vibration and acoustic properties of honeycomb sandwich structures subject to variable incident

102 Pages·2017·4.77 MB·English

Clemson University
TigerPrints
All Theses Theses
5-2013
VIBRATION AND ACOUSTIC PROPERTIES
OF HONEYCOMB SANDWICH
STRUCTURES SUBJECT TO VARIABLE
INCIDENT PLANE-WAVE ANGLE PRESSURE
LOADS
Jiaxue Yan
Clemson University, [email protected]
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Recommended Citation
Yan, Jiaxue, "VIBRATION AND ACOUSTIC PROPERTIES OF HONEYCOMB SANDWICH STRUCTURES SUBJECT TO
VARIABLE INCIDENT PLANE-WAVE ANGLE PRESSURE LOADS" (2013).All Theses. 1668.
https://tigerprints.clemson.edu/all_theses/1668
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VIBRATION AND ACOUSTIC PROPERTIES OF HONEYCOMB SANDWICH
STRUCTURES SUBJECT TO VARIABLE INCIDENT PLANE-WAVE ANGLE
PRESSURE LOADS

A Thesis
Presented to
the Graduate School of
Clemson University

In Partial Fulfillment
of the Requirements for the Degree
Master of Science
Mechanical Engineering

by
Jiaxue Yan
May 2013

Accepted by:
Dr. Lonny Thompson, Committee Chair
Dr. Gang Li
Dr. Mohammed Daqaq

i
ABSTRACT
Honeycomb structures are widely used in many areas for their material
characteristics such as high strength-to-weight ratio, stiffness-to-weight, sound
transmission, and other properties. Honeycomb structures are generally constructed
from periodically spaced tessellations of unit cells. It can be shown that the effective
stiffness and mass properties of honeycomb are controlled by the local geometry and
wall thickness of the particular unit cells used. Of particular interest are regular
hexagonal (6-sided) honeycomb unit cell geometries which exhibit positive effective
Poisson’s ratio, and modified 6-sided auxetic honeycomb unit cells with Poisson’s
ratio which is effectively negative; a property not found in natural materials. One
important honeycomb meta-structure is sandwich composites designed with a
honeycomb core bonded between two panel layers. By changing the geometry of the
repetitive unit cell, and overall depth and material properties of the honeycomb core,
sandwich panels with different vibration and acoustic properties can be designed to
shift resonant frequencies and improve intensity and Sound Transmission Loss (STL).
In the present work, a honeycomb finite element model based on beam
elements is programmed in MATLAB and verified with the commercial finite element
software ABAQUS for frequency extraction and direct frequency response analysis.
The MATLAB program was used to study the vibration and acoustic properties of
different kinds of honeycomb sandwich panels undergoing in-plane loading with
different incident pressure wave angles and frequency. Results for the root mean
square intensity I based on normal velocity on the transmitted side of the panel
RMS
measure vibration magnitude are reported for frequencies between 1 and 1000 Hz.
The relationship between the sound transmission loss computed with ABAQUS and
ii
the inverse of the intensity of surface velocity is established. In the present work it is
demonstrated that the general trend between the STL pressure response and the
inverted intensity metric have similar response characteristics over both the stiffness
frequency region and the resonance frequency region, showing that an increase in
I corresponds to a decrease in STL. The ABAQUS model was used to verify the
RMS
MATLAB program for natural frequencies and mode shapes, and to compute the STL
on the top surface of the honeycomb sandwich structure. Resonant peaks in the
frequency response of intensity and STL are identified with natural frequencies and
mode shapes of the honeycomb sandwich structure.
A unique feature of this research is the ability to apply the time-harmonic
acoustic pressure as a load on the transmitting surface of the honeycomb sandwich
panel with variable incident angle ranging between 0to 90. When the incident angle
is nonzero, the pressure load is complex valued, with sinusoidal distribution, and
frequency dependent. The finite element implementation of the complex-valued
variable incident pressure distribution is programmed in MATLAB to give complete
control of the angle, frequency and distribution. Commercial finite element software
such as ABAQUS has limited ability to directly apply frequency dependent and
distributed real and imaginary pressure distributions in a direct steady state frequency
analysis over a large number of frequency evaluations.
In the present work, I results for a family of honeycomb sandwich panels
RMS
with systematic increment in internal cell wall angle, subject to incremental changes
in incident angle pressure loads are studied and compared. Results show that for
honeycomb sandwich panels with positive internal cell wall angle, on average,
intensity for the nonzero incident angles is higher than the 0normal incident angle.
iii
For the honeycomb sandwich panels with positive internal angle, the intensity
consistently increases with larger nonzero incident angles. Furthermore, under the
same incident angle pressure load, the intensity of honeycomb panel with positive
internal angle is consistently larger than honeycomb panels with negative internal
angles.

iv
DEDICATION

This thesis work is dedicated to my mother, Yongping Zhong, for her love.

v
ACKNOWLEDGMENTS

First and foremost, I would like to thank my advisor Dr. Lonny Thompson.
Without his patient instruction and help, I cannot finish my thesis. I have learnt a lot
from him in both his course and during the research. Besides, I also sincerely
appreciate my committee members, Dr. Mohammed Daqaq and Dr. Gang Li, for their
time spending on my thesis and their suggestions. In the end, I would like to thank all
my friends who always give me support and encouragement.

vi
TABLE OF CONTENTS
Page

TITLE PAGE .................................................................................................................... i

ABSTRACT ..................................................................................................................... ii

DEDICATION ................................................................................................................. v

ACKNOWLEDGMENTS .............................................................................................. vi

LIST OF TABLES ........................................................................................................... x

LIST OF FIGURES ........................................................................................................ xi

CHAPTER

1. INTRODUCTION ......................................................................................... 1
1.1 Honeycomb Structure ........................................................................... 1
1.2 Acoustic Finite Element Model ............................................................ 2
1.3 Previous Work ....................................................................................... 3
1.4 Thesis Objectives .................................................................................. 6
1.5 Thesis Outline ....................................................................................... 7

2. GEOMETRIC AND MATERIAL PROPERTIES OF HONEYCOMB
SANDWICH PANELS ...................................................................... 11
2.1 Geometric Properties of Honeycomb Sandwich Panels ..................... 11
2.2 Effective Properties of Honeycomb Sandwich Panels ........................ 14

3. ABAQUS FINITE ELEMENT MODEL ..................................................... 18
3.1 Creating Parts ...................................................................................... 19
3.1.1 Honeycomb Sandwich Panel .................................................... 19
3.1.2 Air Domain Part ....................................................................... 20
3.2 Finite Element Mesh ........................................................................... 21
3.3 Boundary Conditions and Loads ......................................................... 22
3.4 Constraints and Interactions ................................................................ 22
3.5 Natural Frequency Extraction Procedure ............................................ 23
3.6 Steady State Dynamics, Direct Procedure .......................................... 24
3.7 Postprocessing..................................................................................... 25

vii
Table of Contents (Continued)

Page

4. MATLAB FINITE ELEMENT MODEL ..................................................... 26
4.1 Generating the Honeycomb Sandwich Panels .................................... 26
4.2 Mesh and Constraint ........................................................................... 27
4.3 Input Parameters ................................................................................. 27

5. NATURAL FREQUENCY ANALYSIS FOR HONEYCOMB
SANDWICH PANELS ...................................................................... 29
5.1 Comparison of Natural Frequencies in MATLAB
and ABAQUS .................................................................................... 29
5.2 Natural Frequencies for Different Honeycomb
Beam Structures ................................................................................. 31
5.3 Mode Shape ........................................................................................ 33

6. SANDWICH PANELS SUBJECT TO PLANE WAVE OF VARIOUS
INCIDENT ANGLES ........................................................................ 35
6.1 Pressure Load at Various Incident Angles .......................................... 36
6.2 Element Nodal Forces and Moments .................................................. 38
6.3 MATLAB Code for Element Force Vector from
Pressure Loading ................................................................................ 41
6.4 Pressure Load Distribution ................................................................. 42
6.5 Direct Steady State Frequency Response ............................................ 46
6.6 Steady State Beam Shapes at Natural Frequencies ............................. 52
6.7 Intensity of Root Mean Square Velocity ............................................. 58
6.8 Average Acoustic Response of Honeycomb
Sandwich Beam ................................................................................. 68
6.9 Areas under I curves ................................................................... 70
RMS

7. COMPARING VIBRATION AND ACOUSTIC CHARACTERISTICS OF
SANDWICH PANELS ...................................................................... 73
7.1 Comparison of I in MATLAB and ABAQUS ............................ 74
RMS
7.2 Comparison of I Based on Discrete and
RMS
Integral Forms. ................................................................................... 76
7.3 Comparison between the I and STL ........................................... 79
RMS

8. CONCLUSION AND FUTURE WORK ..................................................... 82
8.1 Conclusions ......................................................................................... 82
8.2 Future Work ........................................................................................ 84
viii
Table of Contents (Continued)

Page

REFERENCES ...................................................................................................... 85

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