- #1
NeroBlade
- 11
- 0
Hello Phys Forum
I’m trying to solve a dynamic problem that involves a cantilever beam fixed onto a support that experiences a time history load on the free end of the beam as shown below:
/
/
/--------------------------------[]
/
/
Cross section Beam is rectangular beam with 1m width and height.The objective is to obtain the natural frequency of the beam. I believe this is the equation to use:
\omega_n = \frac{\alpha_n}{L^2} \sqrt{\frac{EI}{m}}
Please correct me if my approach is incorrect.
The paramenters are the following:
\alpha_n = 3.57
L (Length) = 5m
E = 205 KN/mm^2
I = 1m^2
m = 2kg (0.204N)
So the natural frequency \omega_n should be
\omega_n = 45.72 Hz
Now, when I run it through Staad Pro (haven’t tried AnSys yet I heard its powerful tool). With the same parameters where I use a Time History Load of -0.204 N onto the end node of the beam and applied the same parameters plus the self loads of 1 throughout the system, my results indicate that its 22.684 Hz for the 1st Mode. Could you guys tell me where I am going wrong all this time is it the analytical solution my Staad Pro or both?!
Appreciate your help!
The script of the Staad Pro is defined below.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 06-Jul-12
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER NEWTON
JOINT COORDINATES
1 0 0 0; 2 5 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+011
POISSON 0.3
DENSITY 76819.5
ALPHA 1.2e-005
DAMP 0.03
TYPE STEEL
STRENGTH FY 2.532e+008 FU 4.078e+008 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY
1 PRIS YD 1 ZD 1
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
DEFINE TIME HISTORY DT 0.0013888
TYPE 1 FORCE
1 -0.204 2 0
ARRIVAL TIME
1 2
DAMPING 0
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
TIME LOAD
2 FY 1 1 1.000000
CALCULATE RAYLEIGH FREQUENCY
SELFWEIGHT X 1 LIST ALL
SELFWEIGHT Y 1 LIST ALL
SELFWEIGHT Z 1 LIST ALL
PERFORM ANALYSIS PRINT ALL
FINISH
I’m trying to solve a dynamic problem that involves a cantilever beam fixed onto a support that experiences a time history load on the free end of the beam as shown below:
/
/
/--------------------------------[]
/
/
Cross section Beam is rectangular beam with 1m width and height.The objective is to obtain the natural frequency of the beam. I believe this is the equation to use:
\omega_n = \frac{\alpha_n}{L^2} \sqrt{\frac{EI}{m}}
Please correct me if my approach is incorrect.
The paramenters are the following:
\alpha_n = 3.57
L (Length) = 5m
E = 205 KN/mm^2
I = 1m^2
m = 2kg (0.204N)
So the natural frequency \omega_n should be
\omega_n = 45.72 Hz
Now, when I run it through Staad Pro (haven’t tried AnSys yet I heard its powerful tool). With the same parameters where I use a Time History Load of -0.204 N onto the end node of the beam and applied the same parameters plus the self loads of 1 throughout the system, my results indicate that its 22.684 Hz for the 1st Mode. Could you guys tell me where I am going wrong all this time is it the analytical solution my Staad Pro or both?!
Appreciate your help!
The script of the Staad Pro is defined below.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 06-Jul-12
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER NEWTON
JOINT COORDINATES
1 0 0 0; 2 5 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+011
POISSON 0.3
DENSITY 76819.5
ALPHA 1.2e-005
DAMP 0.03
TYPE STEEL
STRENGTH FY 2.532e+008 FU 4.078e+008 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY
1 PRIS YD 1 ZD 1
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
DEFINE TIME HISTORY DT 0.0013888
TYPE 1 FORCE
1 -0.204 2 0
ARRIVAL TIME
1 2
DAMPING 0
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
TIME LOAD
2 FY 1 1 1.000000
CALCULATE RAYLEIGH FREQUENCY
SELFWEIGHT X 1 LIST ALL
SELFWEIGHT Y 1 LIST ALL
SELFWEIGHT Z 1 LIST ALL
PERFORM ANALYSIS PRINT ALL
FINISH