1) The document analyzes the dynamic response of a U-shaped pipe with a viscoelastic damping layer to reduce vibration. 2) Finite element modeling is used to simulate the pipe with damping layer, accounting for cross-section deformation. 3) Experimental tests validate that the damping layer effectively reduces pipe vibration response by up to 79%, with positioning of the layer more influential than width.

1. DYNAMIC RESPONSE RESEARCH OF U SHAPED PIPE
WITH VISCOELASTIC DAMPING LAYER
By:
GUO, YAJUAN
MENG, GUANG;
LI, HONGGUANG
International Journal of Modern Physics B
Vol. 25 Issue 32
12/30/2011
Presented by-
Akshay Kumar Varakala

2. Synopsis
 U shaped pipe is a common component in many engineering applications such
as different cooling and heating system.
 In air conditioner system, pipe vibration is often the main source of system
vibration and noise.In the meantime, fierce vibration can induce the fracture
failure of the pipe system. So attenuating pipe vibration is very important to
reduce the system’s destruction and increase reliability.
 For reducing the pipe vibration, there are two kinds of measures-
o Revising the modal frequencies range to avoid the driving frequency.
o Increasing Structure Damping
 In this paper, a damping attenuation measure of U shaped pipe was proposed
and analyzed through encircling the viscoelastic damping layer on the pipe

3. Introduction
 In recent years, viscoelastic damping material is widely used to
reduce vibration in industrial structure, such as automotive,
commercial airplane, appliance industry and sports industry,
etc.
 In the damping analysis of structures with viscoelastic material,
there are two important problems.
o The material property is frequency dependent and the nonlinear
eigen problem is created for dynamic analysis
o It is difficult to solve the dynamic response directly using
commercial finite element (FE) software.
 In this paper, an easy and effective method based on the FE
software was developed to calculate the dynamic response
characteristics of structure with viscoelastic material.

4. Finite Element Modeling
 Cross-section deformation
o In the bending of circular tubes, the flattening of the cross-section occurs.
o Considering the deformation of the tube in FE modeling can increase the
accuracy of analysis.
o The thickness after bending is shown as follows
o For the bending cross-section, the mould will constrain the change of long
axis of oval. And the short axis will become short. It can be described by the
following expression

5. Finite Element Modeling(Contd..)
 Damping in terms of strain energy quantities
ηr-𝑟 𝑡ℎmodal loss factor ηi-loss factor of the 𝑖 𝑡ℎ element
 Then, the rth modal loss factor for U shaped pipe with partly damping layer is
represented by
 The loss factor of copper is very small in order that it is usually neglected in
calculation.

6.  For obtaining the displacement response of the structure
in some points, mode superposition was proposed in this
paper based on the frequency results.
Where, ωr-rth modal frequency, ξr-rth loss factor of the
structure,
ωr, ξr are obtain from the iterative results.
φ is modal mode, Q(t) is the load vector applied on the
pipe.
Finite Element Modeling(Contd..)

7. Experimental Researches
 Material properties test
o The test was first carried out in a Dynamic Mechanical Thermal Analyzer (DMTA),a
mechanical spectrometer used to study the viscoelastic properties of materials. The
frequency dependency properties of storage modulus, loss modulus and loss factor can be
obtained directly
o The sample was fixed on the temperature-enclosure with a special tension test clamp, as
shown in Fig. 3. In order to minimize the effect of clamp, the length of the sample was
bigger than 6 times of its width.

8. Readings
 For frequency sweep,firstly, the temperature was adjusted to the expected
value in the temp-enclosure. Then, the frequency was changed from 1 Hz to
200 Hz exponentially

9. Experimental Researches(Contd..)
 Response test-The interest frequency range is 0∼200 Hz and the
sweep frequency time is 8 s. The frequency resolution is 0.125 Hz and
bandwidth is 512 Hz, and the measures are composed by a total of
4096 points using Rectangle windows. All the experiments were
conducted under the room temperature (around 20◦C).
 The damping layer is circled around the pipe as shown in Fig. 5. The
vibration energy is dissipated when the damping material has
stretched or sheared distortion. The position and width of the
damping layer are the main parameters which affect the vibration
attenuation of the structure.
 So in this paper, three damping layer configurations were arranged as
shown in Table 1.

10. Result analysis
o It can be seen that the response amplitude drops greatly
with pitched damping layer. And the maximum decrement
is 79.08% compared to the response of the pipe without
damping layer.
o Another conclusion is that the position of the damping
layer has an obvious effect. When the position of the
damping layers is changed, as shown in the case of Damp-2
and Damp-1, the vibration attenuation ratios increase from
49.87% to 75.99%. The attenuation effect is very obvious.
o However, the width of the damping layer has little
influence to vibration reduction. When the width of the
damping layer changed from 50 mm to 100 mm, the
attenuation ratio increases only 3.09%.
o The test results validated the attenuation effect of the
viscoelastic damping layer

11. Result analysis

12. Conclusion
 From the experimental results of U shaped pipe circled viscoelastic damping
layer, it can be seen that the damping layer can reduce vibration effectively.
And the position of the damping layer affects the response results
prominently, while the size of the damping layer has little influence.

13. Advantage
 This method can be performed easily using FE software and a simple program.
Therefore it has the potential capability to deal with actual structures with a
more complex geometry or boundary conditions
Disadvantages
 The frequency dependency property of viscoelastic material leads to the
dynamic analysis of compound structures which are complex and costly.

14. Future Prospects
 The procedure proposed in this paper can be extended to analyze other more
complex structures with viscoelastic material.