By Barus C.
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Additional resources for Acoustic Pressures in Case of Soap Bubbles
The resulting frequency is an upper bound solution, unless an exact eigenfunction of free vibration for the trial function is assumed. Ritz (1909) generalized the Rayleigh method by assuming a set of admissible trial functions, each having independent amplitude coefficients. He showed that a closer upper bound for the frequency could be achieved by minimizing the energy functional H with respect to each of the coefficients. Ritz demonstrated his method on a completely free square plate for which no exact solution is possible.
3 Formulation in Polar Coordinates II,SUM,NTAB,COEF) 60 70 S(II,I,J)=SUM CONTINUE CONTINUE DO 100 I=I,N CALL FFXY(I,FXYSI,IRSI,ISSI,NSI) DO 90 J= 1,N CALL FFXY(J,FXYSJ,IRSJ,ISSJ,NSJ) DO 80 II=6,10 CALL CALCULUS(FXYN,IRN,ISN,NN, FXYN,IRN,ISN,NN, FXYSI,IRSI,ISSI,NSI, FXYSJ,IRSJ,ISSJ,NSJ, II,SUM,NTAB,COEF) S(II,I,J)=SUM 80 CONTINUE 90 CONTINUE 100 CONTINUE DO 130 I=I,N CALL FFXY(I,FXYSI,IRSI,ISSI,NSI) DO 120 J=I,L CALL FFXY(J,FXYSJ,IRSJ,IS SJ,NSJ) DO 110 II=l 1,13 CALL CALCULUS(FXYN,IRN,ISN,NN, FXYL,IRL,ISL,NL, FXYSI,IRSI,ISSI,NSI, FXYSJ,IRSJ,ISSJ,NSJ, II,SUM,NTAB,COEF) S(II,I,J)=SUM 110 CONTINUE 120 CONTINUE 130 CONTINUE DO 160 I=I,L CALL FFXY(I,FXYSI,IRSI,ISSI,NSI) DO 150 J=I,L CALL FFXY(J,FXYSJ,IRSJ,IS SJ,NSJ) DO 140 II= 14,18 CALL CALCULUS (FXYL,IRL,ISL,NL, FXYL,IRL,ISL,NL, FXYSI,IRSI,ISSI,NSI, FXYSJ,IRSJ,ISSJ,NSJ, II,SUM,NTAB,COEF) S(n,U)=SUM 140 CONTINUE 150 CONTINUE 160 CONTINUE 53 See.
53) i=l where ~bi(x,y ) are the approximate functions which individually satisfies at least the geometric boundary conditions. 54) which yields a set of homogeneous equations expressed in terms of the coefficients q. 57) According to the Ritz method, the limit of the approximations in Eq. (x, y) are linearly independent. 9 Functions ~bi (x, y) form a complete system of functions. 9 Functions ~bi (x, y) satisfy the kinematic boundary conditions. It is not necessary for the chosen functions qki(x,y) to satisfy the static boundary conditions.
Acoustic Pressures in Case of Soap Bubbles by Barus C.