diff options
Diffstat (limited to '2378/CH1')
22 files changed, 385 insertions, 0 deletions
diff --git a/2378/CH1/EX1.11/Exa_1_11.png b/2378/CH1/EX1.11/Exa_1_11.png Binary files differnew file mode 100644 index 000000000..4f6f8f88d --- /dev/null +++ b/2378/CH1/EX1.11/Exa_1_11.png diff --git a/2378/CH1/EX1.11/Exa_1_11.sce b/2378/CH1/EX1.11/Exa_1_11.sce new file mode 100644 index 000000000..a61918dfe --- /dev/null +++ b/2378/CH1/EX1.11/Exa_1_11.sce @@ -0,0 +1,14 @@ +//addition of harmonic motion +//Exa_2_11 +clc; +clear; +close; + +A=sqrt((10+15*cos(2))^2 + (15*sin(2))^2); + +alpha=atand((15*sin(2))/(10+15*cos(2))); + +disp("x(t)=R*%e^(i*(omega*t+alpha))"); +disp("where "); +disp(A,"A ="); +disp(alpha,"alpha =");
\ No newline at end of file diff --git a/2378/CH1/EX1.13/Exa_1_13.png b/2378/CH1/EX1.13/Exa_1_13.png Binary files differnew file mode 100644 index 000000000..051d843b9 --- /dev/null +++ b/2378/CH1/EX1.13/Exa_1_13.png diff --git a/2378/CH1/EX1.13/Exa_1_13.sce b/2378/CH1/EX1.13/Exa_1_13.sce new file mode 100644 index 000000000..b8cbb06fd --- /dev/null +++ b/2378/CH1/EX1.13/Exa_1_13.sce @@ -0,0 +1,57 @@ +//numerical fourier analysis +//Exa_1_13 +clc; +clear; +close; + +n=12;
//number of time stations +m=3;
//number of harmonics required +time=0.12; //time period
+ +x=[20000.0;34000.0;42000.0;49000.0;53000.0;70000.0;60000.0;36000.0;22000.0;
+ 16000.0;7000.0;0.0]';
//presure in N/m^2 +t=0.01:0.01:0.12; //time in second
+ +sumz=0.0;
//temporary variable +for i=1:n //calculating the coefficients
+ sumz=sumz+x(i);
+end
+azero=2.0*sumz/n;
//first term of fourier series +for ii=1:m
+ sums=0.0;
+ sumc=0.0;
+ for i=1:n
+ theta=2.0*%pi*t(i)*ii/time;
+ coss(i)=x(i)*cos(theta);
+ sinn(i)=x(i)*sin(theta);
+ sums=sums+sinn(i);
+ sumc=sumc+coss(i);
+ end
+ a(ii)=2.0*sumc/n;
//coefficient of cos terms + b(ii)=2.0*sums/n; //coefficient of sin term
s +end
+ + +//printing the table of values +printf('Fourier series expansion of the function x(t)\n\n');
+printf('Data:\n\n');
+printf('Number of data points in one cycle = %3.0f \n',n);
+printf(' \n');
+printf('Number of Fourier Coefficients required = %3.0f \n',m);
+printf(' \n');
+printf('Time period = %8.6e \n\n',time);
+printf('Station i ')
+printf('Time at station i: t(i) ')
+printf('x(i) at t(i)')
+for i=1:12
+ printf('\n %8d%25.6e%27.6e ',i,t(i),x(i));
+end
+printf(' \n\n');
+printf('Results of Fourier analysis:\n\n');
+printf('azero=%8.6e \n\n',azero);
+printf('values of i a(i) b(i)\n');
+for i=1:3 + printf('%10.0g %8.6e%20.6e \n',i,a(i),b(i));
+end +
+
\ No newline at end of file diff --git a/2378/CH1/EX1.14/Exa_1_14.png b/2378/CH1/EX1.14/Exa_1_14.png Binary files differnew file mode 100644 index 000000000..4ad9e37f4 --- /dev/null +++ b/2378/CH1/EX1.14/Exa_1_14.png diff --git a/2378/CH1/EX1.14/Exa_1_14.sce b/2378/CH1/EX1.14/Exa_1_14.sce new file mode 100644 index 000000000..18e2807db --- /dev/null +++ b/2378/CH1/EX1.14/Exa_1_14.sce @@ -0,0 +1,46 @@ +//Exa_1_14 +//Graphical representation of fourier series +clc; +clear; +A = 1; +w = %pi; +tau = 2; +for i = 1: 101 + t(i) = tau * (i-1)/100; + x(i) = A * t(i) / tau; +end +subplot(231); +plot(t,x); +ylabel('x(t)'); +xlabel('t'); +title('x(t) = A*t/tau'); +for i = 1: 101 + x1(i) = A / 2; +end +subplot(232); +plot(t,x1); +xlabel('t'); +title('One term'); +for i = 1: 101 + x2(i) = A/2 - A * sin(w*t(i)) / %pi; +end +subplot(233); +plot(t,x2); +xlabel('t'); +title('Two terms'); +for i = 1: 101 + x3(i) = A/2 - A * sin(w*t(i)) / %pi - A * sin(2*w*t(i)) / (2*%pi); +end +subplot(234); +plot(t,x3); +ylabel('x(t)'); +xlabel('t'); +title('Three terms'); +for i = 1: 101 + t(i) = tau * (i-1)/100; + x4(i) = A/2 - A * sin(w*t(i)) / %pi - A * sin(2*w*t(i)) / (2*%pi) - A * sin(3*w*t(i)) / (3*%pi); +end +subplot(235); +plot(t,x4); +xlabel('t'); +title('Four terms'); diff --git a/2378/CH1/EX1.15/Exa_1_15.png b/2378/CH1/EX1.15/Exa_1_15.png Binary files differnew file mode 100644 index 000000000..1747f4549 --- /dev/null +++ b/2378/CH1/EX1.15/Exa_1_15.png diff --git a/2378/CH1/EX1.15/Exa_1_15.sce b/2378/CH1/EX1.15/Exa_1_15.sce new file mode 100644 index 000000000..f3251f1e0 --- /dev/null +++ b/2378/CH1/EX1.15/Exa_1_15.sce @@ -0,0 +1,13 @@ +// Exa_1_15 +// Graphical representation of beats +A = 1; +w = 20; +delta = 1; +for i = 1: 1001 //making t and x matrix for various points + t(i) = 15 * (i-1)/1000; + x(i) = 2 * A * cos(delta*t(i)/2) * cos((w + delta/2)*t(i)); +end +plot(t,x); //plotting +xlabel('t'); +ylabel('x(t)'); +title('Phenomenon of beats'); diff --git a/2378/CH1/EX1.16/Exa_1_16.png b/2378/CH1/EX1.16/Exa_1_16.png Binary files differnew file mode 100644 index 000000000..7d111b0c6 --- /dev/null +++ b/2378/CH1/EX1.16/Exa_1_16.png diff --git a/2378/CH1/EX1.16/Exa_1_16.sce b/2378/CH1/EX1.16/Exa_1_16.sce new file mode 100644 index 000000000..dad682113 --- /dev/null +++ b/2378/CH1/EX1.16/Exa_1_16.sce @@ -0,0 +1,63 @@ +//numerical fourier analysis +//Exa_1_16 +clc; +clear; + +n=12; + //number of time stations +m=5; + //number of harmonics required +time=0.12; //time period + +x=[20000.0;34000.0;42000.0;49000.0;53000.0;70000.0;60000.0;36000.0;22000.0; + 16000.0;7000.0;0.0]'; + //presure in N/m^2 +t=0.01:0.01:0.12; //time in second + +sumz=0.0; + //temporary variable +for i=1:n //calculating the coefficients + sumz=sumz+x(i); +end +azero=2.0*sumz/n; + //first term of fourier series +for ii=1:m + sums=0.0; + sumc=0.0; + for i=1:n + theta=2.0*%pi*t(i)*ii/time; + coss(i)=x(i)*cos(theta); + sinn(i)=x(i)*sin(theta); + sums=sums+sinn(i); + sumc=sumc+coss(i); + end + a(ii)=2.0*sumc/n; + //coefficient of cos terms + b(ii)=2.0*sums/n; //coefficient of sin term + +end + + +//printing the table of values +printf('Fourier series expansion of the function x(t)\n\n'); +printf('Data:\n\n'); +printf('Number of data points in one cycle = %3.0f \n',n); +printf(' \n'); +printf('Number of Fourier Coefficients required = %3.0f \n',m); +printf(' \n'); +printf('Time period = %8.6e \n\n',time); +printf('Station i ') +printf('Time at station i: t(i) ') +printf('x(i) at t(i)') +for i=1:12 + printf('\n %8d%25.6e%27.6e ',i,t(i),x(i)); +end +printf(' \n\n'); +printf('Results of Fourier analysis:\n\n'); +printf('azero=%8.6e \n\n',azero); +printf('values of i a(i) b(i)\n'); +for i=1:5 + printf('%10.0g %8.6e%20.6e \n',i,a(i),b(i)); +end + +
\ No newline at end of file diff --git a/2378/CH1/EX1.17/Exa_1_17.png b/2378/CH1/EX1.17/Exa_1_17.png Binary files differnew file mode 100644 index 000000000..7d111b0c6 --- /dev/null +++ b/2378/CH1/EX1.17/Exa_1_17.png diff --git a/2378/CH1/EX1.17/Exa_1_17.sce b/2378/CH1/EX1.17/Exa_1_17.sce new file mode 100644 index 000000000..7f9c544ef --- /dev/null +++ b/2378/CH1/EX1.17/Exa_1_17.sce @@ -0,0 +1,64 @@ +//numerical fourier analysis (note:this example is same as Exa_1_13) +//Exa_1_17 +clc; +clear; +close; + +n=12; + //number of time stations +m=5; + //number of harmonics required +time=0.12; //time period + +x=[20000.0;34000.0;42000.0;49000.0;53000.0;70000.0;60000.0;36000.0;22000.0; + 16000.0;7000.0;0.0]'; + //presure in N/m^2 +t=0.01:0.01:0.12; //time in second + +sumz=0.0; + //temporary variable +for i=1:n //calculating the coefficients + sumz=sumz+x(i); +end +azero=2.0*sumz/n; + //first term of fourier series +for ii=1:m + sums=0.0; + sumc=0.0; + for i=1:n + theta=2.0*%pi*t(i)*ii/time; + coss(i)=x(i)*cos(theta); + sinn(i)=x(i)*sin(theta); + sums=sums+sinn(i); + sumc=sumc+coss(i); + end + a(ii)=2.0*sumc/n; + //coefficient of cos terms + b(ii)=2.0*sums/n; //coefficient of sin term + +end + + +//printing the table of values +printf('Fourier series expansion of the function x(t)\n\n'); +printf('Data:\n\n'); +printf('Number of data points in one cycle = %3.0f \n',n); +printf(' \n'); +printf('Number of Fourier Coefficients required = %3.0f \n',m); +printf(' \n'); +printf('Time period = %8.6e \n\n',time); +printf('Station i ') +printf('Time at station i: t(i) ') +printf('x(i) at t(i)') +for i=1:12 + printf('\n %8d%25.6e%27.6e ',i,t(i),x(i)); +end +printf(' \n\n'); +printf('Results of Fourier analysis:\n\n'); +printf('azero=%8.6e \n\n',azero); +printf('values of i a(i) b(i)\n'); +for i=1:5 + printf('%10.0g %8.6e%20.6e \n',i,a(i),b(i)); +end + +
\ No newline at end of file diff --git a/2378/CH1/EX1.18/Exa_1_18.png b/2378/CH1/EX1.18/Exa_1_18.png Binary files differnew file mode 100644 index 000000000..7d111b0c6 --- /dev/null +++ b/2378/CH1/EX1.18/Exa_1_18.png diff --git a/2378/CH1/EX1.18/Exa_1_18.sce b/2378/CH1/EX1.18/Exa_1_18.sce new file mode 100644 index 000000000..15bcc74d7 --- /dev/null +++ b/2378/CH1/EX1.18/Exa_1_18.sce @@ -0,0 +1,64 @@ +//numerical fourier analysis (note:this example is same as Exa_1_13) +//Exa_1_18 +clc; +clear; +close; + +n=12; + //number of time stations +m=5; + //number of harmonics required +time=0.12; //time period + +x=[20000.0;34000.0;42000.0;49000.0;53000.0;70000.0;60000.0;36000.0;22000.0; + 16000.0;7000.0;0.0]'; + //presure in N/m^2 +t=0.01:0.01:0.12; //time in second + +sumz=0.0; + //temporary variable +for i=1:n //calculating the coefficients + sumz=sumz+x(i); +end +azero=2.0*sumz/n; + //first term of fourier series +for ii=1:m + sums=0.0; + sumc=0.0; + for i=1:n + theta=2.0*%pi*t(i)*ii/time; + coss(i)=x(i)*cos(theta); + sinn(i)=x(i)*sin(theta); + sums=sums+sinn(i); + sumc=sumc+coss(i); + end + a(ii)=2.0*sumc/n; + //coefficient of cos terms + b(ii)=2.0*sums/n; //coefficient of sin term + +end + + +//printing the table of values +printf('Fourier series expansion of the function x(t)\n\n'); +printf('Data:\n\n'); +printf('Number of data points in one cycle = %3.0f \n',n); +printf(' \n'); +printf('Number of Fourier Coefficients required = %3.0f \n',m); +printf(' \n'); +printf('Time period = %8.6e \n\n',time); +printf('Station i ') +printf('Time at station i: t(i) ') +printf('x(i) at t(i)') +for i=1:12 + printf('\n %8d%25.6e%27.6e ',i,t(i),x(i)); +end +printf(' \n\n'); +printf('Results of Fourier analysis:\n\n'); +printf('azero=%8.6e \n\n',azero); +printf('values of i a(i) b(i)\n'); +for i=1:5 + printf('%10.0g %8.6e%20.6e \n',i,a(i),b(i)); +end + +
\ No newline at end of file diff --git a/2378/CH1/EX1.2/Exa_1_2.sce b/2378/CH1/EX1.2/Exa_1_2.sce new file mode 100644 index 000000000..4d26c392c --- /dev/null +++ b/2378/CH1/EX1.2/Exa_1_2.sce @@ -0,0 +1,13 @@ +//Equivalent k of a suspension system +//Exa_1_2 +clc; +clear; +close; +G=80e+9 ; //shear modulus of spring material in N/m^2 +n=5; //effective turns +D=0.2; //mean coil diameter in m +d=0.02; //wire diameter in m +k=(d^4*G)/(8*D^3*n); //stiffness of each helical spring +//the three springs are identical and parallel +keq=3*k; +disp(keq,"equivalent spring constant of the suspension system in N/m =");
\ No newline at end of file diff --git a/2378/CH1/EX1.2/Exa_1_2_screenshot.png b/2378/CH1/EX1.2/Exa_1_2_screenshot.png Binary files differnew file mode 100644 index 000000000..52099641c --- /dev/null +++ b/2378/CH1/EX1.2/Exa_1_2_screenshot.png diff --git a/2378/CH1/EX1.3/Exa_1_3.png b/2378/CH1/EX1.3/Exa_1_3.png Binary files differnew file mode 100644 index 000000000..393a729b5 --- /dev/null +++ b/2378/CH1/EX1.3/Exa_1_3.png diff --git a/2378/CH1/EX1.3/Exa_1_3.sce b/2378/CH1/EX1.3/Exa_1_3.sce new file mode 100644 index 000000000..744b27186 --- /dev/null +++ b/2378/CH1/EX1.3/Exa_1_3.sce @@ -0,0 +1,18 @@ +//Torsional spring constant of a propeller shaft +//Exa_1_3 +clc; +clear; +//refer fig:1.25 +G=80e+9; //shear modulus of shaft in N/m^2 +D12=0.3; //outer diameter of AA section in m +d12=0.2; //inner diameter of AA section in m +l12=2; //length of 12 segment in m +kt12=(G* %pi *(D12^4-d12^4))/(32*l12); //spring constant of section 12 + +D23=0.25; //Outer diameter of BB section in m +d23=0.15; //inner diameter of BB section in m +l23=3; //length of 23 segment in m +kt23=(G* %pi *(D23^4-d23^4))/(32*l23); //spring constant of section 23 + +kteq=(kt12*kt23)/(kt12+kt23); +disp(kteq,"Torsional spring constant of a propeller shaft in N-m/rad = "); diff --git a/2378/CH1/EX1.5/Exa_1_5.png b/2378/CH1/EX1.5/Exa_1_5.png Binary files differnew file mode 100644 index 000000000..f92f4264d --- /dev/null +++ b/2378/CH1/EX1.5/Exa_1_5.png diff --git a/2378/CH1/EX1.5/Exa_1_5.sce b/2378/CH1/EX1.5/Exa_1_5.sce new file mode 100644 index 000000000..df07fea13 --- /dev/null +++ b/2378/CH1/EX1.5/Exa_1_5.sce @@ -0,0 +1,20 @@ +//equivalent k of crane +//Exa_1_5 +clc; +clear; + +//refer fig_1_27 +l1=sqrt(3^2 + 10^2 -(2*3*10*cosd(135))); //length FC in m +l2=10 //length of AB in m +A1=100e-6; //cross section area of FB in m^2 +A2=2500e-6; //cross section area of AB in m^2 +E1=207e9; //youngs modulus of material +E2=207e9; //youngs modulus of material +theta= acosd(( l1^2 + 3^2 -10^2) / (2*l1*3)); //angle theta in degree + +k1=(A1 * E1)/ l1; //spring constant of FB +k2=(A2 * E2)/ l2; //spring constant of AB + +keq= (k1*(cosd(45))^2) + (k2*((cosd(90-theta))^2)); //equivalent spring constant of system +disp(keq,"equivalent spring constant of system in N/m = "); +//note: the answer in the book is printed incorrectly as 26430400 N/m diff --git a/2378/CH1/EX1.8/Exa_1_8.png b/2378/CH1/EX1.8/Exa_1_8.png Binary files differnew file mode 100644 index 000000000..175a8ff75 --- /dev/null +++ b/2378/CH1/EX1.8/Exa_1_8.png diff --git a/2378/CH1/EX1.8/Exa_1_8.sce b/2378/CH1/EX1.8/Exa_1_8.sce new file mode 100644 index 000000000..ba6bf3667 --- /dev/null +++ b/2378/CH1/EX1.8/Exa_1_8.sce @@ -0,0 +1,13 @@ +//clearance in a bearing +//Exa_1_5 +clc; +clear; + +F=400; //damping resistance in N +v=10; //velocity in m/s +mu=0.3445; //absolute viscosity in Pa-s +A=0.1; //area of plates in m^2 +c=F/v; //damping constant in N-s/m +//modelling as flat plate type damper +h=mu*A/c; //clearance between the plates +disp(h,"clearance between the plates in m = "); |
