Using a design based on fractal geometry, a theoretical model of a piezoelectric ultrasound **transducer** was produced and analysed in this paper. This showed that the fractal design has certain advantages over the current technology. The critical innovation was to base the design on the complement of the Sierpinski gasket as this introduces a range of length scales within the resonating structure. Using a **finite** **element** methodology, the weighted graph counterpart of this fractal (denoted SG) was used to support the electrical and mechanical fields. New basis functions were derived; however, since this is the first **finite** **element** **analysis** on this graph. These are resonating devices and since the standard design typically has a single length scale, while the fractal design has multiple length scales, it is unsurprising that this results in a much richer set of resonance frequencies; it is well known in fact that musical instruments and naturally occurring auditory systems rely precisely on this very principle. The **finite** **element** formulation discretized the problem to produce a matrix equation and, benefitting from its block diagonal structure, the inversion of this matrix was achieved using a renormalization approach. The symmetry of the structure is embedded in these renormalization equations and this enabled us to describe the dynamics of the structure via only two coupled recursion relationships. These pivotal Green’s functions were then used in expressions for the transmission and reception sensitivities of the device. From a practical perspective, it will only be possible to manufacture these devices for a small number of fractal generation levels. Hence, the results produced in this paper focus on low-generation levels (pre-fractals) but it is worth emphasizing that the dynamics of the true fractal can also be examined by studying the steady states of the recursion relationships. As anticipated, the model predicts that, in comparison to the standard **transducer**

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orientation of the unidirectional layers were determined from the micrograph of the laminate surface. However, using this method it is not possible to tell if the 45° fibres are in plus or minus direction, so all are assumed in the plus direction. The sample was modelled immersed in a water load and a dummy material was introduced to represent the **transducer**. This would also provide the source for the pressure load to apply the drive function into the model. The resulting CFRP laminate geometry created in PZFlex can be seen in Figure 5 where each colour represents a different ply orientation.

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bar whose only degree of freedom was in the plane of the lattice. This model did not therefore allow for other types of motion of the lattice, or directions of the electric field, and was essentially a local de- scription of the dynamics of each edge that when joined to the other edges to form the lattice, led to the global dynamics of the device. This paper will derive the governing equations from the general tensor equations for the whole lattice so that the three dimensional world that the device is embedded within is accounted for. This framework allows different parameterisations to be deployed and in this paper we will examine the case where the displacement acts out of the plane of the lattice whereas the electric field operates within the plane of the lattice. This will allow us to consider the transverse modes of the device. In addition, this paper will be the first to use a **finite** **element** methodology as the basis for the renormalisation approach and it is precisely this global approach to modelling the device that permits this type of **analysis**. This renormalisation approach will be used in this paper to derive expressions for the key operational characteristics of the device. Of course, from a manufacturing respective only the pre-fractal (**finite** fractal generation level) gaskets can be feasibly constructed and so an investigation into the dependency of the device characteristics at a low fractal generation level is undertaken here. The fractal that will be used in this article to simulate this self-similar **transducer** is the Sierpinski gasket ( Falconer & Hu (2001)). Such an **ultrasonic** **transducer** would start with an equilateral triangle of piezo- electric crystal, and the next generation (n = 1) would be obtained by replacing this by three copies of itself, each of which being half the size of the original triangle. This process is then repeated for several generations (see Figure 1). The Sierpinski gasket lattice of degree 3, SG (n) (3), is the lattice counterpart of the Sierpinski gasket ( Schwalm (1988)) (see Figure 2). This lattice is constructed by a process which starts from the Sierpinski gasket of order n = 1 (which consists of three piezoelectric triangles), assigns a vertex to the centre of each of these triangles and, by connecting these vertices together with edges, the lattice at generation level n = 1 (SG (1) (3)) is constructed. The lattice has side length L units which remains constant as the generation level n increases. Therefore, as n increases, the length of the edge between adjacent vertices tends to zero and in this limit the lattice will perfectly match the space filling properties of the original Sierpinski gasket ( Mulholland (2008)). The total number of vertices is N = 3 n and h (n) = L/(2 n − 1) is the edge length of the fractal lattice. The vertex degree is 3 apart from the

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The model was constructed to perform FMC inspections with an array **transducer** directly coupled over the weld with stainless steel either side. To illustrate the feasibility of using FEA simulations to investigate numerous parameters quickly, simulations were done for varying frequencies and array aperture length. It was demonstrated in [10] that the through transmission spectra of the weld structure is highly frequency dependent and above 1.5 MHz the SNR was inadequate. Therefore, selected frequencies to investigate were identified as 0.5, 1.0 and 1.5MHz - each simulated array layout satisfied the half wavelength (λ/2) spatial sampling criterion in order to prevent grating lobes. The number of elements was then varied to produce arrays equal in length to: half weld width; weld width; and one and a half times weld width. The arrays were positioned at the center of the weld and the width of the weld at the surface was ~90mm. Table 6 contains the complete list of simulations run and each of their respective array parameters. The 9 simulations were then repeated to include a side drilled hole to act as a defect. The side drilled hole was positioned centrally in the weld and had a diameter of 1mm.

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Gas flow measurement has always been a key requirement in all industrial operations including natural gas distribution, compressed air systems, air conditioning, and process control. **Ultrasonic** flowmeters are one of the fast-growing technologies in these fields [1,2]. In **ultrasonic** flowmeters, acoustic waves would be used to determine the velocity, and consequently the flow rate of a fluid flowing in a pipe. Since the first multipath gas **ultrasonic** meters were introduced in the early 1990’s, they have now become the preferred technology for most custody transfer and non-custody transfer installations on all 5 continents. These flowmeters feature high accuracy and reproducibility. Moreover, containing no moving parts, it does not create extra pressure drop and allows bi-direction measurement. Finally, this system can be conveniently maintained on-line without interrupting the fluid transport. Thus, the **ultrasonic** flowmeters have been more and more widely applied in the general field of process monitoring, measurement and control [3-5].

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Very recently, a dual-frequency approach based on the “pulse high, listen low” scheme previously described by Sheeran et al. 22 has been validated for isolating and extract- ing the droplet vaporization events. Using this approach, droplets are activated at high frequency (8 MHz) while the vaporization signal is detected by a second **transducer** cen- tered at low frequency (1 MHz). This technique, requiring the use of two mechanically scanned confocal piston trans- ducers, has been adapted to develop an imaging system for capturing droplet vaporization events and generating high-sensitivity, high-contrast images. 24 The large difference between the activation pulse frequency and the listening fre- quency results in a weak response from microbubbles and tissue. In vitro results showed that ADV imaging was capa- ble of generating a contrast-to-tissue ratio (>18 dB), as good as standard contrast agent imaging techniques. 24 Imaging ADV at low frequency has several advantages. First, the penetration depth is increased because of the weak attenua- tion of low-frequency droplet content in tissue. Additionally, the absence of non-linear propagation in tissue at the listen- ing frequency facilitates the detection of the vaporization signal. However, one drawback remains the poor resolution induced by the newly generated bubble ringing. Another major limitation lies in the requirement for two transducers to transmit and receive at separate frequencies.

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K.B.Waghulde and Dr. Bimlesh Kumar,[2012] have studied, the locations of actuators and sensors over a structure determine the effectiveness of the controller in controlling vibrations. If we need to control a particular vibration mode, we have to place actuators and sensors in locations with high control. In many cases of vibration control, low frequency modes are considered to be important. Hence, we only need to consider a certain number of modes in the placement of actuators and sensors. We extended the methodology for finding optimal placement of general actuators and sensors over a flexible structure. For vibration **analysis** ANSYS software is used. Experimentation is done for control vibration and to find optimal position of piezoelectric actuator/sensor over a thin plate. To obtain frequency response from PZT actuators and sensors, Spectra plus software is used.

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In the field of dentistry, **finite** **element** **analysis** was used to stimulate the process of bone remodeling, to examine the internal pressure acting on the teeth, different type of dental material and to optimize the shape of the recovery. Borcic and Braut (2012) conducted an **analysis** of mouthguard using **finite** **element** (FE) technique to determine the behavior of air flow as shown in Figure-3. However, due to complexity of subject structure, conventional methods and morphology due to mechanical and chemical properties the results were not accurate and precise. This is because; the conventional methods like photo elasticity and strain gauge method are not reliable to predict the pressure distribution in the subject. The use of traditional method such as load-to-failure bench-top testing unable to create a mechanism of failure seen clinically. Thompson and his co-workers (2011) have summarized that the use of method **finite** **element** **analysis** (FEA) is becoming more popular because of its ability to accurately evaluating the biomechanical behavior of the complex artificial material structures are irregular and heterogeneous.

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specified size map using advancing - front combined method for defining the field points and connected using optimization technique. Leonid V.Tasap et al., (2002) proposed a new general framework for application of Nonlinear FEM to non rigid motion **analysis**. Patra et al., (2003) proposed adaptive **finite** **element** methods in which both grid size 'h' and local polynomial 'p' are dynamically altered, are very effective discretization schemes for the numerical solution of a large class of partial differential equations. Phillip Frauenfelder, Christoph Schwab and Radu Alexander Todor (2004) described a deterministic **finite** **element** (FE) solution algorithm for a stochastic elliptic boundary value problems whose coefficients are assumed to be random fields with **finite** second moments and known piece wise smooth two point spatial correlation coefficient. J.J. del Coz Diaz (2006) determined the distribution of strains and stresses throughout a sheet cover known as "umbrella" due to the dead and alive loads taking into account large displacements by FEM. Irfan Anjum et al. (2006) carried out Numerical **Analysis** of heat transfer by convection, conduction and radiation in a saturated porous medium enclosed in a square cavity using a thermal non- equilibrium model. The governing Partial Differential Equation were non-dimensionalised and solved numerically using FEM. Ladislav Musil (2006) dealt with numerical simulation of the dynamic phenomena in an electromagnetic feeder of molten zinc. The mathematical model consists of one Partial Differential Equation (PDE) describing distribution of magnetic fields for various levels of zinc and a system of nonlinear ordinary differential equation.

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In 1933 the concept of levitation by acoustic radiation pressure was first proposed by [8], [9] derived the theoretical background in 1934. A typical acoustic levitator generates an acoustic standing wave between a **transducer** and a reflector separated by a multiple integer number of half wavelengths of the acoustic wave. The small samples are levitated against gravity by the pressure forces and tend towards a stable equilibrium position close to the acoustic nodal points. Acoustic levitation in combination with analytical applications like Raman spectroscopy is a very powerful technique in analytical chemistry or process engineering and has been used in a lot of applications. This combination was first introduced by [10], [11] to observe the solidification process of acoustically levitated solutions. Acoustic levitation has been used by [12] for simplifying the handling of micro samples in laser spectroscopy. By monitoring the malaria pigment hemozoin in vital blood cells and online monitoring of environmentally stressed living cells [13], [14] applied this technique into the field of biospectroscopy. Spectroscopy in combination with acoustic levitation has been used for airborne chemistry and protein crystallization by [2], [15]. The backscattered Raman signal was used by [16] for the chemical **analysis** of levitated drops. [17] showed theoretically and experimentally the possibility of Raman scattering on deformed acoustically levitated droplets by a scattering angle of 90°. A method of calculation of the acoustic radiation pressure based on the boundary **element** method was presented by [18] and the influence of the acoustic field on the external flow is described in [19].

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In addition, the finite element analysis model is in good agreement with the impact test results, therefore this finite element model and the analysis procedure will be [r]

Volume 3, Issue 5, May – 2018 International Journal of Innovative Science and Research Technology ISSN No 2456 2165 IJISRT18MY317 www ijisrt com 399 A Review on Finite Element Analysis of Leaf Spring[.]

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The mathematical model used in this article is a transmission line (1D in space) model introduced by Walker & Mulholland (2010) and discussed further by Walker & Mulholland (2016). The model outputs the transmission voltage response (TVR) and the reception force response (RFR) of the **ultrasonic** **transducer**, from which the bandwidths are calculated and compared against the standard **transducer** de- sign. As mentioned, standard electrostatic transducers operate by electrically ex- citing a stretch mylar membrane over a conducting backplate. The novel design considered in this approach uses acoustic amplifying conduits emanating from an air-filled cavity in the backplate. A simplified exploded sketch of the design is shown in Figure 2.

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A method and apparatus for electronically driving an **ultrasonic** acoustic **transducer**. The **transducer** is operable in two modes; in a first mode, the lock-in frequency of the **transducer** is determined; in a second mode, the lock-in frequency determined in the first mode is used to modulate a tone-burst pulse to drive the **transducer** in an efficient manner. Operating in the first mode, the lock-in frequency is determined by exciting the **transducer** with a series of tone bursts, where each tone burst comprises an electronic pulse modulated by a tone of one frequency selected from a range of frequencies, and measuring the response of the **transducer** to each tone burst. In an alternative embodiment, the excitation of the **transducer** in the first mode is provided by a signal whose frequency is swept over a range. The response of the **transducer** is sampled at various times during the sweep. The lock-in frequency is chosen by examining the responses and choosing the frequency which gives the best response. Operating in the second mode, the **transducer** is driven with an electronic tone burst generated by modulating said an electronic pulse with a tone of the determined lock-in frequency.

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Vehicle suspension system fulfils various purposes. It provides a vertical obedient **element** between un-sprung and sprung mass in order to maintain contact between ground and wheel, by reducing the sprung mass motion. It maintain proper attitude of the vehicle during various operating conditions like braking, cornering, accelerating. It also road holding and steering characteristics. Overall performance of suspension system is limits on maximum suspension travel, transmissibility of forces, road holding, minimum weight and cost[1]. There are three different types of suspensions namely: Dependent (Rigid Axle), independent and semi-independent suspensions. In the independent suspension system, there are no linkages between two hubs of same axle and it allows each wheel to move vertically without affecting the opposite wheel. This system has inherent advantages over dependent system such as more space for engine, better roll resistance, lesser un-sprung weight and better resistance to steering vibration. Dependent suspension or rigid axles provide a solid connection between two wheels of the same axle. Therefore motion of one wheel is transferred to the other wheel while travelling along

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A high frequency **ultrasonic** system was fabricated using a piezoelectric **transducer**. For the power system, a voltage adjustable power supply has been assembled to suit for the **ultrasonic** piezoelectric **transducer** with 1.7 MHz and 14 mm diameter, which functioned as a convertor that convert the electrical power to **ultrasonic** waves. The **ultrasonic** piezoelectric **transducer** was mounted in an **ultrasonic** holder with direct contact configuration with the distilled water without transmission horn. The **ultrasonic** total dissipation power was directly measured from the electrical dissipation across the **ultrasonic** piezoelectric **transducer**, which is expressed as in Equation (1):

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This chapter elaborates the process that was conducted in fulfilling the objectives of the project. It also discuss about the data requirements, data collection, properties of used materials and beams. This study analyzed 5 beams using the ABAQUS **finite** **element** program to predict the ultimate loading capacity of reinforced concrete continuous beams strengthened by CFRP applied at different orientation. A total of five beams were analyzed where one of them was treated as control specimen while the other four beams were strengthened using CFRP. Table 3.1 shows the information of all beams. This study also compare between results of using ABAQUS **finite** **element** program with the result of experimental work which was done by other student.

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System of oral cavity and dentition is similar to biomechanical conditions which are very complicated and the accessibility to it is very restricted. The researches and the study done in oral cavity are mostly in vitro rather than in vivo due to its complicated conditions. This requires a proper method to analyse the condition of stress in a numerical way. The modern tool for this stress **analysis** which is numerical is **Finite** **Element** **Analysis** (FEA). It has an advantage of being applied to solids of irregular geometry that contain heterogeneous material properties 1 . The clear understanding of the

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Also, it was shown that significant correlations exist between many modes of shape and density variations in the shoulder. Finally, while contralateral bone shapes were found to be symmetric, asymmetry, to some extent, was noted regarding their bone density distributions. These results encourage the use of contralateral bones as templates for shoulder reconstruction and can also help guide designs of population-based prostheses. Use of more compliant stems (e.g., hollow-stemmed implants or implants manufactured from less stiff materials like porous titanium) could mitigate the effect of stress shielding, and consequently reduce needs for revision surgeries [152], [158]–[161], [172]. Recent advances in AM have enabled the production of titanium alloy parts with complex geometries, such as hollow stems [156], [157]. The second objective of this study was to determine if such hollow titanium stems can mitigate stress shielding at the proximal humerus for a variety of bone qualities, using **finite** **element** methods. While the improvements in the bone-implant mechanics of hollow versus solid stems for femurs seemed promising [158], [160], [161], our results suggested a marginal improvement for the humerus, for which osteoporosis could exacerbate stress shielding to some extent, regardless of stem design. One of the interesting findings of this study was that healthy and possibly younger patients who undergo TSA might benefit more from using more compliant stems than do osteoporotic patients. By making stems hollow, the stem stresses remained well below the yield stress of titanium for all bone material properties and loading conditions, suggesting that further increasing the compliance of these stems can be achieved, which may be beneficial. For instance, adding pores to the walls, or reducing the inner-wall thickness of stems, possibly using optimization techniques, may improve their performance and further limit stress shielding and bone resorption.

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