From 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 Mon Sep 17 00:00:00 2001 From: prashantsinalkar Date: Tue, 10 Oct 2017 12:27:19 +0530 Subject: initial commit / add all books --- 1325/CH15/EX15.1/15_1.PNG | Bin 0 -> 86810 bytes 1325/CH15/EX15.1/15_1.sce | 21 +++++++++++++++++++++ 1325/CH15/EX15.11/15_11.PNG | Bin 0 -> 102970 bytes 1325/CH15/EX15.11/15_11.sce | 28 ++++++++++++++++++++++++++++ 1325/CH15/EX15.2/15_2.PNG | Bin 0 -> 95016 bytes 1325/CH15/EX15.2/15_2.sce | 24 ++++++++++++++++++++++++ 1325/CH15/EX15.3/15_3.PNG | Bin 0 -> 80910 bytes 1325/CH15/EX15.3/15_3.sce | 10 ++++++++++ 1325/CH15/EX15.4/15_4.PNG | Bin 0 -> 89717 bytes 1325/CH15/EX15.4/15_4.sce | 14 ++++++++++++++ 1325/CH15/EX15.5/15_5.PNG | Bin 0 -> 92259 bytes 1325/CH15/EX15.5/15_5.sce | 18 ++++++++++++++++++ 1325/CH15/EX15.6/15_6.PNG | Bin 0 -> 91784 bytes 1325/CH15/EX15.6/15_6.sce | 18 ++++++++++++++++++ 1325/CH15/EX15.7/15_7.PNG | Bin 0 -> 94307 bytes 1325/CH15/EX15.7/15_7.sce | 27 +++++++++++++++++++++++++++ 1325/CH15/EX15.8/15_8.PNG | Bin 0 -> 91135 bytes 1325/CH15/EX15.8/15_8.sce | 24 ++++++++++++++++++++++++ 1325/CH15/EX15.9/15_9.PNG | Bin 0 -> 99228 bytes 1325/CH15/EX15.9/15_9.sce | 25 +++++++++++++++++++++++++ 20 files changed, 209 insertions(+) create mode 100644 1325/CH15/EX15.1/15_1.PNG create mode 100644 1325/CH15/EX15.1/15_1.sce create mode 100644 1325/CH15/EX15.11/15_11.PNG create mode 100644 1325/CH15/EX15.11/15_11.sce create mode 100644 1325/CH15/EX15.2/15_2.PNG create mode 100644 1325/CH15/EX15.2/15_2.sce create mode 100644 1325/CH15/EX15.3/15_3.PNG create mode 100644 1325/CH15/EX15.3/15_3.sce create mode 100644 1325/CH15/EX15.4/15_4.PNG create mode 100644 1325/CH15/EX15.4/15_4.sce create mode 100644 1325/CH15/EX15.5/15_5.PNG create mode 100644 1325/CH15/EX15.5/15_5.sce create mode 100644 1325/CH15/EX15.6/15_6.PNG create mode 100644 1325/CH15/EX15.6/15_6.sce create mode 100644 1325/CH15/EX15.7/15_7.PNG create mode 100644 1325/CH15/EX15.7/15_7.sce create mode 100644 1325/CH15/EX15.8/15_8.PNG create mode 100644 1325/CH15/EX15.8/15_8.sce create mode 100644 1325/CH15/EX15.9/15_9.PNG create mode 100644 1325/CH15/EX15.9/15_9.sce (limited to '1325/CH15') diff --git a/1325/CH15/EX15.1/15_1.PNG b/1325/CH15/EX15.1/15_1.PNG new file mode 100644 index 000000000..ea5469f2d Binary files /dev/null and b/1325/CH15/EX15.1/15_1.PNG differ diff --git a/1325/CH15/EX15.1/15_1.sce b/1325/CH15/EX15.1/15_1.sce new file mode 100644 index 000000000..e983bc7c9 --- /dev/null +++ b/1325/CH15/EX15.1/15_1.sce @@ -0,0 +1,21 @@ +//to find the frequencies of the free longitudinal, transverse and torsional vibrations +clc +//given +W=.3*2240//lb +l=36//in +D=3//in +k=15//in +A=%pi*(D/2)^2 +E=30*10^6//youngs modulus +C=12*10^6 +g=32.2//ft/s^2 +d=W*l/(A*E) +Fl=187.8/(d)^(1/2) +I=%pi*(d/2)^4 +d1=W*(l^3)*64/(3*E*%pi*(3^4)) +Ft=187.8/(d1)^(1/2) +j=%pi*3^4/32 +q=C*j/l +Ftor=(1/(2*%pi))*(q*g*12/(W*k^2))^(1/2) +F1=Ftor*60 +printf("\na) Frequency of Longitudinal vibrations = %.f per min\nb) Frequency of the transverse vibrations = %.f per min\nc) Frequency of the torsional vibration = %.f per min",Fl,Ft,F1) diff --git a/1325/CH15/EX15.11/15_11.PNG b/1325/CH15/EX15.11/15_11.PNG new file mode 100644 index 000000000..4a94d2d2c Binary files /dev/null and b/1325/CH15/EX15.11/15_11.PNG differ diff --git a/1325/CH15/EX15.11/15_11.sce b/1325/CH15/EX15.11/15_11.sce new file mode 100644 index 000000000..9be8a056d --- /dev/null +++ b/1325/CH15/EX15.11/15_11.sce @@ -0,0 +1,28 @@ +//to find the natural frequencies of the torsional vibration of the system when inertia is neglected and when it is taken into account +clc +//given +g=32.3//ft/s^2 +l2=25.5//in +d1=2.75//in +d2=3.5//in +C=12*10^6//modulus of rigidity +G=1/0.6//given speed ratio +Ib=54//lb in^2 +Ic=850//lb in^2 +Id=50000//lb in^2 +Id1=Id/G^2//15.62 +Ia=1500//lb in^2 +la=Id1/(Id1+Ia)*66.5 +J=%pi*d1^4/32 +q=C*J/la//torsional stiffness +n=(1/(2*%pi))*(q*g*12/Ia)^(1/2) +nf=n*60//for minutes +//case b) +Ib1=Ib+Ic/(G^2) +a=63.15//in; distance of the node from rotor A (given) +b=3.661//in; distance of the node from rotor A (given) +N1=n*(la/a)^(1/2) +N2=n*(la/b)^(1/2) +N1f=N1*60//for minutes +N2f=N2*60//for minutes +printf("\na) The frequency of torsional vibrations n = %.1f per sec or %.f per min\nb) The fundamental frquency = %.1f per sec or %.f per min\n and the two node frequency = %.f per sec or %.f per min",n,nf,N1,N1f,N2,N2f) diff --git a/1325/CH15/EX15.2/15_2.PNG b/1325/CH15/EX15.2/15_2.PNG new file mode 100644 index 000000000..1913f0ec1 Binary files /dev/null and b/1325/CH15/EX15.2/15_2.PNG differ diff --git a/1325/CH15/EX15.2/15_2.sce b/1325/CH15/EX15.2/15_2.sce new file mode 100644 index 000000000..dc8e933c9 --- /dev/null +++ b/1325/CH15/EX15.2/15_2.sce @@ -0,0 +1,24 @@ +//To find the natural frequencies of the longitudinal, transverse and torsional vibration of the system +clc +//given +l1=3//ft +l2=2//ft +l=l1+l2//ft +W=.5*2240//lb +k=20//in +d=2//in +Wa=2*W/5 +E=30*10^6 +A=%pi*(d/2)^2 +d1=Wa*l1*12/(A*E) +N1=187.8/(d1)^(1/2) +I=%pi*(d)^4/64 +d2=W*(l1*12)^3*(l2*12)^3/(3*E*(l*12)^3*I) +N2=187.8/(d2)^(1/2) +C=12*10^6//given +g=32.2//given +J=%pi*d^4/32 +q=C*J*((1/(l1*12))+(1/(l2*12))) +n=(1/(2*%pi))*(q*g*12/(W*k^2))^(1/2) +N3=n*60 +printf("\na)Longitudinal vibration = %.f per min\nb)Transverse Vibration = %.f per min\nc)Torsional Vibration = %.f per min\n",N1,N2,N3) diff --git a/1325/CH15/EX15.3/15_3.PNG b/1325/CH15/EX15.3/15_3.PNG new file mode 100644 index 000000000..5ab75a7c1 Binary files /dev/null and b/1325/CH15/EX15.3/15_3.PNG differ diff --git a/1325/CH15/EX15.3/15_3.sce b/1325/CH15/EX15.3/15_3.sce new file mode 100644 index 000000000..03cf93309 --- /dev/null +++ b/1325/CH15/EX15.3/15_3.sce @@ -0,0 +1,10 @@ +//to find frequency of the natural transverse vibration +clc +//given +l=10//ft +d=4//in +E=30*10^6//youngs modulus +d1=0.0882//inches; maximum deflection as shown in the figure +N=207/(d1)^(1/2)//From 15.20 +printf("\nFrequency of natural transverse vibration = %.f per min",N) + diff --git a/1325/CH15/EX15.4/15_4.PNG b/1325/CH15/EX15.4/15_4.PNG new file mode 100644 index 000000000..b204f02c5 Binary files /dev/null and b/1325/CH15/EX15.4/15_4.PNG differ diff --git a/1325/CH15/EX15.4/15_4.sce b/1325/CH15/EX15.4/15_4.sce new file mode 100644 index 000000000..517438f67 --- /dev/null +++ b/1325/CH15/EX15.4/15_4.sce @@ -0,0 +1,14 @@ +//To find the resistance offered by the dashpot +clc +//given +m=50//lb +k=100//lb/in +g=32.2//ft/s +d=m/k//static deflection +n=(1/(2*%pi))*(g*12/d)^(1/2) +//part 2 +b=g*12/d +a=(b/20.79)^(1/2) +nd=(1/(2*%pi))*((b-(a/2)^2))^(1/2) +A=nd/n +printf("\nFrequency of free vibrations = %.3f per sec\nFrequency of damped vibrations = %.3f per sec \nThe ratio of the frequencies of damped and free vibrationsis %.3f \n",n,nd,A) diff --git a/1325/CH15/EX15.5/15_5.PNG b/1325/CH15/EX15.5/15_5.PNG new file mode 100644 index 000000000..78dd674bc Binary files /dev/null and b/1325/CH15/EX15.5/15_5.PNG differ diff --git a/1325/CH15/EX15.5/15_5.sce b/1325/CH15/EX15.5/15_5.sce new file mode 100644 index 000000000..6c525fa5b --- /dev/null +++ b/1325/CH15/EX15.5/15_5.sce @@ -0,0 +1,18 @@ +//To find the ratio nd/n +clc +//given +//damping torque is directly proposrtional to the angular velocity +C=12*10^6//Modulus of rigidity +l=3//ft +d=1//in +g=32.2//ft/s^2 +I=500//lb ft^2 ; moment of inertia +J=%pi*d^4/32 +q=C*J/(l*12) +n=(1/(2*%pi))*(q*g*12/(I*12^2))^(1/2) +//part 2 +b1=(q*g*12/(I*12^2)) +a1=(b1/10.15)^(1/2)//by reducing equation 15.28 +nd=(1/(2*%pi))*(b1-(a1/2)^2)^(1/2) +A=nd/n +printf("\nThe frequency of natural vibration = %.2f per sec\nThe frequency of damped vibration = %.2f per sec\nThe ratio nd/n = %.3f\n",n,nd,A) diff --git a/1325/CH15/EX15.6/15_6.PNG b/1325/CH15/EX15.6/15_6.PNG new file mode 100644 index 000000000..85bdcde90 Binary files /dev/null and b/1325/CH15/EX15.6/15_6.PNG differ diff --git a/1325/CH15/EX15.6/15_6.sce b/1325/CH15/EX15.6/15_6.sce new file mode 100644 index 000000000..4e62ef86d --- /dev/null +++ b/1325/CH15/EX15.6/15_6.sce @@ -0,0 +1,18 @@ +//to find the amplitude if the period of the applied force coincided with the natural period of vibration of the system +clc +//given +m=20//lb +k=50//lb/in +F=30//lb +w=50//sec^-1 +g=32.2//ft/s^2 +d=m/k +x=F/k//extension of the spring +b=g*12/d +a=(b/30.02)^(1/2)//from equation 15.28 +D=1/((1-w^2/b)^2+a^2*w^2/b^2)^(1/2) +Af=D*x//amplitude of forced vibration +D=(b/a^2)^(1/2)//At resonance +A=D*x//amplitude at resonance +printf("\nAmplitude of forced vibrations = %.3f in\nAmplitude of the forced vibrations at resonance = %.2f in",Af,A) + diff --git a/1325/CH15/EX15.7/15_7.PNG b/1325/CH15/EX15.7/15_7.PNG new file mode 100644 index 000000000..1f95a6e9b Binary files /dev/null and b/1325/CH15/EX15.7/15_7.PNG differ diff --git a/1325/CH15/EX15.7/15_7.sce b/1325/CH15/EX15.7/15_7.sce new file mode 100644 index 000000000..840abf0f0 --- /dev/null +++ b/1325/CH15/EX15.7/15_7.sce @@ -0,0 +1,27 @@ +//to find the fraction of the applied force transmitted at 1200 rpm and the amplitude of forced vibrations of the machines at resonance +clc +//given +e=1/30 +n=1200//rpm +w=%pi*n/30 +m=3//lb +g=32.2//ft/s^2 +stroke=3.5//in +r=stroke/2 +k=(1+1/e)^(1/2)//nf/n=k +d=(k/187.7)^2 +W=200//lb ; given +s=W/d//combined stiffness +p=1/14.1//As a^2/b=1/198 +T=((1+p^2*k^2/((1-k^2)^2+p^2*k^2)))^(1/2)//actual value of transmissibility +F=(m/g)*w^2*r/12//maximum unbalanced force transmitted on the machine +Fmax=F*T//maximum force transmitted to the foundation +//case b +E=((1+p^2)/(p^2))^(1/2) +Nreso=215.5//rpm +Fub=F*(Nreso/n)^2 +Ftmax=E*Fub +D=E//dynamic magnifier +del=Fub/152//static deflection +A=del*D +printf("\na) Maximum force transmitted at 1200 rpm = %.f lb\nb) The amplitude of the forced vibrations of the machine at resonance = %.3f in\n Force transmitted = %.f lb\n",Fmax,A,Fub) diff --git a/1325/CH15/EX15.8/15_8.PNG b/1325/CH15/EX15.8/15_8.PNG new file mode 100644 index 000000000..14a885501 Binary files /dev/null and b/1325/CH15/EX15.8/15_8.PNG differ diff --git a/1325/CH15/EX15.8/15_8.sce b/1325/CH15/EX15.8/15_8.sce new file mode 100644 index 000000000..a7b64e5a3 --- /dev/null +++ b/1325/CH15/EX15.8/15_8.sce @@ -0,0 +1,24 @@ +//To find the frequency of the natural torsional oscillations of the system +clc +//given +l1=11//in +l2=10//in +l3=15//in +l4=4//in +l5=10//in +d1=3//in +d2=5//in +d3=3.5//in +d4=7//in +d5=5//in +I1=1500//lb ft^2 +I2=1000//lb ft^2 +leq=3//in from 15.49 +g=32.2//ft/s^2 +C=12*10^6 +J=%pi*leq^4/32 +l=l1+l2*(leq/d2)^4+l3*(leq/d3)^4+l4*(leq/d4)^4+l5*(leq/d5)^4 +la=I2*l/(I1+I2) +qa=C*J/la +n=(1/(2*%pi))*(qa*g*12/(I1*12^2))^(1/2) +printf("\nThe frequency of the natural torsional oscillation of the system = %.1f per sec",n) diff --git a/1325/CH15/EX15.9/15_9.PNG b/1325/CH15/EX15.9/15_9.PNG new file mode 100644 index 000000000..b3c67de9a Binary files /dev/null and b/1325/CH15/EX15.9/15_9.PNG differ diff --git a/1325/CH15/EX15.9/15_9.sce b/1325/CH15/EX15.9/15_9.sce new file mode 100644 index 000000000..84df93a92 --- /dev/null +++ b/1325/CH15/EX15.9/15_9.sce @@ -0,0 +1,25 @@ +//To find the frequencies of the free torsional vibrations of the system +clc +//given +Ia=2.5//ton ft^2 +Ib=7.5//ton ft^2 +Ic=3//ton ft^2 +g=32.2//ft/s^2 +AB=9.5//ft +BC=25//ft +d=8.5//in +C=11.8*10^6//lb/in^2 +k=Ic/Ia//la/lc=k +lc1=(25.6+(25.6^2-4*114.1)^(1/2))/2//from 1 and 2 , reducing using quadratic formula +lc2=(25.6-(25.6^2-4*114.1)^(1/2))/2//from 1 and 2 , reducing using quadratic formula +la1=lc1*k +la2=lc2*k +J=%pi*d^4/32 +q=C*J/(lc1*12)//torsional stiffness +IC=Ic*2240*12^2/(g*12)//moment of inertia +nc=(1/(2*%pi))*(q/IC)^(1/2)//fundamental frequency of vibration +a1=nc*60 +a=floor(a1) +n=16*(lc1/lc2)^(1/2) +b=n*60 +printf("\nFundamental frequency of vibration = %.f per min\nTwo node frequency = %.f per min\n",a,b) -- cgit