
V ending=1
2∫0
L
E! (v' ' )2 dx
