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Dear users,

In my attached file I have two PDES, (PDE1 and PDE2). PDE1 is a function of v(t) and w(x,t) and PDE2 is also a function of v(t) and w(x,t). I can solve PDE2 if I say v(t) is 1 for example and you can see the plot. But what if I put v(t) back in PDE2 and want to find v(t) and w(x,t) from PDE1 and PDE2 together? 

Many Thanks,



Define PDE Euler-Bernoulli Beam




Parametrs of piezoelectric and cantilever beam



Ys := 70*10^9: # Young's Modulus structure

Yp := 11.1*10^10: # Young's Modulus pieazo

ha := -0.00125: # Position

hb := 0.001: # Position

hc := 0.0015: # Position

d31 := -180*10^(-12): # Piezoelectric constant

b := 0.01: #Width of the beam

tb := 0.002:

epsilon33 := 15.92*10^(-9):

hp :=0.00025: # Position

hpc := 0.00125: # Position

YI := b*(Ys*(hb^3- ha^3)+Yp*(hc^3-hb^3))/3: # Bending stiffness of the composit cross section

cs := 0.564: # The equivqlent coefficient of strain rate damping

ca := 0: # Viscous air damping coefficient

Ibeam := (b * tb^3 )/12: # The equivalent moment of inertia

m := 0.101: # Mass of the structure

upsilon := - Yp*d31*b*(hc^2-hb^2)/(2*hp): # Coupling term

lb := 0.57:# Length of the structure (Cantilever Beam)

lp := 0.05:# Length of the Piezoelectric

R:= 10000: # Shunted resistor

Electrical circuit equation


PDE1:=(epsilon33 * b*lp / hp) * diff(v(t), t) + (v(t)/R)+ int(d31*Yp*hpc*b* diff(w(x, t),$(x, 2))*diff(w(x, t), t),x = 0..lp)=0;

0.3184000000e-7*(diff(v(t), t))+(1/10000)*v(t)+int(-0.2497500000e-3*(diff(diff(w(x, t), x), x))*(diff(w(x, t), t)), x = 0 .. 0.5e-1) = 0




PDE Equation


fn := 3.8:# Direct Excitation frequency;

wb(x,t) := 0.01*sin(fn*2*Pi*t):#Direct Excitation;

plot(wb(x,t),t = 0 .. 0.25*Pi,labels = [t,wb], labeldirections = ["horizontal", "vertical"], labelfont = ["HELVETICA", 15], linestyle = [longdash], axesfont = ["HELVETICA", "ROMAN", 10], legendstyle = [font = ["HELVETICA", 10], location = right],color = black);



FunctionAdvisor(definition, Dirac(n,x));

[Dirac(n, x) = (1/2)*(Int((I*_k1)^n*exp(I*_k1*x), _k1 = -infinity .. infinity))/Pi, `with no restrictions on `(n, x)]



PDE2 := YI*diff(w(x, t),$(x, 4))+ cs*Ibeam*diff(w(x, t),$(x, 4))*diff(w(x, t), t)+ ca* diff(w(x, t), t) + m * diff(w(x, t),$(t, 2))+ upsilon*v(t)*(Dirac(1,x) -Dirac(1,x-lp) ) =-m*diff(wb(x, t),$(t, 2))-ca*diff(wb(x, t), t);#PDE

1.567812500*(diff(diff(diff(diff(w(x, t), x), x), x), x))+0.3760000000e-11*(diff(diff(diff(diff(w(x, t), x), x), x), x))*(diff(w(x, t), t))+.101*(diff(diff(w(x, t), t), t))+0.4995000000e-3*Dirac(1, x)-0.4995000000e-3*Dirac(1, x-0.5e-1) = 0.583376e-1*sin(7.6*Pi*t)*Pi^2


tmax := 0.3:

xmin := 0:

xmax := lb:


bc1 := dw(xmin, t) = 0:

bc2 := dw(xmax, t) = 0:

bc3 := w(xmin, t) = 0:

ic1 := wl(x, 0) = 0:

Maple's pdsolve command




bcs := { w(x,0)=0 , D[2](w)(x,0)=0 , w(0, t) = rhs(bc1), D[1](w)(0, t)= rhs(bc1), D[1,1](w)(lb,t) = rhs(bc2), D[1,1,1](w)(lb,t) = rhs(bc2)}; # Boundary conditions for PDE2.

{w(0, t) = 0, w(x, 0) = 0, (D[1](w))(0, t) = 0, (D[2](w))(x, 0) = 0, (D[1, 1](w))(.57, t) = 0, (D[1, 1, 1](w))(.57, t) = 0}


PDES := pdsolve(PDE2, bcs, numeric, time = t, range = 0 .. xmax, indepvars = [x, t], spacestep = (1/1000)*xmax, timestep = (1/1000)*tmax);


module () local INFO; export plot, plot3d, animate, value, settings; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; end module


PDES:-plot3d(t = 0 .. tmax, x = 0 .. xmax, axes = boxed, orientation = [-120, 40], shading = zhue, transparency = 0.3);






I wnat to print the polar that contain a part of loops,but it always contains all loops.

how do I solve this preblem?

Any one can help me,please?





Dear Maple users


I have a question about applying pdsolve MAPLE for solving two dimensional heat equations:

My codes have been provided but it shows to me this error:

Error, (in pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent variables, got {t, x, y}

If kindly is possible, please help me in this case.


With kind regards,

Emran Tohidi.


> restart;
> with(plots);
print(??); # input placeholder
> with(PDEtools);
print(??); # input placeholder
> declare(u(x, y, t));
print(`output redirected...`); # input placeholder
                    u(x, y, t) will now be displayed as u
> S := 1/100; tR := 0 .. 1; xR := 0 .. 1; yR := 0 .. 1; NF := 30; NP := 100;
print(??); # input placeholder
> N := 3; L1 := [red, blue, green]; L2 := [0, 1/2, 1]; Ops := spacestep = S, timestep = S;
print(??); # input placeholder
> Op1 := frames = NF, numpoints = NP;
print(??); # input placeholder
> PDE1 := diff(u(x, y, t), t)-(diff(u(x, y, t), `$`(x, 2)))-(diff(u(x, y, t), `$`(y, 2))) = 0;
print(??); # input placeholder
> IC := {u(x, y, 0) = exp(x+y)}; BC := {u(0, y, t) = exp(2*t+y), u(1, y, t) = exp(2*t+y+1), u(x, 0, t) = exp(2*t+x), u(x, 1, t) = exp(2*t+x+1)};
print(??); # input placeholder
> Sol := pdsolve(PDE1, `union`(IC, BC), numeric, u(x, t), Ops);
Error, (in pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent variables, got {t, x, y}

A linear system with three variables has augmented matrix that is row-equivalent to the 
following matrix: 

k + 3 2 k − 4 = 3 
0 2 −9 = 5 
0 0 k^2 + k − 2 = k − 1 
Determine the values of k for which the system has: 
(a) exactly one solution, 
(b) infinitely many solutions, 
(c) no solutions.

(a) Write down the augmented matrix corresponding to the linear system: 
4x1 + 2x2 − 7x3 − 11x4 = 5 
2x1 + 1x2 − 2x3 − 4x4 = 2 
4x1 + 2x2 − 10x3 − 14x4 = 6 

(b) Use Gauss-Jordan elimination to reduce this matrix to reduced row-echelon form. 

(c) Solve the linear system.

I am having problems with the curly brackets in math mode. I am using a Danish keyboard, and since changing to Maple 17, the inline evaluation (usually [CTRL]+=) has been placed as [CTRL]+[ALT]+0 which - by Maple - is interpreted the same way as [ALT-GR]+0. Unfortunately [ALT-GR]+0 is the way to get the end-bracket for curly brackets, i.e. }

Therefore, I am not able to write } in math mode. Maple interprets my keystrokes as a wish to do inline evaluation when trying to write }.

Has anyone experienced this issue - and if so: Is there a way to fix it?

Is there a way to change the shortcut keys in Maple (e.g. make an alternative shortcut for inline evaluations)?



I am new in Maple and I'm trying to get functions from system of equations.

Constants are defined in line 4 and equations are:

eq1 := E2 = fE2(1+(KaE2+Ca)/(1+KaE2*fE2+KaT*fT+KaDHT*fDHT)+KsE2*Cshbg/(1+KsE2*fE2+KsT*fT+KsDHT*fDHT))

eq2 := T = fT(1+KaT*Ca/(1+KaE2*fE2+KaT*fT+KaDHT*fDHT)+KsT*Cshbg/(1+KsE2*fE2+KsT*fT+KsDHT*fDHT))

eq3 := DHT = fDHT(1+KaDHT*Ca/(1+KaE2*fE2+KaT*fT+KaDHT*fDHT)+KsDHT*Cshbg/(1+KsE2*fE2+KsT*fT+KsDHT*fDHT))

KsT = 0.10e11; KaT = 4.6*0.10e6; KsE2 = 3.14*0.10e10; KaE2 = 4.21*0.10e6; KsDHT = 3*0.10e6; KaDHT = 3.5*0.10e6;

fT, fE2 and fDHT are variables, not functions (i.e. fT is not f(T) ) and I am trying to get fT=f(E2,T,DHT,Ca,Cshbg), fE2=f(E2,T,DHT,Ca,Cshbg) and fDHT=f(E2,T,DHT,Ca,Cshbg).

When I type:

eliminate({eq1, eq2, eq3}, {fE2, fT, fDHT})

Maple gives me a blank field. No error, no other comment.

I have no idea where I'm making mistakes.

Any suggestion is appreciated.


Thanks in advance.

Could you tell me what the maple player is ?

How can I calculate the residue of a function with complex variable in maple ?

Ok so i have a matrix M filled with complex roots of unity. I want to execute the following code but it seems to be failing to do so correctly

t:=exp(2 Pi I/11);

m := (i, j) -> M[(i mod 11)+1, (j mod 11)+1] ;  

mu :=(i,j)->(add(add(add(a[k]*a[m]*a[n]*t^(m)*m((i+k-m),(j+n-m))),n=0..10),m=0..10),k=0..10));


Something is wrong with my indexing of the matrix . or when the mod procs.



ans := pdsolve(pde);

ics:=(D[1](U))(0, z) = 0,(D[2](U))(r, 0)-B*U(r,0) = 0;

bcs:=(D[2](U))(r, 1)+B*U(r,1) = B,(D[1](U))(1, z)+B*U(1,z) = 0;


S:= pdsolve(pde, {bcs, ics}, numeric);

Error, (in pdsolve/numeric) unable to handle elliptic PDEs

anyway around this?

I have a matrix with repeated columns


Q := Matrix([1,1,1,0,0,0,-2,-1],[0,0,0,1,1,1,0,-3]);

I'd like to write a loop that defines u[1],...,u[n] to be the unique columns of Q. Is there a way to do this?

I'm writing some code that computes a positive integer N and I'd like Maple to define a function of N variables. I've tried writing 

f := (seq(t[i],i=1..N))-> MY EXPRESSION;

but I receive the error

Error, invalid parameter; functional operators require their parameters to be of type symbol or (symbol::type)

Is there anything I can do here?

i make two component that the left named MathContainer0 and right named MathContainer1

which can enter any numers on it

and i want to solve the eqution such as  

x*%MathContainer0+y*%MathContainer1=0 ,and y*%MathContainer0+x*%MathContainer1=0

but it still not shows the answers i want

anyone can help thx

Hello everyone!

I'm working with Maple for 8 years and this is the first time I encounter such a problem:

I solve a linear ODE system for my quantum Mechanics research and i want to calculate a quantity formed by the solutions of the system. Everything is going fine with laplace transformation and the symbolic answer is very fast although extremely big (it uses RootOf simplification)

When i use evalf to take numerical approximations of the quantity, the answer is very fast. OK

When i leave unspecified two parameters in order to get a 3d plot the answer takes about 40mins to appear. I think it is too slow but anyway, i can live with it. OK

I want this 3d plot for different parameters of the ODE so i have to do the above process many times. But for some parameter values of the ODE, i get a 3dplot for which:

1) The display of numpoints (surface and line) is incorrect.

2) Plot gets deformed as long as i rotate it!!! The orientation angle changes the appearance of the plot, something obviously unacceptable. I have access to maple 17, 15, 14, and 12. Maple 17 and 15 exhibit this behavior (64 bit Maple editions). But when i tried with Maple 12-standard interface(64 bit) and Maple 14 -Classical interface (32bit) everything went fine, but at the cost of  300 extra secs. I got a solid 3d-plot that is invariant under rotations.

My video card is Ati radeon 6800 HD and i installed the latest drivers. I don't know why is this happening. I thought of putting the blame on me, but in maple 12 and maple 14 everything is fine. It is a pity, because Maple 17 gives very nice and smooth 3d plots.

The first plot is the correct one with maple 12. The second is produced with maple 14. All good.

The third and the second are produced with different orientations of the same plot (Maple 17). Wrong display of data and change of image after rotation. The final one is again from Maple 17 but with style=points. It is in is in full agreement with the first two plots. 

Conclusion: Style=surface and line doesnt produce the correct plot, while style=point does. As for hardware acceleration, i unticked it with no results.

Extra information: When i try to open the maple 12 worksheet which is correct, with Maple 17, again i take the wrong displayed and unstable picture. Moreover only maple 14 classical edition works well. Maple 14 standard interface is also pathological.

Heeeeelp guys!!!



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