(B-1) The definite integrals were evaluated using wxMaxima with the following commands. integrate((sin(m*%pi*x/a))^2,x,0,a);positive; integrate((sin(m*%pi*x/a))*(cos(m*%pi*x/a)),x,0,a);positive; (B-2) (B-3) (B-4) APPENDIX C Example Consider a rectangular plate with the following properties: Boundary Conditions Simply Supported on All Sides Material Aluminum Thickness h = 0.125 inch Length a = 10 inch Width b = 8 inch Elastic Modulus E = 10E+06 lbf/in^2 Mass per Volume = 0.1 lbm / in^3 ( 0.000259 lbf sec^2/in^4 ) Mass per Area = 0.0125 lbm / in^2 (3.24E-05 lbf sec^2/in^3 ) Viscous Damping Ratio = 0.05 The normal modes and frequency response function analysis are performed via a Matlab script.
(B-1) The definite integrals were evaluated using wxMaxima with the following commands. integrate((sin(m*%pi*x/a))^2,x,0,a);positive; integrate((sin(m*%pi*x/a))*(cos(m*%pi*x/a)),x,0,a);positive; (B-2) (B-3) (B-4) APPENDIX C Example Consider a rectangular plate with the following properties: Boundary Conditions Simply Supported on All Sides Material Aluminum Thickness h = 0.125 inch Length a = 10 inch Width b = 8 inch Elastic Modulus E = 10E+06 lbf/in^2 Mass per Volume = 0.1 lbm / in^3 ( 0.000259 lbf sec^2/in^4 ) Mass per Area = 0.0125 lbm / in^2 (3.24E-05 lbf sec^2/in^3 ) Viscous Damping Ratio = 0.05 The normal modes and frequency response function analysis are performed via a Matlab script.
ss_plate_oblique_incidence_revF.docx