Fluid–structure interaction on concentric composite cylinders containing fluids in the annulus
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Dynamic response of two concentric horizontal composite cylinders containing water in the annulus was investigated under impact loading so as to examine the load transfer from the outer cylinder to the inner through a fluid medium. Different water filling levels in the annulus were considered along with different magnitudes of impact loading. Both of the composite cylinders were 254 mm long, had a diameter of 76.2 mm and 88.9 mm, respectively, and were assembled concentrically. Both experimental and numerical studies were conducted to supplement each other. The experimental set-up was designed and constructed. Both cylinders were constrained at both ends, and the water level was varied in the annulus of the two cylinders. The experimental set-up used strain gages at certain locations. For each experiment, the strain data were collected and examined. Then, the fast Fourier transform was applied to the strain data to identify major vibrational frequencies and to examine the effect of the added mass. The numerical study provided additional results which were not measured by the experiment, such as the fluid pressure in the annulus and the dynamic motion of the cylinders. The fluid–structure interaction resulted in significant coupling of the outer and inner composite cylinders.
KeywordsFluid-structure interaction Structural coupling by fluid Composite structure Impact loading
With composite materials advanced in the twentieth century, these materials have been used with growing interest in vehicles, planes, aircrafts and ships. The first vehicle to have a composite part was the Corvette C1 in 1950, and the airplane manufacturer Airbus S.A.S used composites for the rudder of their first plane family A300/A310 or the glass fiber hull in the Eurofighter Typhoon. The aerospace industry has consistently increased the usage percentage of composites because high specific strength and stiffness are important for aircrafts. On the other hand, the marine industry has also increased the usage of composite materials.
One of the unique environmental factors for marine applications is the structural interaction with water, mostly seawater. Water has approximately 800 times higher density than air. Thus, composites used for marine applications encounter greater drag forces than their flying counterparts from the fluid–structure interaction (FSI). This phenomenon gained great attention in 1940 when the Tacoma Narrows Bridge collapsed due to FSI. Airflow around the bridge induced vibrations on the bridge structure that hit resonance and led to failure.
There has been an extensive research on FSI. There are two groups of FSI problems depending on which medium initiates the FSI. In one group, the fluid medium starts the interaction with the structure. A good example of this group is the flow-induced vibration of pipes and pipe bundles (Blevins 1990; Paidoussis 1983; Weaver and Fitzpatrick 1988; Weaver et al. 2000). Another set of examples are vortex-induced vibration (Sarpkaya 2004; Williamson and Govardhan 2004; Bearman 2011; Zhang et al. 2018). The other group is the FSI problems excited by the solid medium, i.e. structures. Sloshing problems in storage tanks subjected to seismic loading belong to this group (Vathi et al. 2017; Matsui 2006). Other FSI studies considered mechanical dynamic loading to structures (Kwon et al. 2010, 2012, 2013, 2016a, b; Kwon 2011; Kwon and Plessas 2014).
While the vast majority of the FSI studies examined steel structures, a much smaller number of papers investigated FSI of polymer composite structures. Some of the studies on composite structures were published in the Refs. (Kwon et al. 2010, 2012, 2013, 2016a, b; Kwon 2011; Perotti et al. 2013; You and Inaba 2013; Kwon and Plessas 2014; Kwon and Bowling 2018; Bowling and Kwon 2018).
Very recently, coupling effects of composite structures via a fluid medium were studied (Kwon and Bowling 2018; Bowling and Kwon 2018]. This research considered two independent structures with water between them. As dynamic loading was applied to one structure, the motion of the structure resulted in pressure wave in water, which finally excited the other structure. Both experimental and numerical studies were conducted. The water level between the structures was also varied from no water to full water incrementally. The study showed the coupling effect depended on many parameters such as the stiffness of the structures, water level, the distance between the structures, and loading type.
Previous research was concentrated on flat composite plates while this research examined the coupling of curved composite structures. In other words, two same-length cylinders with different diameters were arranged concentrically with different water volumes in the annulus of the cylinders. Both experimental and numerical studies were conducted to supplement each other.
The next section describes the experimental set-up that was designed and fabricated for this study. Numerical modeling is then presented followed by discussion of results. Finally, conclusions are provided.
2 Experimental set-up
Material properties of composites made of T700S and ProSetM1002
Impact loading was applied using a pendulum mechanism. The spherical shape of impactor made of steel had a load cell to measure the impact force, and its magnitude was controlled from the drop angle of the pendulum. The drop angle was measured from the vertical downward reference line. In other words, when the pendulum of 1.46 kg is freely hanging, the angle is zero. The drop angle varied such as 20°, 30° and 45°. The impactor was set to apply the force to the front side of the middle section as sketched in Fig. 2.
Throughout the paper, the following notations are used consistently. The mid-section of a cylinder is denoted by “M” while the left section was designated by “L” as far as the location along the longitudinal direction of the cylinder is concerned. Along the circumferential direction, “F” indicates the front (i.e. impact side), “T’ is for the top, “B” is for the bottom, and “P” is for the posterior side. Furthermore, OC is used for the outer cylinder and IC is used for the inner cylinder. As a result, any location of a cylinder is denoted using three symbols such as OC–M–F. The first symbol indicates the cylinder, the second one is for the axial direction and the third one is for the hoop direction. Thus, OC–M–F indicates the front side of the mid-section of the outer cylinder. One exception is IC–M–T–P. Because of the limited accessibility, the strain gage could not be attached to the top and posterior sides, respectively. As a result, one gage was attached between the top and posterior sides. Therefore, T–P suggests the middle location of the top and posterior sides. The water level in the annulus was measured by the percentage ratio of the water to the volume of the annulus. It was designated as “50 W” for the 50% water level. Finally, different drop angles are denoted by “20”, “30” and “45”, respectively.
3 Numerical model
A numerical analysis was conducted to supplement the experimental study qualitatively. Some parameters were not measured from the experiments, and those values could be obtained from the numerical study. Those parameters are transient fluid pressure, displacement, velocity, acceleration of the structures.
Three different water volumes were considered between the cylinders: 0% (no water), 50% and 100% (full) water. When water was filled partially in the annulus, the remaining space was modelled as air. Conforming meshes were generated for both structures and fluid such that nodal points of the fluid and structures could match at their interface boundary surfaces. At the fluid–structure interfaces, equilibrium of loads and deformation compatibility were applied between the two media. Two different analyses for structures and fluid, respectively, were solved in the staggered manner and repeated until the interface conditions were satisfied for each time increment.
4 Results and discussion
4.1 Experimental results
When the drop angle was 20°, the impact force had a gradual change as a function of time without a clear peak force. However, as the drop angle was increased to 45°, the impact force had a very clear peak force. The case of the 30° drop angle was between the two other cases. Comparison of the contact time periods showed that the 20° drop angle had a shorter contact duration while the 45° drop angle had a longer contact duration. However, the difference among the contact durations was not significant. The FFT of the force time-histories showed that the frequency distribution of the impact forces resulting from three different drop angles was more or less similar.
As impactor stroke the OC at the front side of the mid-section, the strain at OC went to compression. On the other hand, the strain at IC showed an early compression followed by a major tension. For the most of time, both cylinders move out of phase at the front side of the mid-section. The OC had a larger peak strain than the IC.
4.2 Numerical results
Structural coupling of two independent, concentric cylindrical shells via an internal fluid was studied numerically and experimentally. The composite cylinders were constructed using the filament winding technique, and the test set-up was designed and fabricated for this study. External impact loading was applied to the center of the outer cylinder. The dynamic response of both cylinders as well as the fluid pressure were either measured or calculated.
The results showed that the coupling effect was significant and dependent on the water amount between the two cylinders. The water level influenced the vibrational frequency of both outer and inner cylinders. As expected, the frequency decreased as the water level increased. However, the degree of reduction was different between the outer and inner cylinder.
While the same impact condition was used for the testing, the water level also affected the impact force time-histories. The peak impact force did not necessarily increase with the increase of the water level. The peak impact force was smallest with the 75% water level and largest with the 100% water level. Furthermore, the hoop strain at OC–M–F was largest for the 50% water level even though the peak impact force was not necessarily the largest at the 50% water level.
The strains at IC–M–F and OC–M–F with 100% water showed the opposite signs in their major responses. In other words, the outside surface of OC had the maximum compressive strain while the outside of IC had the maximum tensile strain. The outer cylinder had an approximately 20% larger strain than the inner cylinder. On the other hand, at the L–P location, the IC showed a larger strain than the OC.
The numerical study showed that the 50% water level resulted in larger displacements with higher oscillatory motions than 0% and 100% water levels at the locations of IC–M–P and OC–M–P. However, the displacement at IC–M–F was greater for the 100% water level, and the displacement at OC–M–F was the largest for the no water case. The inner cylinder had a small acceleration for the 50% water level and a much larger acceleration for the 100% water level, which was also comparable to that of the outer cylinder.
Both experimental and numerical studies demonstrated significant coupling effects of two concentric cylinders. As shown in a previous study (Bowling and Kwon 2018), the coupling effect would vary depending on the stiffness of each cylinder and their radial spacing. Additional studies will be conducted and reported later.
The technical assistance from Chanman Park and Jarema Didoszak is greatly appreciated. In addition, one of the authors (YW Kwon) acknowledges the financial support from the Solid Mechanics Program of the Office of Naval Research. Dr. Yapa Rajapakse is the program manager.
Compliance with ethical standards
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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