V. 弹簧支撑梁的自振频率

计算一个带有集中质量的梁在两个弹簧支撑下的自由振动周期。

References

Timoshenko, S., Young, D., and Weaver, W., Vibration Problems in Engineering, John Wiley & Sons, 第4th版, 1974. 第11页, 问题1.1-3.

Details

一个简支梁由两个弹簧支撑，如图所示。忽略梁的分布质量，计算梁在荷载W作用下的自由振动周期。

EI = 30,000.0 ksi
A = 7.0 ft
B = 3.0 ft.
W = 1,000 lbf
K = 300.0 lb/in.
Figure 1. 弹簧支撑梁

Results

Table 1. 结果比较
结果类型 理论 STAAD.Pro 差异
周期（秒） 0.533 0.53317 可忽略

Input

文件 C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \Verification Models\08 Dynamic Analysis\Natural Frequency of Beam on Springs.STD 通常随程序安装。

STAAD

STAAD PLANE : NATURAL FREQUENCY OF BEAM ON SPRINGS
START JOB INFORMATION
ENGINEER DATE 14-Sep-18
END JOB INFORMATION
*
*  REFERENCE 'VIBRATION PROBLEMS IN ENGINEERING' BY
*  TIMOSHENKO,YOUNG,WEAVER. (4TH EDITION, PAGE 11, PROB 1.1-3)
*  THE ANSWER IN THE BOOK IS T = 0.533 sec., viz., F = 1.876 CPS
*
UNIT FEET POUND
JOINT COORDINATES
1 0 0 0; 2 7 0 0; 3 10 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3;
UNIT INCHES POUND
SUPPORTS
1 3 FIXED BUT MZ KFY 300
MEMBER PROPERTY AMERICAN
1 2 PRIS AX 1 IZ 1
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 3e+07
POISSON 0.3
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
CUT OFF MODE SHAPE 1
LOAD 1 1000 LB LOAD AT JOINT 2
JOINT LOAD
2 FY -1000
MODAL CALCULATION REQUESTED
PERFORM ANALYSIS
FINISH

Output

               CALCULATED FREQUENCIES FOR LOAD CASE       1
       MODE            FREQUENCY(CYCLES/SEC)         PERIOD(SEC)
         1                       1.876                  0.53317 
            MODAL WEIGHT (MODAL MASS TIMES g) IN POUN         GENERALIZED
      MODE           X             Y             Z              WEIGHT
         1       0.000000E+00  9.999999E+02  0.000000E+00    9.999999E+02
 MASS PARTICIPATION FACTORS 
                     MASS  PARTICIPATION FACTORS IN PERCENT
                     --------------------------------------
           MODE    X     Y     Z     SUMM-X   SUMM-Y   SUMM-Z
             1     0.00 100.00   0.00    0.000  100.000    0.000