How do i use boundary conditions to find variables in an equation

Question

Ramneet Sidhu 2019-11-14

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https://ww2.mathworks.cn/matlabcentral/answers/491004-how-do-i-use-boundary-conditions-to-find-variables-in-an-equation

评论： Muhammad Usman 2019-11-14

Hi all. I am trying to find 4 variables which are c1, c2, c3, c4 in my equation using 4 boundary conditions. The value of lambda is known. But i donot know how to proceed. Any help is much appreciated.

My code is as follows:

lambda = 0.0275;
%Solution of the governing equation for beam-on-elastic-foundation is:
syms x c1 c2 c3 c4
u(x) = exp(lambda*x)*(c1*cos(lambda*x) + c2*sin(lambda*x)) +exp(-lambda*x)*(c3*cos(lambda*x) + c4*sin(lambda*x));
du(x) = diff(u,x);
%The boundary condition for the pile under node 01 on applying unit force on dof-01 is:
eqn1 = u(0)==1; 
eqn2 = u(Lp)==0; 
eqn3 = du(0)==0; 
eqn4 = du(Lp)==0;
eqns = [eqn1 eqn2 eqn3 eqn4];
vars = [C1 C2 C3 C4];
soln = solve(u,eqns,vars);