Ultrasound as the acoustic waves

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Introduction

Ultrasound can be defined as the acoustic waves which of high frequencies, which are above human perceptions, is non invasive externally applied and traumatic but is also safe in fact at its intensities and duty cycles which is commonly used now a days in diagnostic medical equipments. The frequencies above 20kHz is to be known as ultrasonic waves. Advantages of these waves includes easily focused, suitable for many application such as medical, aeronautical, shorter wavelength. Different modes are present for wave motion, such as longitudinal, transverse or shear. For medical purpose longitudinal mode of wave propagation is normally used as it can be easily propagated in media, such as solid, liquids and gases. There are various tools used in ultrasound device for transmitting and receiving the acoustic signal. The given tool has the application in gynecology. These tools are made of commercially pure titanium as it is the best biomaterial because of its high biocompatibility, mechanical resistance and resistance to corrosion. The commercially pure titanium posses the elastic modulus of 110GPa and density of 4500kg/m3 which makes advantage compared to other alloys of titanium.

With the dimension of the tool measured, a proper design is made using Solid works which is of almost accurate shape.

Theoretical Consideration

TOOL: Ultrasound tool given was of length of 318mm and 4mm width. The tool was made in Solid Work software of same dimensions and saved as Para solid format (file.x_t) or IGES format (file.igs).

FINITE ELEMENT ANALYSIS: For variety of application there are various element types such as structure, fluid flow, thermal and magnetic analysis. In this analysis we uses Solid 45 because it is used for 3D modeling of solid structures with the ability of model plasticity, swelling, creep, stress stiffening, large deflection and large strain. It is one of the techniques which were developed in structural mechanics, for the solution of numeric of complex problems. In this method, the structural system is designed by a finite set of elements interconnected at points known as nodes. As Solid 45 possess eight nodes (I, J, K, L, M, N, O and P) as shown in Fig.1. From this each node, the three degree of freedom are interpreted into x, y and z directions. Elements may have property such as physical which includes density, thickness, Young's modulus, coefficient of thermal expansion, Poisson's ratio and shear modulus.

Reference: http://www.kxcad.net/ansys/ANSYS/ansyshelp/Hlp_E_SOLID5.html

In practically, usually a finite element analysis consists of three main steps:

1.Pre-processing: “The user builds the model of the structure that is to be analyzed in which the geometry is alienated into a number of discrete sub regions, or “elements," connected at discrete points called “nodes.” Certain of these nodes are having displacements fixed and others will have loads which are prescribed. These models consume more time to set up and commercial codes vie with other to have the most easy to use graphical “pre-processor" to aid in this rather deadly task. Some of these pre-processors can superimpose a mesh on a pre-existing solid work file, so that FEA can be completed easily as division of the computerized design and drafting.

2.Analysis: Input of the finite element code is the dataset which was prepared by the pre-processor, which solves and constructs a linear or nonlinear system of algebraic equations

Mijvj = ti

where v and t are the displacements and external forces applied at the point of nodes. The M matrix formed is dependent on the problem type being known, and this module will summarize the approach for linear elastic stress and truss analyses. One of advantage of FEA is that wide problem types can be addressed with the same code, simply by specifying the suitable types of element from the library.

3.Post processing: In the past days of FEA, it was done by the pore through reams of numbers generated by the listing displacements, code, and stresses at discrete positions within the model. It is simple to miss significant trends and hot spots this way, and existing codes use graphical displays to aid in the results in visual. A characteristic postprocessor show overlay colored contours demonstrating stress levels on the model, which illustrate a full-field image alike to that of photo elastic experimental results.

Tool Analysis:

Various analyses can perform by using ANSYS software such as modal analysis, harmonic analysis and transient analysis so on. In this paper it shows Modal Analysis and Harmonic Analysis.

MODAL ANALYSIS: Typically used to find out the vibration characteristics such as natural frequencies and mode shapes of a structure or a machine part while it is being designed. It can also provide as an opening point for another more detailed, dynamic analysis, such as a harmonic response or dynamic analysis. One of the most basic dynamic analysis types existing in ANSYS is the Modal analyses, can also be more computationally consume more time than a static analysis. A reduced solver, selected master degrees of freedom is used to radically reduce the size of the task and solution time. Many times saving modal solution methods are handy in ANSYS for mode extraction from the reduced solution, such as:

Ø Block Lanczos method - “typically used for large symmetric eigen value problems. This method utilize a light matrix solver”

Ø PCG Lanczos method - “used for very large symmetric eigen value problems (500,000+ DOFs), and is especially useful to acquire a solution for the lowest modes to learn how the model will perform”.

Ø Subspace method - “used for large symmetric eigen value problems, though in most cases the Block Lanczos method is chosen for shorter run times with corresponding accuracy”

Ø Reduced method - “quicker than the subspace technique because it uses condensed system matrices to calculate the solution, but is normally less accurate because the reduced mass matrix is fairly accurate”.

Ø Unsymmetric method - “used for problems with unsymmetric matrices, such as fluid-structure interaction problems.”

Ø Damped method - “used for problems where damping cannot be ignored, such as journal bearing problems”.

Ø QR damped method - “quicker than the damped method, this method uses the reduced modal damped matrix to calculate approximately complex damped frequencies”.

In this Ultrasound tool analysis Block Lanczos method is used to find out the modes.

Given “suitable” primary conditions, the structure will vibrate at

  • One of its natural frequencies.
  • The shape of the vibration will be a scalar multiple of a mode shape.

Given “arbitrary” initial conditions, the resulting vibration will be a superposition of mode shapes.

Harmonic Analysis:

Solves the “time-dependent” motion equations for linear structures go through steady-state vibration. To this end all loads and displacements are held to vary sinusoidally at the frequency known. Analyses can build plots of amplitudes of displacement at known points in structure as a function of forcing frequency.

ANSYS provides 3 methods for performing a harmonic analysis. These 3 methods are the Full,Reduced and Modal Superposition methods.

 The Reduced Method: “According to this method it reduces the system matrices to only regard as the Degrees of Freedom. Because of the reduced dimension of the matrices, the calculations are much faster. But, this method handles only linear problems such as cantilever case”.

 The Full Method: “This is one of the easiest methods to use. This allows all types of non-linearities; it is on the other hand very CPU intensive to go this way as full system matrices are used”.

The Mode Superposition Method: “This is one of the easiest method used, in this it needs an initial modal analysis, as factored mode shapes are added to calculate the response of the structure”.

In this tool analysis The Full method is used for conducting harmonic analysis.

Finite Element Procedure

Modal Analysis:

1. Initially the CAD file of the given tool of exact dimension is made using Solid Work Software and save the file as IGES.

2.ANSYS is started by clicking on “Interactive”

Ø Choose running directory.

Ø Choose the file name and import the file name. IGES or filename. x_t.

Defining The Material Properties

Ø As it is solid material chooses STRUCTURAL.

Defining Element Types

Pre-processor> Element Type> Add/Edit/Delete>

Add> Structural-Solid45- Brick 8 node> OK

Close Element Types window.

Material Properties

Pre-processor>Material Props> Material Models> Structural> click on

“Linear”> “Elastic”> “Isotropic”>

Input value EX=110e9 (Young's modulus), PRX= 0.33(poison ratio)> OK

Continue from same spot: Click on the “Density”> Input DENS=4500> OK

Meshing The Model

Pre-processor> Meshing> Mesh tool> Smart Size - Global - Size 5>

Choose either edge length of an element or number of divisions (only one is applied).

In this analysis Element edge length=0.5> OK

Close Size Controls window

Pre-processor>Meshing - Mesh> Lines> pick all lines> OK

Close the mesh window.

Meshed tool look as this

Saving the work:

Menu> File> Save as File.db

Now the file will be saved as db format in the definite working directory.

Solutions

Defining the analysis type

Main Menu> Solution> New Analysis> Modal Analysis> OK

Main Menu> Solution> Analysis Options> Block Lanczos method, Number of modes “50” (how many we want to calculate), OK> Starting frequency- 10 kHz> Ending frequency-50kHz> OK.

Performing the analysis

Main Menu> Solution> Solve - Current LS> OK.

Warning was shown about zero thickness of the elements, but this does not affect the tool analysis. So click on Yes.

Click Close

Close Report window.

Reviewing The Results

Tabular

Main Menu> General Post-processor> Results Summary>

It can be seen that the window with the frequencies of structural modes in Hz.

Graphical

Main Menu> General Post-processor> Read Results (First Set)> Plot Results> Deformed Shape> Def+undeformed> OK.

For next mode: Read Results (Next Set)> Plot Results> Deformed Shape> Def+undeformed> OK.

Animation

In order to animate the graphical:

Main menu> plot controls> Animate> Mode shape> time delay 0.1.

Hence the animated mode shapes of frequencies ranging from 10 kHz - 50 kHz are obtained. From this in order to show the graphical output in the report click print screen on the keyboard, then edit the picture using imaging software's.

Harmonic Analysis:

The easiest method is to continue current analysis this way:

Main Menu> Solution> Define Loads Apply> Structural > Displacements- 10e-6> On Nodes> Pick nodes where defined > OK> mark “ROTZ” and unmark “ALL DOF”> OK

Load step option> Time frequency (10 kHz- 50 kHz)> OK.

It is added to the existing system.

Close that window.

Now solve the current system: Solution> Solve-> Current LS> OK

Close that window.

Step 5 above is repeated to view the result.

As performing harmonic analysis the steady- state behaviour of the tool subject to cyclic load at the end can be predicted.

Results

Modal Analysis

From the Modal Analysis it can be noted that natural frequency of the designed tool is found to be 23.447 kHz also there possess 43 mode shapes around the frequency range of 10- 50 kHz.

Out of 43 modes shapes for the tool at the given frequency range, 4 modes shapes figures are also shown below at various frequency range.

To predict the steady- state behavior of the tool subject to cyclic load at the end, it has given cyclic displacement load of 10µm is produced by the transducer.

Discussion

Modal Analysis

Ultrasound tool analysis by using Modal Analysis shown that the natural frequency is 23.447kHz of which is nearer to the working frequency 25 kHz.

Harmonic Analysis

When the tool was subjected to cyclic load at the end it is able to know the steady-state behavior of the tool which was found that if the natural frequency is not 25 kHz as mentioned, the harmonic analysis result will show a deformation.

Conclusions

In order to perform the tool analysis using ANSYS, the CAD tool made using solid work must be properly designed such that only it can be meshed. From the Modal analysis it can be noted that the tool which was made using solid works software is a good tool which will not break at high frequency and also shows the natural frequency near to the working frequency, When Harmonic analysis was done on the tool when subjected to cyclic load at the end it is seen that if the frequency is not 25 kHz it will show change in shape, it can be seen that the needle shape is not straight or symmetrical in width.

Reference

1. Moaveni, S., Finite Element Analysis, Theory and application with ANSYS, Prentice Hall, page 1-6.

2. David Roylance, Finite Element Analysis, 2001

3. Tim Langlais, ANSYS Short Course, 1999.

4. http://en.wikipedia.org/wiki/Finite_element_method_in_structural_mechanics

5. http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/num/widas/history.html

6. http://courses.cit.cornell.edu/ansys/

7. http://www.ansys.com/solutions/solid-mechanics-modal.asp

8. http://en.wikipedia.org/wiki/Harmonic_analysis

9. http://www3.sympatico.ca/peter_budgell/home.html

10. http://www.kxcad.net/ansys/ANSYS/ansyshelp/Hlp_E_SOLID5.html

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