magpie
Modal analysis of 2D Plates with Generalised Elastic Boundary Conditions
Contents
Syntax
Om = magpie (density, Youngs, poisson, dim, h, BCs) [Om,Q,Dm] = magpie (density, Youngs, poisson, dim, h, BCs) [Om,Q,Nxy] = magpie (density, Youngs, poisson, dim, h, BCs) [Om,Q,Nxy,biharm] = magpie (density, Youngs, poisson, dim, h, BCs) [Om,Q,Nxy,biharm,Dm] = magpie (density, Youngs, poisson, dim, h, BCs)
[Om, Q] = magpie (density, Youngs, poisson, dim, h, BCs, Number_of_modes)
[Om,Q] = magpie (density, Youngs, poisson, dim, h, BCs, Number_of_modes, plot_type, normalisation)
Description
Om = magpie (density, Youngs, poisson, dim, h, BCs) calculates all possible angular modal frequencies Om for the given plate parameters.
Om = magpie (density, Youngs, poisson, dim, h, BCs)
[Om,Q,Dm] = magpie (density, Youngs, poisson, dim, h, BCs)
[Om,Q,Nxy] = magpie (density, Youngs, poisson, dim, h, BCs)
[Om,Q,Nxy,biharm] = magpie (density, Youngs, poisson, dim, h, BCs)
[Om,Q,Nxy,biharm,Dm] = magpie (density, Youngs, poisson, dim, h, BCs) optional outputs of eigenvectors Q adjusted grid size Nxy, biharmonic biharm and eigenvalues Dm.
Om = magpie (density, Youngs, poisson, dim, h, BCs, Number_of_modes) avaialable with all the optional outputs above, but for a given number of modes. Usefull for large grids where calculating all modes is not feasible with memory constraints.
Example
Lx = 1.10; Ly = 0.8; Lz = 5e-3;
ldim = [Lx Ly Lz]; % plate dimensions [x, y, z] in metres
E = 117e9; %-- Young's mod [Pa] rho = 8765; %-- density [kg/m^3] nu = 0.3; %-- poisson's ratio Nm = 6; %-- number of modes to compute h = sqrt(Lx*Ly)*1e-2; %-- Grid Spacing BCs = zeros(4,2); %-- elastic constants BCs (:,1) = 1e15; %-- Felxural restraint high (simply supported condition)
Om = magpie(rho,E,nu,ldim, h, BCs, Nm);
Input Arguments
- density : plate density in kg/m^3
- Youngs : Young's modulus of plate material
- poisson : Poisson number of plate material
- dim : 3 element array describing plate dimensions in metres of the form [Lx Ly Lz]
- h : Grid spacing for the plate
- BCs : 4-by-2 matrix of eleastic boundary constants around each edge of the plate. Column 1 flexural and Column 2 the rotational constraint
Output
- Om : Angular modal frequencies
- Q : A matrix of column eigenvector(s)
- Nxy : 2-element array of grid points [Nx Ny] used for calculation.
- biharm : Discrete biharmonic operator matrix
- Dm : the eigenvalues of the biharmonic matrix