Corresponding author: Wei Zhang E-mail: wei.zhang@dlut.edu.cn

Journal of Bionic Engineering 11 (2014) 282–287

Frequency Analysis and Anti-Shock Mechanism of Woodpecker’s Head Structure

Zhaodan Zhu, Chengwei Wu, Wei Zhang

State Key Lab of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, P. R. China

Abstract The mechanical properties of the skull and the anti-shock characteristics of woodpecker’s head were investigated by ex-

periment and numerical simulation. We measured the micro-Young’s modulus of the skull by nano-indentation method and calculated the macro-equivalent Young’s modulus of the skull at different positions using homogenization theory. Based on the Computerized Tomography (CT) images of woodpecker head, we then built complete and symmetric finite element models of woodpecker’s skull and its internal structure and performed modal analysis and stress spectrum analysis. The numerical results show that the application of pre-tension force to the hyoid bone can increase the natural frequency of woodpecker’s head. The first natural frequency under the pre-tension force of 25 N reaches 57 Hz, which is increased by 21.3% from the non-pre-tension state and is more than twice the working frequency of woodpecker (20 Hz – 25 Hz). On the application of impact force to the tip of beak for 0.6 ms, high magnitudes of stress component occur at around 100 Hz and 8,000 Hz, far away from both the working frequencies and the natural frequencies of woodpecker head. The large gaps among the natural, working and stress response frequencies enable the woodpecker to effectively protect its brain from the resonance injury.

Keywords: woodpecker, anti-shock, frequency, modal analysis, stress spectrum Copyright © 2014, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(14)60045-7

1 Introduction

Woodpeckers peck trees at a frequency of 20 Hz – 25 Hz without causing cerebral concussion[1]. Their head, which has the energy-absorption and anti-shock function, has received much attention since 1979. Especially in recent years, numerous experiments and numerical simulations have been carried out to find out the anti-shock mechanism of the woodpecker head.

May et al.[2] recorded the drilling action of an acorn woodpecker using a high speed camera, and found that the woodpecker’s head moved in straight trajectory and reached the maximum speed of 5 m·s−1 – 7 m·s−1 and the deceleration of 600 g – 1500 g within a 0.5 ms – 1 ms impacting duration. On the same impacting duration, the human being’s brain would be injured severely as the upmost tolerance is only 300 g deceleration[3]. Gibson[4] compared the skull structure and impact resistance of woodpeckers with those of human beings. They pro-posed that small sized head, short impact duration and large contact area between brain and skull will be bene-

ficial for alleviating the injury to brain upon shock. Oda et al.[5] set up a stereo lithography head model which is three times larger than the actual head, and measured the strain of the model under 2 N impact force experimen-tally. Then a 2D Finite Element (FE) model was built to prove that little cerebral liquid and the existence of hyoid bone can effectively protect its brain from shock damage. In experiments, Zhou et al.[6] found the hyoid is com-posed of the fiber-typed hierarchical micro-structure, which renders the hyoid high strength and good flexi-bility.

Yoon and Park[7] simplified the head structure as a mass-damper-spring model and made the bio-inspired shock-absorbing equipment consisting of close-packed micro-glasses. The equipment can protect the micro mechanical and electronic device in it from high-g damage. Wang et al.[8] found that the pecking force and velocity are around 8 N and 7.6 m·s−1, respectively. Based on the micro-CT scanning, they set up a FE model and analyzed the pecking impact on the rigid wall. They concluded that most of pecking forces were transferred

Zhu et al.: Frequency Analysis and Anti-Shock Mechanism of Woodpecker’s Head Structure 283

by the longer beak during the pecking. Zhu et al.[9] ob-served that the upper beak is longer than the lower one and interpreted the mechanism of shock absorption in terms of stress wave propagation. The structure of skull facilitates the spreading of the stress wave and the viscosity of biomaterials decreases the stress am-plitude.

The papers published in the literature so far were mainly focused on the stress and strain in the wood-pecker head and little is known on the frequency re-sponse characteristics of the head under shock. Based on the CT scanning technology, in this paper, the wood-pecker head model with hyoid was established. Then its anti-shock characteristic was studied from the aspects of modal analysis and stress spectrum analysis with par-ticular attention to the natural, working and stress spec-trum frequencies of the head.

2 FE model and material property

2.1 FE model Woodpeckers have small head, little amount of

cerebrospinal fluid, big eyeballs, hard beaks and long flexible hyoid bone. The hyoid bone is four times the length of the beak with one end fixing on the right nostril and the other end binding the skull tightly and stretching out from the mouth to reinforce the head[6,10]. The woodpecker investigated here is a female grey-faced one widely living in the Northern China.

The FE model was obtained by the following pro-cedure. The woodpecker was put on a CT scanning de-vice and the inner structure of head can be discerned through the CT images of scattered points. Then Mimics and ProE software were used to establish 3D geometric configurations by integrating the scattered points. Eventually, the FE model of the head was obtained and analyzed using Abaqus software.

2.2 Mechanical property experiment

The woodpecker skull is a small and spheroid-like structure, and the typical tension test cannot measure the local property of the skull. In this paper, we measured the mechanical properties of the bone in different posi-tions of the skull by nano-indentation (Triboindenter, Hysitron TI-950, Hysitron, USA). Nano-indentation method was thought as the primary technique for measuring the mechanical properties of materials on micrometer and nanometer scales[11,12]. Bone samples

Specimen

Skull2 mm

Fig. 1 Positions of the samples on woodpecker’s skull (the grey zone is the brain in the skull).

with the average size of 2.5 mm×2.5 mm were cut from a green woodpecker skull using a sharp operation blade. The marrow of the specimens was washed away with deionized water. The resultant specimens were subse-quently ultrasonicated in deionized water bath for 5 min and then air-dried. As shown in Fig. 1, thirteen speci-mens were obtained along the symmetric line of the skull and fifteen specimens were cut from one side part of the skull.

The total twenty-eight specimens obtained from different positions were placed on a stainless steel plat-form and applied with a trapezoidal load function from 50 μN to 1,250 μN. The average value of Young’s modulus of the whole skull bone is 6.4 GPa ± 2.4 GPa, which is comparable with the average modulus of bo-vine and cervine bones, being about 22 GPa and 14 GPa respectively[13,14]. The coefficient of variation of meas-ured Young’s modulus of each specimen ranges from 16% to 40%. The Young’s modulus of woodpecker skull has large standard deviation, presumably owing to the huge differences in micro-structures of the bone in dif-ferent positions around the skull, as shown in Fig. 2.

Apparently, there are various microstructures in SEM (Scanning Electron Microscope, Quanta 200, FEI, the Netherlands) images, as diverse as plate-like (a, g), layered (e, f), rod-like (d, h, etc.) and porous (j, k, etc.) structures, indicating the non-uniform macro mechanical properties. It is really hard, actually almost impossible, to build up such a multi-scale FE model and get the accurate resolutions. In response to this, we used macro-equivalent modulus instead of the local mi-cro-Young’s modulus measured by nano-indentation to set up a continuum model. In the following section, we will describe how to obtain the macro-equivalent modulus using homogenization method.

Journal of Bionic Engineering (2014) Vol.11 No.2 284

Fig. 2 SEM images of microstructures of the bone around woodpecker skull.

You

ng’s

mod

ulus

(GPa

)

Vol

ume

frac

tion

ratio

(%)

12

10

8

6

4

2

0

Positiona b c d e f g h i j k

1

10

100

Volume fraction ratioMeasured Young’s modulusMacro-equivalent modulus

Fig. 3 Volume fraction ratio of bone, local measured modulus and macro-equivalent modulus around the skull.

Fig. 4 3D complete model of woodpecker head and hyoid. Note that the modulus of the skull and hyoid is non-uniform.

2.3 Homogenization of the bone

Homogenization theory is widely used to calculate the property of spongy and compact bone in biome-chanics because bones usually have many different pe-riodic micro structures[15–18]. Chen et al.[17] set up six

kinds of micro-cell model of trabecular bones and ob-tained near linear relationship between macro-equiva-lent Young’s modulus and the Volume Fraction Ratio (VFR) of the bone. In the structure of woodpecker head, there are several microstructures similar to Chen’s mi-cro-cells. Thus, we adopt the Chen’s method to calculate the macro-equivalent Young’s modulus.

Here we denote macro-equivalent Young’s modulus as EM, VFR of bone as VB, measured local modulus as EL. The relationship among them is ap-proximated to be linear, as expressed in Eq. (1).

.M L BE E V= × (1)

EL was obtained in former experiments of each specimen. We counted the number of pixels of the pores and the bone in the high resolution SEM images and calculated the values of VB in positions of b, c, d, h, i, j and k, as shown in Fig. 2. As the microstructures of skull at posi-tions of a, e, f, and g are denser and ordered, we assumed the VB to be one. In this way, we got the EM of skull. Fig. 3 shows the EL, VB, and EM in different positions of skull. It is interesting that the modulus changes peri-odically along the symmetric line of the skull; the maximum modulus is four times larger than the mini-mum one.

3 Modal analysis

The modal frequency is mainly dependent on the modulus and mass. It has been verified that the bio-logical fluids and soft tissue in the pores of the bone do not affect the bone’s modulus significantly [19–21]. Thus we built a continuum model without tissue fluids, and then assigned the macro-equivalent modulus and the total mass (bone plus tissue fluids) to the skull. The hyoid has non-uniform modulus and the modulus at given positions was assigned to the corresponding value in accordance to Ref. [6]. The other parameters regard-ing material properties can be found in our previous paper[9] and finally the complete model of woodpecker head was set up, as shown in Fig. 4. The top of the skull and the middle of the hyoid have the maximum modulus in the individual part.

The natural frequency is highly dependent on the material properties and boundary conditions. To simu-late the actual conditions, we fixed the woodpecker head at the bottom of neck. As documented, the woodpecker geniohyoid muscle contracts a millisecond before

Zhu et al.: Frequency Analysis and Anti-Shock Mechanism of Woodpecker’s Head Structure 285

Pre-tension force of hyoid (N)0 5 10 15 20 25

1st Natural frequency

100

90

80

70

60

50

1st 2nd 3rd 4th 5th 6th 7th 8thMode

9th 10th

46

48

50

52

54

56

58

25 N20 N15 N10 N5 N0 N

Fig. 5 The first ten natural frequencies of the woodpecker head under 0 N to 25 N pre-tension force on hyoid.

strike[6–8], and the contraction of muscle will produce a pre-tension force on the hyoid. We wonder whether the woodpecker would change the frequency response of head by applying pre-tension force on the hyoid. To examine the effect of pre-tension force on hyoid, we applied different pre-tension forces to the model of the hyoid. As the maximum tension strength and the across-section area of the hyoid were reported to be about 131 MPa and 0.2 mm2 respectively[6], we esti-mated the maximum pull force of the hyoid bone is around 26 N. As such, in the model, we assumed the upper limit of pre-tension force to be 25 N. With one end of the hyoid fixed on the nostril, the other end was pulled with a force of 0 N to 25 N. The first thirty modes of woodpecker head were obtained. It is found that they are the local vibration occurring within the brain due to its low Young’s modulus. The whole vibration frequency of woodpecker head must be higher than the local one. Fig. 5 shows the first ten natural frequencies of wood-pecker head.

Fig. 5 indicates that the first ten natural frequencies of woodpecker head are in the range of 47 Hz – 100 Hz. These frequencies are more than twice the working frequency (20 Hz – 25 Hz) of the woodpecker. Appar-ently, such natural frequencies can protect the wood-pecker head from resonance damage when pecking the trees. To imitate the contract of hyoid bone of a wood-pecker on pecking, we investigated the effect of the application of pre-tension forces on the natural fre-quencies of woodpecker’s head. As illustrated in Fig. 5, the larger the pre-tension force of hyoid, the higher the

natural frequency of the head. Take the first natural fre-quency as an example, when the applied pre-tension is increased from 0 N to 25 N, the natural frequency in-creases from 47 Hz to 57 Hz, see the inset to Fig. 5, an increment of 21.3%. The results imply that the application of pre-tension in hyoid can significantly raise the natural frequency of head to alleviate reso-nance.

4 Stress spectrum analysis

We then studied the stress response of woodpecker head under dynamic impact and the effect of distributed modulus on stress wave. Based on the homogenization theory, we got the macro equivalent Young’s modulus around the skull and built complete model of wood-pecker head. In dynamic analysis, the materials were set as viscoelastic. The mean viscosity of fluid phase within bone is 0.086 Pa·s according to the former research[22] and we assumed the viscosity of bone is proportional to the water content, the less the water, the smaller the viscosity. Bone with higher Young’s modulus usually has less water. As a result, the viscosity changes of skull should demonstrate the opposite trend with respect to the Young’s modulus.

As the reaction force of the wood when wood-pecker pecking is about 8 N, we applied an 8 N force on the tip of woodpecker beak for an impact time of 0.6 ms in computing model[8,9], and then removed the force and kept the head free attenuation for several milliseconds. To save computation time in explicit analysis, we sim-plified the complete FE model to a symmetrical model which contains about 256,000 nodes and 1,192,000 tet-rahedral elements and finally ran the programs on Dawning Cluster Workstation with 48 computation nodes 120 GB memory. After a computation period of 40 days, the FE results were obtained.

In order to study the frequency characteristics of stress wave in brain, we set fifteen monitoring points in brain (shown in Fig. 6) to record the change of the stress at different positions. The maximum stress value is be-low 20 kPa which is consistent with the former research[9]. We take the monitoring point S8 as an ex-ample to analyze the frequency spectrum of stress wave. Fig. 7 plots the stress wave and frequency spectrum of the monitoring point of S8. The analysis lasts for 20 ms with 0.6 ms impact interval and about 19 ms free at-tenuation. From Fig. 7a, we can see that stress wave

Journal of Bionic Engineering (2014) Vol.11 No.2 286

View (b)

Brain

(a) (b) Fig. 6 Monitoring points in brain: (a) Monitoring points on symmetric surface of brain, named after O; (b) monitoring points on section surface of brain, named after S.

Time (s)0.0050.000 0.010 0.015 0.020

−10

0

10

20

Stre

ss (k

Pa)

Mag

nitu

de

Frequency (Hz)101 102 103 104 105

(b)8000 Hz

100 Hz

6

4

2

0

(a)

Fig. 7 Stress wave and frequency spectrum of S8 monitoring point in brain. (a) Stress wave of S8 in impact direction; (b) stress spectrum in frequency domain after FFT.

decreases immediately after the pecking, the value of stress falls near zero at about 10 ms and change mar-ginally until the next pecking. It is for this reason that the figure may be expanded and the stress wave in time domain can be obtained, which is essential for the fre-quency spectrum analysis. Then we performed a Fast Fourier Transform (FFT) to the stress wave and got the stress in frequency domain.

Fig. 7b shows the stress frequency spectrum of monitoring point S8. The vertical coordinate stands for the magnitude of stress component at certain frequencies. It can be seen, there are mainly two high magnitude frequency bands of stress component, one is near 100 Hz, the other is near 8,000 Hz, and the magnitude of the latter is the maximum. At the rest frequencies, the mag-nitudes of stress component are low and most of them are similar. This means the frequencies of high magni-

tude stress component are beyond the natural frequen-cies of the woodpecker head, indicating the brain can be protected from resonance damage effectively.

5 Conclusion

The woodpecker head has the unique ability to protect its brain from impact damage. In this paper, we studied the anti-shock mechanism of the woodpecker head and got the conclusions as follows:

(a) There are several kinds of micro-structure in woodpecker skull, and the Young’s modulus around the skull is non-uniform but changes periodically. The maximum Young’s modulus appears at the top of skull. It is believed that the non-uniform distribution of Young’ modulus in the skull hinders the stress propagation.

(b) The application of pre-tension force to hyoid bone can increase the natural frequency of woodpecker head. The first natural frequencies are between 47 Hz – 57 Hz, more than twice the working frequency, i.e. 20 Hz – 25 Hz, of the woodpecker head. The frequencies of high stress component appear near 100 Hz and 8,000 Hz respectively, far away from the working frequencies and natural frequencies of the head. The large gaps among the natural, working and stress response frequencies enable the woodpecker to effectively protect its brain from the resonance injury.

(c) The inhomogenous mechanical property and special structure of the woodpecker’s skull inspire one to design light engineering structure which not only itself shows a good shock-absorbing function, but also can protect the instruments or the important elements inside the structure, for example, light and high performance helmets, spacecraft, etc. The special design of the woodpecker’s skull also inspires us to improve the g-force tolerance of micromachined devices at high-g and high-frequency mechanical excitations.

Acknowledgment

This work was supported by the National Natural Science Foundation of China (11272080) and the Doc-toral Education Foundation of China Education Ministry (20110041110021).

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