This thesis entitled "Acoustic Analysis of Honeybee Hive" by Patkulkar Ajay Sanjay has been approved for the degree of Master of Technology from IIT Hyderabad. Suryakumar and also the research scholars and staff in Metrology Lab in IIT Hyderabad for their support in finding dimension of the honey bee hive with non-contact type measuring instruments. I would like to thank the bus drivers Imran and Mahindar for removing vacated honey beehive from the unreachable place.
Motivation
Basics of Acoustics
- Acoustic Wave
- Noise
- Acoustic Variables
- Acoustic Properties
Absorption coefficient is related to the absorptive ability of the panel and transmission loss is an ability not to transfer sound through a panel. The transmission loss (T L) is ten times the logarithmic base ten reciprocal of the transmission coefficient τ. The transmission coefficient is the ratio of the transmitted sound power transmitted by the WT to the incidentWIncident sound power.
Problem Statement
But problems arise when we operate at lower frequencies; we need very thick material. According to the mass law [3], the transmission loss (TL) depends on the areal density of the panel and the frequency. It can be observed that the panel stiffness and damping improve the TL at lower frequencies.
Objectives
Design
At panel resonant frequency there is a dip in TL and this is improved by introducing damping to the panel. Coincidence frequency can be calculated by equating bending wavenumber of panel and tracking incident acoustic wavenumber of panel. There is only way we can make the panel rigid by adding stiffeners to a panel instead of increasing the thickness of the material.
Design Parameters
In periodic cell as shown in Figure 1.7, each cell with periodic structure will act as a monopole and radiate sound in all directions. Cell size can be defined as distance between opposite faces of cell as shown in Figure 1.9. It is a thickness of cell wall and membrane that occurs between two arrays as shown in Figure 1.9.
Literature Survey
A slight advantage in transmission loss is seen when using two perpendicular rib patterns with one panel free and another attached to the pattern over the configuration of both panels attached to the rib pattern. In this periodic model, the ribs are modeled as a periodically placed lumped mass attached to panels throughout the structure with periodically spaced springs having torsional stiffness and longitudinal stiffness. It can be understood that periodic structures are one of the possible design options to ensure noise control at low frequencies based on the literature study.
Organization of Thesis
The gain in transmission loss with two ribs in a perpendicular configuration is more than with a panel configuration with single ribs of the same mass. This work can be applied to uniform beams, plates and shells. Energy method analysis can also be used to work on non-uniform periodic structures. According to him, acoustic metamaterials with negative dynamic mass density have been shown to exhibit a fivefold increase in transmission loss (TL) over narrowband (100 Hz) mass law predictions at low frequencies (Hz).
Experimental Setup and Instrumentation
- Tubes
- Microphones
- DAQ System
- Power Amplifier
- Calibrator
This chapter discusses experimental work done for measuring absorption coefficient and transmission loss of honeycomb structure. There are two different size tubes used for different frequency ranges for measuring absorption coefficient and transmission loss of samples. These tubes have a built-in speaker on one end of the tube and provision for mounting the microphones along the tube wall surface.
This microphone fits into the mount on the pipe and measures the acoustic pressure inside the pipe in that position. Gain toggle is used to adjust the sound pressure level inside the tube between 90 and 110 dB. The output of the DAQ system connects to the input power amplifier and its output connects to the speaker.
Experimental Procedure
Sample Preparation
First, four were used to check the reproducibility of the transmission loss and absorption coefficient of the beehive. The dimensions of the first four samples are given in Appendix B, and the remaining sample dimensions are given in Appendix D. In addition to the hexagonal cell shape, round cell samples are also prepared using polypropylene pipes.
In making these samples we used plastic straws, cello tape, sharp cutter and measuring scale. Second phase is to mark the desired length of the tubes and cut them with a sharp cutter. Different samples were prepared to do parametric studies and also typical dimension information given in Table 2.1.
Measurement of Absorption Coefficient
Measurement of Transmission Loss
Test Configurations
Honeybee Hive Samples
Circular Cell Samples
Dimensions of Honeybee Hive
Optical Microscope
Distance between two opposite wall surfaces 4.97 Total length of two unit cells back to back 34.00. This method takes some time and focus, adjustments are required for each reading.
Image Processing
Introduction
Hypotheses
Helmholtz Resonator
Where cis is the speed of sound, S is the cross-sectional area of the neck, is the length of the neck, and V is the volume of the Helmholtz resonator. Consider the beehive as a Helmholtz resonator, the opening as the neck, and the hexagonal tube as the volume of the resonator.
Dipole Phenomenon
Dissipation of Sound Energy
Where k is the addition of mechanical and fluid stiffness, cm is the mechanical damping of the spring, mp is the mass of the top plate. Where cis is the speed of sound in the cylinder, pis is acoustic pressure, is time, ¯β is the normalized access and l is the circumference of the cylinder. In the form of a transfer matrix [17], we can obtain the relationship in upstream and downstream acoustic variables as eq.
P (e−jkz zz+Roejkz zz)dθ (3.9) where w(θ, z) is the displacement of the wall along the radial direction [18] that can be calculated using Eq.
Transmission Loss Calculation
- Mass Law
- Inclusion of Stiffness and Damping in Mass Law
- Narrow Tube Theory
- Total Transmission Loss
Two losses must be considered in the boundary layer effect, namely viscosity loss and thermal conduction loss [19]. It is associated with stored kinetic energy and disappears due to the viscosity of a medium at the boundary. Where is the internal radius of the tube and µ is the viscosity of a medium propagated by sound.
Transmission loss calculated from mass law including stiffness and damping and transmission loss due to effect of the narrow tube can be added to calculate total transmission loss as given in eq.
Modal Analysis of Honeybee Hive
- Structural Modal Analysis of Unit cell
- Structural Modal Analysis of Total Complete Sample
- Acoustic Modal Analysis of Hexagonal Tube
- Coupled Modal Analysis
Lines forming a hexagon are divided into 10 elements and lines along the length of the cell are divided into 30 elements. Model surface is masked using element Shell 63 with actual constant equal to thickness of cell as shown in Figure 4.1. In this analysis, the assumption is that the unit cell is simply supported in the axial direction at the end.
The same unit cell is copied to the location such that the sloped surface of the unit cell matches the opposite sloped surface of the copied unit cell. All the lines forming the hexagon are divided into three elements, and all the remaining lines parallel to the z-axis are connected into ten elements. In the impedance tube, the sample is fixed along its circumference in a tube and the acoustic properties are measured.
So the geometry for the acoustic modal analysis becomes a hexagonal tube with one dimension of the air volume inside the unit cell of a beehive. In the acoustic analysis grid, an element of size equal to one-sixth of the minimum wavelength is required to be formed. So the volume is meshed such that at least six elements will be in all directions.
Structure and acoustic meshing mapped at the boundary surfaces using mapping tool in LMS Virtual.Lab.
Vibro-acoustic Response Analysis
TL Calculation for Cylinder Open at Both Sides
In acoustic analysis, boundary conditions are given in the form of pressure, velocity and impedance [22, 23]. Unit velocity at the inlet face and characteristic impedance (ρc) as the outlet boundary condition apply in the acoustic model. After solving the vibroacoustic response analysis, the pressure at the inlet (pinlet) and outlet (poutlet) is calculated [22].
TL Calculation for Unit Cell of Honeybee Hive
Repeatability
It is similar to sample 4, but one tone is observed to split into two tones forming two peaks and one dip. In all samples the pattern of absorption coefficient is the same with one or two peaks below 1000Hz and after 1000Hz constant coefficient of almost 0.2 to 3500Hz followed by one peak at 4000Hz. One interesting finding about the tonal behavior of the absorption coefficient is that it is at a frequency of honey bee wing.
In sample 3, a maximum transmission loss of 40 dBis was observed, while the other samples show a maximum transmission loss of 35 dB. For all transmission losses sampled below 1000 Hz and ranging from 5 to 20 dBand above 1000 Hz, the average value is 25 dB. From the graph above, it can be concluded that the results are consistent and any measurement process we followed has the optimal error.
Parametric Study using Honeybee Hive Samples
Cell Size
Larger cell samples broaden the effective frequency range and also the peak value of an absorption coefficient. It concludes that as cell size increases, the overall behavior of transmission loss in lower and higher frequency ranges decreased and not significant change in middle frequency range.
Cell Wall Thickness
Number of Layers
The results of the absorption coefficients show dominant tonal behavior in multilayer configuration compared to single samples. Each sample layer is approximated as equivalent spring and mass system, and the layer arrangement is represented as the series model. If the peak of the absorption coefficient is at fa and fb, then this peak comes in layers at ffafb.
It is proven that if peaks are fa andfb for different samples then that peak in layer configuration comes to feq.
Parametric Study using Circular Cell Samples
Cell Size
Cell Wall Thickness
Membrane
TL using Mass Law, Narrow Tube and Experiment
Analytical Results
Helmholtz Resonator
Dipole Phenomenon
Dissipation of Energy
Transmission Loss for With and Without Membrane Sam- plesples
Modal Analysis
Coupling between Structure and Acoustic
Unit Cell
Total Sample
Summary
Future Works
According to literature, bees hear through Johnston's organ (JO) in the base of the antenna as shown in Figure A.1. JO consists of about 300-320 scolopidia connected with about 48 cuticular buttons around the circumference of the pedicel JO neurons are best tuned to detect 250-300 Hz sound. Frings and Little induced vibrations of the combs by loud air noise and used the freezing response of worker bees to estimate the frequency range (300–1000 Hz) to which the bees respond behaviorally.
Michelsen et al (1986b) [25], who used the freezing response to vibrations of the combs of known amplitudes to study the behavioral thresholds. They showed that physiological threshold is lowest at 2.5kHz, while behavioral threshold is lowest at around 500 Hz. Michelsen et al the dance sound signals are emitted as airborne sound by dorsoventral vibrations of the wings where the frequency is 200–300 Hz.
Looking at this literature, we can say that there is a relationship that is not known about the tonal behavior of the absorption coefficient between the frequency range of 300-500 Hz and the wing frequency of honey bees.
Absorption Coefficient
Transmission Loss
Characteristic Impedance
Equivalent Surface Density
Area Moment of Inertia
Standard test method for measuring the transmission of normal incident sound of acoustic materials based on the transmission matrix method.
