diff options
Diffstat (limited to '698/CH7')
| -rw-r--r-- | 698/CH7/EX7.10/10_angular_displacement_of_flywheel.txt | 10 | ||||
| -rw-r--r-- | 698/CH7/EX7.10/P10_angular_displacement_of_flywheel.sce | 39 | ||||
| -rw-r--r-- | 698/CH7/EX7.12/12_spring_stiffness.txt | 29 | ||||
| -rw-r--r-- | 698/CH7/EX7.12/P12_spring_stiffness.sce | 71 | ||||
| -rw-r--r-- | 698/CH7/EX7.6/6_parameters_of_sdof.txt | 13 | ||||
| -rw-r--r-- | 698/CH7/EX7.6/P6_parameters_of_sdof.sce | 42 | ||||
| -rw-r--r-- | 698/CH7/EX7.7/7_stiffness_of_fan.txt | 9 | ||||
| -rw-r--r-- | 698/CH7/EX7.7/P7_stiffness_of_fan.sce | 37 | ||||
| -rw-r--r-- | 698/CH7/EX7.9/9_base_excitation.txt | 14 | ||||
| -rw-r--r-- | 698/CH7/EX7.9/P9_base_excitation.sce | 38 |
10 files changed, 302 insertions, 0 deletions
diff --git a/698/CH7/EX7.10/10_angular_displacement_of_flywheel.txt b/698/CH7/EX7.10/10_angular_displacement_of_flywheel.txt new file mode 100644 index 000000000..51883390b --- /dev/null +++ b/698/CH7/EX7.10/10_angular_displacement_of_flywheel.txt @@ -0,0 +1,10 @@ +(a) Torsional amplitude of vibration is given by:
+ theta=To/sqrt((Kt-Jw2)^2+(Ct*w^2)^2)
+
+ theta=0.3334 rad
+
+(b) Maximum damping couple= Ct*w*theta = 0.5334 N-m
+
+(c)Phase angle phi =
+ tan(phi)=(Ct*w)/(Kt-J*w^2)
+phi=117.248 degrees
\ No newline at end of file diff --git a/698/CH7/EX7.10/P10_angular_displacement_of_flywheel.sce b/698/CH7/EX7.10/P10_angular_displacement_of_flywheel.sce new file mode 100644 index 000000000..6782edb49 --- /dev/null +++ b/698/CH7/EX7.10/P10_angular_displacement_of_flywheel.sce @@ -0,0 +1,39 @@ +clc
+//Example 7.10
+//Angular displacement of flywheel
+
+//------------------------------------------------------------------------------
+
+//Given data
+//Moment of Inertia
+J=0.125 //kg-m^2
+//Torsional stiffness
+Kt=1.176 // N-m/rad
+//Torque
+To=0.6 //N-m
+//frequency
+w=4 //rad/s
+//Damping couple
+Ct=0.4 //N-m
+
+res10=mopen(TMPDIR+'10_angular_displacement_of_flywheel.txt','wt')
+mfprintf(res10,'(a) Torsional amplitude of vibration is given by:\n')
+mfprintf(res10,'\ttheta=To/sqrt((Kt-Jw2)^2+(Ct*w^2)^2)\n\n')
+
+//Torsional amplitude:
+theta=To/sqrt((Kt-(J* w^2))^2 + (Ct* w)^2 )
+mfprintf(res10,'\ttheta=%0.4f rad\n\n',theta)
+
+//Maximum Damping couple
+Cmax=Ct*w*theta
+mfprintf(res10,'(b) Maximum damping couple= Ct*w*theta = %0.4f N-m\n\n',Cmax)
+
+mfprintf(res10,'(c)Phase angle phi =\n\ttan(phi)=(Ct*w)/(Kt-J*w^2)\n')
+//Phase angle
+phi=atand((Ct*w)/(Kt- J* w^2))
+mfprintf(res10,'phi=%0.3f degrees',180+phi) //Adding 180 to make it positive angle
+
+mclose(res10)
+editor(TMPDIR+'10_angular_displacement_of_flywheel.txt')
+//------------------------------------------------------------------------------
+//-----------------------------End of program-----------------------------------
\ No newline at end of file diff --git a/698/CH7/EX7.12/12_spring_stiffness.txt b/698/CH7/EX7.12/12_spring_stiffness.txt new file mode 100644 index 000000000..5fa4f8e8a --- /dev/null +++ b/698/CH7/EX7.12/12_spring_stiffness.txt @@ -0,0 +1,29 @@ +In absence of damping,
+ TR=1/(1- r^2)
+ where r=w/wn
+Natural frequency wn=20.57 rad/s
+
+(a) Combined stiffness=42.30 N/mm
+
+(b) In actual conditions, successive vibrations are reduced by 30%
+Logarithmic decrement delta=ln(X/Xn+1)
+ X/Xn+1 = 1/1-0.3
+ delta= ln(X/Xn+1)= (2*pi*zeta)/sqrt(1-zeta^2),
+ where zeta=damping factor
+zeta=0.05668
+
+Transmissibility ratio is given by
+ TR=sqrt(1 + (2*zeta*r)^2)/sqrt((1- r^2)^2 + (2*zeta*r)^2)
+TR=0.05632
+
+The Maximum unbalance force is Fo=999.30 N
+Force transmitted is Ftr=Fo*TR =56.28 N
+
+(c) At resonance, r=1
+ TR=sqrt(1 + (2*zeta)^2)/(2*zeta)
+TR=8.879
+
+Maximum unbalanced force due to resonance Fo=47.59 N
+Force transmitted at resonance Ftr=422.50 N
+
+(d)Amplitude at resonance X=Ftr/Ke =9.989 mm
\ No newline at end of file diff --git a/698/CH7/EX7.12/P12_spring_stiffness.sce b/698/CH7/EX7.12/P12_spring_stiffness.sce new file mode 100644 index 000000000..f848008d8 --- /dev/null +++ b/698/CH7/EX7.12/P12_spring_stiffness.sce @@ -0,0 +1,71 @@ +clc
+//Example 7.12
+//Spring stiffness
+//------------------------------------------------------------------------------
+
+//Given data
+//mass of machine
+m1=100 // kg
+//mass of reciprocating parts
+m2=2.25 //kg
+//speed
+N=900 //rpm
+w=(2*%pi*N)/60 //rad/s
+//displacement
+x=0.1 //m
+//Transmissibility ratio
+TR=1/20
+
+res12=mopen(TMPDIR+'12_spring_stiffness.txt','wt')
+
+//In absence of damping
+mfprintf(res12,'In absence of damping,\n\tTR=1/(1- r^2)\n\twhere r=w/wn\n')
+//Natural frequency
+r=sqrt(abs(-1- 1/TR))
+wn=w/r
+mfprintf(res12,'Natural frequency wn=%0.2f rad/s\n\n',wn)
+
+//Combined stiffness
+Ke=wn^2 *m1
+mfprintf(res12,'(a) Combined stiffness=%0.2f N/mm\n\n',Ke* 10^-3)
+
+//Damping factor
+mfprintf(res12,'(b) In actual conditions, successive vibrations are reduced by 30%%\n')
+mfprintf(res12,'Logarithmic decrement delta=ln(X/Xn+1)\n')
+mfprintf(res12,'\tX/Xn+1 = 1/1-0.3\n')
+delta=log(1/(1-0.3))
+mfprintf(res12,'\tdelta= ln(X/Xn+1)= (2*pi*zeta)/sqrt(1-zeta^2),\n\twhere zeta=damping factor\n')
+zeta=delta/(sqrt(delta^2 + (2*%pi)^2))
+mfprintf(res12,'zeta=%0.5f\n\n',zeta)
+
+//Transmissibility ratio with damping
+mfprintf(res12,'Transmissibility ratio is given by\n\t')
+mfprintf(res12,'TR=sqrt(1 + (2*zeta*r)^2)/sqrt((1- r^2)^2 + (2*zeta*r)^2)\n')
+TR_new=sqrt(1 + (2*zeta*r)^2 )/sqrt( (1- r^2)^2 + (2*zeta*r)^2 )
+mfprintf(res12,'TR=%0.5f\n\n',TR_new)
+
+//Maximum unbalance force
+Fo=m2*TR*(w^2)
+//Force transmitted
+Ftr=Fo*TR_new
+mfprintf(res12,'The Maximum unbalance force is Fo=%0.2f N\n',Fo)
+mfprintf(res12,'Force transmitted is Ftr=Fo*TR =%0.2f N\n\n',Ftr)
+
+//At resonance
+mfprintf(res12,'(c) At resonance, r=1\n\t')
+mfprintf(res12,'TR=sqrt(1 + (2*zeta)^2)/(2*zeta)\n')
+TR_res=sqrt(1 + (2*zeta)^2)/(2*zeta)
+mfprintf(res12,'TR=%0.3f\n\n',TR_res)
+Fo_res=m2*TR*(wn^2)
+Ftr_res=Fo_res*TR_res
+mfprintf(res12,'Maximum unbalanced force due to resonance Fo=%0.2f N\n',Fo_res)
+mfprintf(res12,'Force transmitted at resonance Ftr=%0.2f N\n\n',Ftr_res)
+
+//Amplitude
+X=Ftr_res/Ke
+mfprintf(res12,'(d)Amplitude at resonance X=Ftr/Ke =%0.3f mm',X* 10^3)
+
+mclose(res12)
+editor(TMPDIR+'12_spring_stiffness.txt')
+//------------------------------------------------------------------------------
+//-----------------------------End of program-----------------------------------
diff --git a/698/CH7/EX7.6/6_parameters_of_sdof.txt b/698/CH7/EX7.6/6_parameters_of_sdof.txt new file mode 100644 index 000000000..d9b4f34a5 --- /dev/null +++ b/698/CH7/EX7.6/6_parameters_of_sdof.txt @@ -0,0 +1,13 @@ +(a) General equation of any single degree of freedom system is given by
+ma + cv + kx = F(t) = Fo sin(wt)
+ a is the acceleration (x_dotdot)
+ v is the velocity (x_dot)
+ x is the amplitude
+
+(b)Natural Frequency=SQRT(k/m) = 5.00rad/s
+
+(c)Damped Frequency=SQRT( (k/m) - ( (c/ (2*m) ) ^2) ) = 4.54rad/s
+
+(d)Damping ratio= c/ (2* SQRT(k*m)) = 0.42
+
+(e)Amplitude of steady state vibration, Y= Fo/ sqrt( (k- (m*(w^2)))^2 + (c*w)^2 ) =0.01163m
\ No newline at end of file diff --git a/698/CH7/EX7.6/P6_parameters_of_sdof.sce b/698/CH7/EX7.6/P6_parameters_of_sdof.sce new file mode 100644 index 000000000..61dba813b --- /dev/null +++ b/698/CH7/EX7.6/P6_parameters_of_sdof.sce @@ -0,0 +1,42 @@ +clc
+//Example 7.6
+//Parameters of single degree of freedom system
+
+//------------------------------------------------------------------------------
+
+res6=mopen(TMPDIR+'6_parameters_of_sdof.txt','wt')
+
+mfprintf(res6,'(a) General equation of any single degree of freedom system is given by\n')
+mfprintf(res6,'ma + cv + kx = F(t) = Fo sin(wt)\n')
+mfprintf(res6,'\ta is the acceleration (x_dotdot)\n\tv is the velocity (x_dot)\n\tx is the amplitude\n\n')
+
+m=5 //kg
+c=21 // N-s/m
+k=125 //N/m
+Fo=5 //N
+w=10 //rad/s
+
+// Natural frequency
+wn = sqrt(k/m)
+
+mfprintf(res6,'(b)Natural Frequency=SQRT(k/m) = %0.2frad/s\n\n',wn)
+
+//Damped Frequency
+wd=sqrt((k/m) - ((c/(2*m))^2))
+
+mfprintf(res6,'(c)Damped Frequency=SQRT( (k/m) - ( (c/ (2*m) ) ^2) ) = %0.2frad/s\n\n',wd)
+
+//Damping ratio
+z=c/ (2* sqrt(k*m))
+
+mfprintf(res6,'(d)Damping ratio= c/ (2* SQRT(k*m)) = %0.2f\n\n',z)
+
+//Amplitude of steady state vibration
+Y= Fo/ sqrt( (k- (m*(w^2)))^2 + (c*w)^2 )
+
+mfprintf(res6,'(e)Amplitude of steady state vibration, Y= Fo/ sqrt( (k- (m*(w^2)))^2 + (c*w)^2 ) =%0.5fm',Y)
+
+mclose(res6)
+editor(TMPDIR+'6_parameters_of_sdof.txt')
+//------------------------------------------------------------------------------
+//-----------------------------End of program-----------------------------------
\ No newline at end of file diff --git a/698/CH7/EX7.7/7_stiffness_of_fan.txt b/698/CH7/EX7.7/7_stiffness_of_fan.txt new file mode 100644 index 000000000..0de648bc7 --- /dev/null +++ b/698/CH7/EX7.7/7_stiffness_of_fan.txt @@ -0,0 +1,9 @@ +Transmissibility ratio = 1/(1 - r^2)
+ where r is the frequency ratio w/wn
+
+Natural Frequency wn=16.419 rad/s
+
+ wn=sqrt(k/m)
+where k is the stiffness and m is the mass
+Collective stiffness of the springs=10782.792 N/m
+Stiffness of each spring=3594.264 N/m
\ No newline at end of file diff --git a/698/CH7/EX7.7/P7_stiffness_of_fan.sce b/698/CH7/EX7.7/P7_stiffness_of_fan.sce new file mode 100644 index 000000000..b30cd0d41 --- /dev/null +++ b/698/CH7/EX7.7/P7_stiffness_of_fan.sce @@ -0,0 +1,37 @@ +clc
+//Example 7.7
+//Stiffness of fan
+
+//------------------------------------------------------------------------------
+
+//Given data
+
+//mass of fan
+m=40 //kg
+//operating speed
+N=520 // rpm
+w=(2*%pi*N)/60 //rad/s
+
+//Transmissibility ratio
+TR=0.1
+
+res7=mopen(TMPDIR+'7_stiffness_of_fan.txt','wt')
+mfprintf(res7,'Transmissibility ratio = 1/(1 - r^2)\n\twhere r is the frequency ratio w/wn\n')
+
+//Natural frequency
+wn=sqrt((w^2)/((1+(1/TR)))) // we take absolute value of denominator since it
+ // may be negative, and thus the expression rendered null
+
+mfprintf(res7,'\nNatural Frequency wn=%0.3f rad/s\n',wn)
+
+//Finding the stiffness
+
+mfprintf(res7,'\n\twn=sqrt(k/m)\nwhere k is the stiffness and m is the mass\n')
+k=(wn^2)*m
+mfprintf(res7,'Collective stiffness of the springs=%0.3f N/m\n',k)
+mfprintf(res7,'Stiffness of each spring=%0.3f N/m',k/3)
+
+mclose(res7)
+editor(TMPDIR+'7_stiffness_of_fan.txt')
+//------------------------------------------------------------------------------
+//-----------------------------End of program-----------------------------------
\ No newline at end of file diff --git a/698/CH7/EX7.9/9_base_excitation.txt b/698/CH7/EX7.9/9_base_excitation.txt new file mode 100644 index 000000000..83dabe396 --- /dev/null +++ b/698/CH7/EX7.9/9_base_excitation.txt @@ -0,0 +1,14 @@ +This is a forced, steady state vibration situation.
+
+There are 2 supporting springs, hence net stiffness Ke=2k
+Damping coefficient Ce = 0.05 Cc = 0.05*2*sqrt(Ke*m)
+
+The expression for desired amplitude Y is
+
+ Y=Fo/sqrt((ke-m*w^2)^2+(Ce*w)^2)
+Y will be maximum at resonance, i.e., w=wn
+Thus the design condition is k=(1/2)m*w^2
+ k=21.73 kN/m
+
+At resonance, Y=Fo/c*w
+The peak solenoid force required is 2.17 N
\ No newline at end of file diff --git a/698/CH7/EX7.9/P9_base_excitation.sce b/698/CH7/EX7.9/P9_base_excitation.sce new file mode 100644 index 000000000..31ca46f87 --- /dev/null +++ b/698/CH7/EX7.9/P9_base_excitation.sce @@ -0,0 +1,38 @@ +clc
+//Example 7.9
+//Base_excitation
+
+//------------------------------------------------------------------------------
+
+//Given data
+
+//Desired amplitude
+Y=0.5*(10^-3) //m
+//Desired frequency
+f=6 //Hz
+w=f*2*%pi //rad/s
+//mass of the table
+m=300/9.81 //kg
+
+
+res9=mopen(TMPDIR+'9_base_excitation.txt','wt')
+mfprintf(res9,'This is a forced, steady state vibration situation.\n\n')
+mfprintf(res9,'There are 2 supporting springs, hence net stiffness Ke=2k\n')
+mfprintf(res9,'Damping coefficient Ce = 0.05 Cc = 0.05*2*sqrt(Ke*m)')
+mfprintf(res9,'\n\nThe expression for desired amplitude Y is\n')
+mfprintf(res9,'\n\tY=Fo/sqrt((ke-m*w^2)^2+(Ce*w)^2)\n')
+mfprintf(res9,'Y will be maximum at resonance, i.e., w=wn\n')
+mfprintf(res9,'Thus the design condition is k=(1/2)m*w^2\n')
+
+k=0.5*m*(w^2)
+
+mfprintf(res9,'\tk=%0.2f kN/m\n',k* 10^-3)
+mfprintf(res9,'\nAt resonance, Y=Fo/c*w')
+
+Fo=(0.05*2*sqrt(2*k*m))*w*Y
+mfprintf(res9,'\nThe peak solenoid force required is %0.2f N',Fo)
+
+mclose(res9)
+editor(TMPDIR+'9_base_excitation.txt')
+//------------------------------------------------------------------------------
+//-----------------------------End of program-----------------------------------
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