RESOLUCION DE LA ECUACION DE PLACAS DE GERMAIN-LAGRANGE
Definimos la ecuacion diferencial de placas
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EDO:=Diff(y(x),x$4)+k=0; |
Soluci?n general
Soluciones particulares seg?n las diferentes condiciones de borde
Condiciones de borde para apoyado-apoyado
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AA:=y(0)=0,y(a)=0,D(D(y))(0)=0,D(D(y))(a)=0; |
Solucion particular con tales condiciones
Condiciones de borde para empotrado-libre
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EL:=y(0)=0,D(y)(0)=0,D(D(y))(a)=0,D(D(D(y)))(a)=0; |
Soluci?n particular con tales condiciones
Condiciones de borde para empotrado-empotrado
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EE:=y(0)=0,D(y)(0)=0,y(a)=0,D(y)(a)=0; |
Solcion particular con tales condiciones
Representaci?n gr?fica de los diferentes casos. Suponemos k = 0.001 y a = 4
Caso apoyado-apoyado
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plot((-0.001/24)*(x^4)+(0.001*4/12)*(x^3)-(0.001*4^3)*x/24,x=0..4); |
Caso empotrado-libre
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plot((-0.001/24)*(x^4)+(0.001*4/6)*(x^3)-(0.001*4^2)*(x^2)/4,x=0..4); |
Caso empotrado-empotrado
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plot((-0.001/24)*(x^4)+(0.001*4/12)*(x^3)-(0.001*4^2)*(x^2)/24,x=0..4); |
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