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Sensitivity of the PDE interface in implementing the equations
Posted 06.09.2011, 19:31 GMT-4 1 Reply
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Hello all,
I am working with PDE interface and I have seen very very very strange behaviours in implementing the equations by this interface. For example the equation: ("lambda" and "mu" are known Lame parameters)
Case 1: (lambda+2*mu)*(d^2(u)/dx^2)+(rho*d^2(u)/dt^2)=0
Normalizing the equation by (lambda+2*mu):
Case 2: (d^2u/dx^2)+(rho/((lambda+2*mu)*)*d^2u/dt^2)=0
Knowing the value of (lambda+2*mu is equal to 2.692e11 (Obvious in parameter definition) and substituting in the first case:
Case 3: (2.692e11)*(d^2(u)/dx^2)+(rho*d^2(u)/dt^2)=0
Considering that:
All cases are fixed by (u=0) in one end and in other node there is "zero flux" condition. (Knowing that the Flux-term changes in case 1 and case 2 but the zeroflux B.C is not changing as it has to be equal to zero) and therefore all have same B.Cs.
The results are totally different for the "EigenFrequency" Study.
Case 1) has COMPLEX eigenfrequencies, Nonzero damping matrix.
Case 2) not complex values, zero damping matrix.
Case 3) (only substituting the vale of "lambda+2*mu" in case1 (a trivial change) resulted in REAL eigenfrequencies.
I am wondering if there is any problem in my solution that has caused these weired resilts. If not, how can I trust the PDE interface? What are the criteria behind implementing the equations that I had to consider?
Three models are attached in adition the stiffness and damping matrixes of the Case 1 and Case 2 are demonstrated in the Excel file.
I appreciate any comment.
Best Regards,
Masoud
I am working with PDE interface and I have seen very very very strange behaviours in implementing the equations by this interface. For example the equation: ("lambda" and "mu" are known Lame parameters)
Case 1: (lambda+2*mu)*(d^2(u)/dx^2)+(rho*d^2(u)/dt^2)=0
Normalizing the equation by (lambda+2*mu):
Case 2: (d^2u/dx^2)+(rho/((lambda+2*mu)*)*d^2u/dt^2)=0
Knowing the value of (lambda+2*mu is equal to 2.692e11 (Obvious in parameter definition) and substituting in the first case:
Case 3: (2.692e11)*(d^2(u)/dx^2)+(rho*d^2(u)/dt^2)=0
Considering that:
All cases are fixed by (u=0) in one end and in other node there is "zero flux" condition. (Knowing that the Flux-term changes in case 1 and case 2 but the zeroflux B.C is not changing as it has to be equal to zero) and therefore all have same B.Cs.
The results are totally different for the "EigenFrequency" Study.
Case 1) has COMPLEX eigenfrequencies, Nonzero damping matrix.
Case 2) not complex values, zero damping matrix.
Case 3) (only substituting the vale of "lambda+2*mu" in case1 (a trivial change) resulted in REAL eigenfrequencies.
I am wondering if there is any problem in my solution that has caused these weired resilts. If not, how can I trust the PDE interface? What are the criteria behind implementing the equations that I had to consider?
Three models are attached in adition the stiffness and damping matrixes of the Case 1 and Case 2 are demonstrated in the Excel file.
I appreciate any comment.
Best Regards,
Masoud
1 Reply Last Post 07.09.2011, 14:28 GMT-4
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Posted:
1 decade ago
I could figure out where the problem is :). Just I mention here for those who may face same issues. In my model, I had defined the parameter (lambda) as my own definition. But, lambda has also another definition by Comsol itself. I just made a mistake by naming va parameter exactly same as another pre-defined parameter in COMSOL.
Be aware and consider this case in your modelling.
Masoud