Abaqus二自由度振动系统模态计算实操

一、理论计算参考csdn

二、Abaqus仿真计算结果

建立刚体动力学模型，不需要网格，只需在。

一阶模态：

二阶模态：

三、Abaqus inp文件

*Heading
** Job name: Job-3 Model name: Model-1
** Generated by: Abaqus/CAE 2016
*Preprint, echo=NO, model=NO, history=NO, contact=NO
**
** PARTS
**
**
** ASSEMBLY
**
*Assembly, name=Assembly
*Node
      1,       -1540.,        -500.,           0.
*Node
      2,       -1540.,           0.,           0.
*Node
      3,           0.,           0.,           0.
*Node
      4,        1290.,           0.,           0.
*Node
      5,        1290.,        -500.,           0.
*Nset, nset=Set-F
 2,
*Nset, nset=_PickedSet31, internal
 3,
*Nset, nset=_PickedSet34, internal
 3,
*Nset, nset=_PickedSet35, internal
 3,
*Nset, nset=_PickedSet41, internal
 1, 5
*Nset, nset=_PickedSet42, internal
 2, 4
** Constraint: Constraint-1
*Rigid Body, ref node=_PickedSet31, tie nset=_PickedSet42
*Element, type=MASS, elset=_PickedSet43_Inertia-1_MASS_
1, 3
*Mass, elset=_PickedSet43_Inertia-1_MASS_
1.34, 
*Element, type=ROTARYI, elset=_PickedSet43_Inertia-1_ROTI_
2, 3
*Rotary Inertia, elset=_PickedSet43_Inertia-1_ROTI_
1., 1., 2.395e+06, 0., 0., 0.
*Spring, elset=Springs/Dashpots-1-spring

40.
*Element, type=SpringA, elset=Springs/Dashpots-1-spring
3, 2, 1
*Spring, elset=Springs/Dashpots-2-spring

44.
*Element, type=SpringA, elset=Springs/Dashpots-2-spring
4, 4, 5
*End Assembly
** 
** BOUNDARY CONDITIONS
** 
** Name: BC-1 Type: Symmetry/Antisymmetry/Encastre
*Boundary
_PickedSet41, ENCASTRE
** Name: BC-4 Type: Symmetry/Antisymmetry/Encastre
*Boundary
_PickedSet34, YASYMM
** Name: BC-5 Type: Symmetry/Antisymmetry/Encastre
*Boundary
_PickedSet35, ZSYMM
** ----------------------------------------------------------------
** 
** STEP: Step-1
** 
*Step, name=Step-1, nlgeom=NO, perturbation
*Frequency, eigensolver=Lanczos, sim=NO, acoustic coupling=on, normalization=displacement
2, , , , , 
** 
** BOUNDARY CONDITIONS
** 
** Name: BC-3 Type: Displacement/Rotation
*Boundary
** 
** OUTPUT REQUESTS
** 
*Restart, write, frequency=0
** 
** FIELD OUTPUT: F-Output-1
** 
*Output, field
*Node Output
CF, RF, U
*End Step

四、Abaqus模态结果、广义质量、模态参与因子、模态有效质量等及计算验证

Abaqus计算结果：

python计算结果：

python计算程序：

import numpy as np
import math

#特征值分解法求平等与转动主模态（振型）：:
#SH760小轿车空载主要参数
m=1.340 #T
a=1540 #mm
b=1290 #mm
Ic=2395000 #%绕质心的转动惯量
k1=40 #N/mm
k2=44 #N/mm
M_sys=np.array([[m,0],[0,Ic]])
K_sys=np.array([[k1+k2,-(k1*a-k2*b)],[-(k1*a-k2*b),k1*a**2+k2*b**2]])

Value, Vector_Matrix = np.linalg.eig(np.linalg.inv(M_sys)@K_sys) 
np.set_printoptions(precision=3, suppress=True)
print('M_sys:\n',M_sys)
print('K_sys:\n',K_sys)
print('wi:\n',np.sqrt(Value))
print('fi:\n',np.sqrt(Value)/2/np.pi)
print('Vector_mode:\n',Vector_Matrix)

#模态质量：
#Abaqus称它为广义质量GENERALIZED MASS！！！
M_mode=Vector_Matrix.T@M_sys@Vector_Matrix
print('M_mode:\n',Vector_Matrix.T@M_sys@Vector_Matrix)

#???当系统在物理坐标系下，施加位移为1的单位激励时，在模态坐标系下的坐标（模态参与因子）为模态向量的逆：
#P A R T I C I P A T I O N   F A C T O R S
phi_inv_paticipation_factors=np.linalg.inv(Vector_Matrix)
print('phi_inv_paticipation_factors:\n',phi_inv_paticipation_factors)

#系统各阶模态有效质量为phi_inv_paticipation_factors.T@M_mode@phi_inv_paticipation_factors:
#E F F E C T I V E   M A S S
#当模态质量归一化后，模态有效质量就是模态参与因子的平方
#模态质量按列排：
M_effective_mass_i=phi_inv_paticipation_factors**2
for i in range((M_mode.shape)[0]):
    M_effective_mass_i[i]*=M_mode[<

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