matlab r14b  (MathWorks Inc)

Journal: Materials

Article Title: Stability Analysis of Free Vibration of Gun Drill Rod

doi: 10.3390/ma18061241

Figure Lengend Snippet: ( a ) The specific cross-sectional shape and dimensions of the gun drill rod (unit m); ( b ) comparison of natural frequency variation with rotational speed: MATLAB theoretical analysis vs. ANSYS analysis.

Article Snippet: In MATLAB R14b, the program for calculating the stiffness matrix elements using the Galerkin method for bending vibration is as follows: syms i j x betajj = zeros(1,6); betajj(1) = 1.8751040687119611138911068337620; betajj(2) = 4.6940911329741741297993939951994; betajj(3) = 7.8547574382376126322924392297864; betajj(4) = 10.995540734875465460618215729482; betajj(5) = 14.137168391046470716787553101312; betajj(6) = 17.278759532088237449443113291636; ii = 1; omega = 500; k11 = zeros(nj,nj); for i = 1:nj for j = 1:nj betai = betajj(i); lambdai = −(cos(betai) + cosh(betai))/(sin(betai) + sinh(betai)); phii = cos(betai*x/L)-cosh(betai*x/L) + lambdai*(sin(betai*x/L) − sinh(betai*x/L)); betaj = betajj(j); lambdaj = −(cos(betaj) + cosh(betaj))/(sin(betaj) + sinh(betaj)); phij = cos(betaj*x/L) − cosh(betaj*x/L) + lambdaj*(sin(betaj*x/L) − sinh(betaj*x/L)); k11ijx1 = E*Iy*diff(phii,4)*phij − rho*A*omega^2*phii*phij; k11ijx = inline(vectorize(k11ijx1),‘x’,‘i’,‘j’); k11(i,j) = quadl(k11ijx,0,L,[],[],i,j); end end The K11 calculation process is also applicable to the calculation of individual elements in the mass matrix and damping matrix.

Techniques: Comparison