中欧学院离散结构动力学实验报告

离散结构力学课程实验报告Report of Discrete Structural Mechanics

Course Experiment

学院：中欧航空工程师学院

专业：航空工程

组员：庄怀风 2017122085

张统 2017122075

赵靖2017122079

刘鹏宇2017122034

指导教师：李湘萍

二零一七年十二月二十九日

目录

Chapter 1Description of Problem (1)

1.1Problem of experiment (1)

1.2Theoretical calculation (1)

Chapter 2Finite Element Simulation (3)

2.1 Patran software introduction (3)

2.2 Numerical Simulation (4)

2.2.1 Simulation process (4)

2.2.2 Simulation results (8)

Chapter 3Conclusion (10)

3.1 The summary of work (10)

3.2 Work shortcomings (10)

3.3 The experience of course learning (10)

ACKNOWLEDGEMENT (12)

Chapter 1 DescriptionofProblem

1.1Problem of experiment

The existing first-class cross-section cantilevers, as shown in Figure 1.1, the left end of the fixed right free. It is known that the elastic modulus E=2.0×1011N/m2, the Poisson's ratio μ=0.3, the density ρ=7800kg/m3, the length L = 0.5 m, the width B = 0.02 m and the heightH=0.01m.

Fig.1.1The left end of the fixed free right cross-section cantilever beam

1.2Theoretical calculation

The differential equation of cantilever bending is

EI ð4w x,t

4

+ρA

ð2w x,t

2

=0

The cantilever boundary conditions are:

w x=0=01

dw

dx

x=0=02

ð2w

2

|x=l=03

ððx EI

ð2w

ðx2

|x=l=04

The free vibration solution of this partial differential equation is:

w x,t=W x T t

This solution can be derived into the differential equations of motion of cantilever,then we have

W x=C1cosβx+C2sinβx+C3cosℎβx+C4sinℎβx

T t=Acoswt+Bsinwt

and

β4=

ρAw2

Substitute the boundary conditions (1)、(2)into the above formula,we have

C1+C3=0,C2+C4=0

Then we will get

W x=C1cosβx−cosℎβx+C2sinβx−sinℎβx

Then substitute the boundary conditions (3)、(4)into the above formula,we have

−C1cosβl+cosℎβl−C2sinβl+sinℎβl=0

−C1−sinβl+sinℎβl−C2cosβl+cosℎβl=0

Then we have

−cosβl+cosℎβl−sinβl+sinℎβl

−−sinβl+sinℎβl−cosβl+cosℎβl

=0

Then we get the frequency equation

cosβn l cosℎβn l=−1

The root of this equation βn l represents the natural frequency of the vibration system

w n=βn l2

EI ρAl4

Chapter 2Finite Element Simulation

Finite Element Analysis (FEA) is a relatively important tool for numerical simulation and analysis. It mainly uses the principle of mathematical approximation to carry out numerical simulation of practical problems. In the simulation, the analysis object needs to be divided into The purpose of this method is to miniaturize the grid. This method is used to divide an infinite number of free-form physical objects into a limited number of tiny elements. This approximate simulation method can effectively simulate real-world problems and obtain better results. Make full use of finite element software simulation method can get most of the corresponding performance parameters and image data with complex structure problems, the method not only in the calculation accuracy is excellent, the simulation efficiency is very high, but also in the user interface design more friendly , Post-processing module is more powerful. Finite element analysis over a short period of 40 years, with the rapid development of science and technology, finite element analysis has been widely used, its application involves a wide range of finite element method because of its practical and efficient features will soon be the majority of users Accepted.

In this chapter, Patran finite element analysis software is mainly introduced. Patran finite element analysis software is used to simulate a given cantilever beam. The results of natural frequencies of the first few orders are given and compared with the theoretical calculation results.

2.1Patran software introduction

Patran is the most widely used finite element analysis (FEA) pre / post processing software in the world that provides solid modeling, meshing, analysis setup and post-processing for multiple solvers, including MSC Nastran, Marc, Abaqus , LS-DYNA, ANSYS and Pam-Crash.

Patran provides a rich set of tools to simplify the creation of analytical models for linear, nonlinear, explicit kinematics, heat and other finite element simulation. Patran not only has geometric cleaning tools that enable engineers to easily work with gaps and crevices in CAD, but also provides solid modeling tools to create models