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AutoFEM Analysis First Natural Frequency of a Spring-Mass System |  |
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AutoFEM Analysis First Natural Frequency of a Spring-Mass System | |
First Natural Frequency of a Spring-Mass System
Let us consider the spring-supported mass.
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The finite element model with restraints |
The length of the cube edge is L. Let L equal 0.1 m.
The material properties are: the Young's modulus E = 2.1E+011 Pа, Poisson's ratio ν=0.28, the density ρ = 7800 kg / m3.
The mass of the cube M is calculated by the following formula:
M= ρ L3
Thus, M = 7.8 kg.
The spring stiffness k is 1000 N/m .
Analytical solution of this problem is given by the following formula:
Thus, f = 1.802 Hz
After carrying out calculation with the help of AutoFEM, the following result is obtained:
Table 1. Parameters of finite element mesh
Finite Element Type |
Number of nodes |
Number of finite elements |
quadratic tetrahedron |
271 |
783 |
Table 2. Result "Frequency"*
Numerical solution |
Analytical solution |
Error δ = 100%*| f* - f| / | f | |
1.802 |
1.802 |
0.00 |
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*The results of numerical tests depend on the finite element mesh and may differ slightly from those given in the table.
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