University of Florida/Eml4507/s13.team4ever.Wulterkens.R5.4

On my honor, I have neither given nor recieved unauthorized aid in doing this assignment.

Problem Statement
Assume the mass density to be 5,000 $$kg/m^{3}$$. Contruct the diagonal mass matrix and find the eigenpairs. With this, design a matlab and calfem program to determine the deformation shape.

Matlab Solution
References for Matlab code: Team 3 Report 4 Team 7 Report 4

CALFEM Solution
function R4p4

Three lowest eigenvalues and eigenvectors

j1eig = eigval(1) j1eigvx = eigvect(:,1) j1eigvy = eigvect(:,2) j2eig = eigval(2) j2eigvx = eigvect(:,3) j2eigvy = eigvect(:,4) j3eig = eigval(3) j3eigvx = eigvect(:,5) j3eigvy = eigvect(:,6) j1eig = -4.1672e-08 j1eigvx = -0.0018   0.0853    0.0136    0.0853   -0.0018    0.0699    0.0136    0.0699   -0.0018    0.0545    0.0136    0.0545   -0.0018    0.0391    0.0136    0.0391   -0.0018    0.0238    0.0136    0.0238   -0.0018    0.0084    0.0136    0.0084   -0.0018   -0.0070    0.0136   -0.0070 j1eigvy = -0.0485   0.0068   -0.0488    0.0068   -0.0485    0.0071   -0.0488    0.0071   -0.0485    0.0074   -0.0488    0.0074   -0.0485    0.0077   -0.0488    0.0077   -0.0485    0.0080   -0.0488    0.0080   -0.0485    0.0083   -0.0488    0.0083   -0.0485    0.0086   -0.0488    0.0086 j2eig = -1.0740e-08 j2eigvx = 0.0155  -0.0334   -0.0053   -0.0334    0.0155   -0.0127   -0.0053   -0.0127    0.0155    0.0081   -0.0053    0.0081    0.0155    0.0289   -0.0053    0.0289    0.0155    0.0496   -0.0053    0.0496    0.0155    0.0704   -0.0053    0.0704    0.0155    0.0912   -0.0053    0.0912 j2eigvy = -0.0242   0.0747    0.0200    0.0761   -0.0197    0.0156    0.0197    0.0202   -0.0092   -0.0374    0.0148   -0.0335    0.0040   -0.0572    0.0040   -0.0572    0.0148   -0.0335   -0.0092   -0.0374    0.0197    0.0202   -0.0197    0.0156    0.0200    0.0761   -0.0242    0.0747 j3eig = 1.2133e-07 j3eigvx = 0.0206  -0.0518   -0.0370   -0.0552    0.0097    0.0333   -0.0347    0.0284   -0.0031    0.0552   -0.0190    0.0633    0.0002   -0.0083   -0.0002    0.0083    0.0190   -0.0633    0.0031   -0.0552    0.0347   -0.0284   -0.0097   -0.0333    0.0370    0.0552   -0.0206    0.0518 j3eigvy = 0.0616  -0.0146    0.0727   -0.0164    0.0453    0.0010    0.0647   -0.0047    0.0125    0.0180    0.0453    0.0165   -0.0204   -0.0017    0.0204    0.0017   -0.0453   -0.0165   -0.0125   -0.0180   -0.0647    0.0047   -0.0453   -0.0010   -0.0727    0.0164   -0.0616    0.0146

Plotting the three lowest mode shapes