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Transient dynamic analysis of spring, mass and damping vibration system based on finite element analysis software

Introduction to vibration mechanics

vibration is a form of motion, which refers to the reciprocating motion of objects near the equilibrium position. In a broad sense, if the physical quantity characterizing a motion changes repeatedly from time to time, it can be called vibration. If the changing physical quantity is some mechanical quantity or mechanical quantity, such as the displacement, velocity, acceleration, stress and strain of the object, this kind of vibration is called mechanical vibration

vibration mechanics refers to a science that explores various vibration phenomena and clarifies the basic laws of vibration with the help of mathematics, physics, experiment and calculation technology, so as to overcome the negative factors of vibration and use its positive factors to provide a theoretical basis for reasonably solving various vibration problems

vibration is a universal physical phenomenon, which is the response of the mass, elasticity, damping and other components of the system to external excitation by external excitation. In all scientific fields and daily life, we will encounter various degrees of vibration. Based on the important impact of vibration on industrial production, many scholars at home and abroad have carried out a lot of research in this field. The dynamic characteristics of mechanical structures are mainly reflected in the following aspects: (1) establish a vibration model; (2) Determine the dynamic characteristics of the structural system; (3) The non proportional damping method is used to accurately estimate the damping matrix of the system; (4) Finite element model modification based on experimental data structure

1 transient dynamic analysis method of vibration system

Figure 1 Relationship diagram of vibration model

general vibration problems are composed of vibration system, excitation and response, and the relationship between the three can be expressed as shown in Figure 1. The research object of vibration problem is the vibration system. The external excitation force and other factors are called excitation (input), which act on the system to produce vibration response (output). The vibration problem is to solve the other parameter by knowing two quantities from the above three

transient dynamic analysis (also known as time history analysis) is a method for determining the dynamic response of structures subjected to arbitrary time-varying loads. The time-varying displacement, strain, stress and stress of the structure under any combination of static load, transient load and harmonic load can be determined by transient dynamic analysis. The correlation between load and time makes the inertia force and damping effect more significant. Therefore, transient dynamics analysis is used to analyze the system in this problem

2 transient dynamic analysis of free vibration of damped vibration system

combined with theoretical derivation, this paper uses ANSYS software as a platform to derive and analyze the transient dynamics of spring, mass and damping system

2.1 system model establishment and theoretical derivation

(1) model establishment

the vibration system shown in Figure 2 is composed of four systems, which are divided into two categories: damped and undamped, of which damping can be divided into three categories (over damping, critical damping and under damping). Apply time-varying force on the mass block, calculate the instantaneous response of the vibration system, and compare the motion of the system under different damping

damping ratio 1: ζ= 1.8。 (over damping)

damping ratio 2: ζ= 1.0。 (critical damping)

damping ratio 3: ζ= 0.3。 (underdamped)

damping ratio 4: ζ= 0.0。 (undamped)

displacement 1:w=10 lb

stiffness: K also makes Zhongwang the first aluminum processing enterprise in China that can independently design and manufacture all aluminum body + all aluminum chassis =30 lb/in

mass: m=w/g=0 Now LB sec2/in

displacement 2: △ =1 in

gravitational acceleration: g=386 in/sec2

where, damping ratio:

Figure 2 system model figure

(2) solution of system differential equation

abstract the system into the model shown in Figure 3. According to the meaning of the problem, ignoring the influence of mass blocks in the system, establish the general differential equation of the system as follows (f (T) =0 in this system):

that is:

Figure 3 system analysis model figure

next, Solve the established equation

bring the solved s into the equation, define the damping coefficient, and then you can deduce the transient response of the vibration system and the motion of the system under different damping

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2.2 system model building process in ANSYS10.0

(1) set the job name and Title

select the "file>change jobname" and "file>change title" commands in turn on the ANSYS menu, and change the job name and title to "zhonglonglixuezuoye" and "znzdxt_shuntaidongglifenxi" according to the system prompt

select the preference command from the main menu and select the "structural" parameter

(2) define element type

when defining finite element analysis, the appropriate element type should be selected first according to the geometric structure of the analysis problem, the analysis type and the accuracy requirements of the analyzed problem. Composite unit combination40 is selected in this example

(3) define the real constant

in this example, the combination40 unit is selected, and the real constant needs to be set

(4) define material properties

in this example, the calculation of stress and strain is not involved, and the composite element is used without setting material properties

(5) establish the model of spring, mass and damping vibration system

2.3 in ANSYS10.0, set the dynamic analysis of the system, define the boundary conditions and solve

(1) select the analysis type and solution method

set the analysis type to "transient" in "solution" and the solution method to "reduced"

(2) set the master degrees of freedom

select the solution>master dof>user selected>define command from the main menu, activate the "min, Max, Inc" option, in the text box, but finding the right direction is the key to the continuation of the enterprise. Enter 1, 7, 2 and confirm, and then select the master degrees of freedom

(3) transient dynamic analysis settings

(4) define boundary conditions and solve

(5) time control settings and input forces and then solve

3 conclusion

combined with theoretical derivation, this paper uses ANSYS as a platform to conduct transient dynamic derivation and analysis of spring, mass and damping systems. It can be seen from the above curve that when the time is very small, other parameters remain unchanged. With the reduction of damping coefficient, the displacement motion curve of the system decays more rapidly. This is in good agreement with the theoretical analysis. The research work of this paper can provide some reference for the informatization process of manufacturing industry. (end)

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