Aim Understand the concept of lumped element modelling Understand variational solution in the mechanical domain Understand Rayleigh Ritz in the mechanical.

Presentasjon om: "Aim Understand the concept of lumped element modelling Understand variational solution in the mechanical domain Understand Rayleigh Ritz in the mechanical."— Utskrift av presentasjonen:

1 Aim Understand the concept of lumped element modelling Understand variational solution in the mechanical domain Understand Rayleigh Ritz in the mechanical domain

2 What is lumped element modelling? Reduction of the number of variables Mapping onto electrical domain (optional) Lowrie et. al 2005

3 It involves Turning partial differential equations into ordinary differential equations Approximations and more approximations (Ab-)use of available tools

4 Procedure Partitioning and choice of variables (x,v) Find values for the parameters (m,k,γ) Couple Analyze x

5 Hvor i Senturia

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10 Partitioning and choice of variables Partitioning and choice of variables (x,v) Find values for the parameters (m,k,γ) Couple Analyze x

11 Parameter extraction Solution of partial differential equations Formulas Experiment Guesswork Partitioning and choice of variables (x,v) Find values for the parameters (m,k,γ) Couple Analyze

12 Løsning av partielle differensialligninger Fokus – på kobling – på dynamikk (egenmoder) Verktøy –FEM/BEM –Analytisk Eksakt Tilnærmet

13 Variational principle Weak form of the differential equation: Minimize U Trial function: Parameters k

14 Applied to membrane (plate) Pre- stress Bending Elongatio n k

15 Rayleigh-Ritz - basis m, ω Best trial function Approximate eigenmode Approximate eigenfrequency t=0

16 Rayleigh-Ritz

17 ω

18 m x2x2 m= 2

19 Motstand R

20 Verktøy for analyse Generaliserte impedanser Tilstandsvariable Krets simuleringsverktøy Transferfunksjoner Transfermatriser Laplace transformasjon Fourier transformasjon Konvolusjon

21 Mekanisk svingesystem x

22 Elektrisk svingesystem

23 Bevegelseslikningen

24 Resonansfrekvens Ved null dempning går transferfunksjonen mot uendelig når: Innfører derfor udempet resonansfrekvens

25 Q-faktor

26 Eksperiment Q,f

27 Systembeskrivelse

28 Observerbarhet

29 Two port elements