DOCSLIB.ORG

Analysis and Design of Piezoelectric Sonar Transducers. Rodrigo, Gerard Christopher

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Analysis and Design of Piezoelectric Sonar Transducers. Rodrigo, Gerard Christopher Analysis and design of Piezoelectric sonar transducers. Rodrigo, Gerard Christopher The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the author For additional information about this publication click this link. http://qmro.qmul.ac.uk/jspui/handle/123456789/1712 Information about this research object was correct at the time of download; we occasionally make corrections to records, please therefore check the published record when citing. For more information contact [email protected] -1- ANALYSIS AND DESIGN OF PIEZOELECTRIC SONAR TRANSDUCERS Gerard Christopher Rodrigo Department of Electrical and Electronic Engineering, Queen Mary College, London E.l. Thesis presented for the Degree of Doctor of Philosophy of the University of London August 1970 -2- ABSTRACT In this study techniques are developed for the analysis and design of piezoelectric sonar transducers based on equivalent circuit representations. For the purposes of analysis, equivalent circuits capable of accurately representing every element of a transducer in the full operating frequency range, are developed. The most convenient fashion in which these equivalents could be derived is also discussed. For the purposes of design the accurate equivalents are approximated by L-C-R circuits. The limits of both representations are discussed in detail. The technique of analysis developed is capable of determining the frequency characteristics as well as the transient response to any electrical or acoustic input which can be specified analytically or numerically in the time domain. The design technique is based on the formulation of a ladder-type generalized circuit incorporating the essential components of any transducer. The generalised circuit is then used to extract particular bandpass filter designs which possess wide pasabands and which are wechanically realizable. By this procedure it is found possible to design transducers exhibiting bandwidths of around 100%. The performance of a 'test' transducer constructed to verify both analysis and design theories is also discussed. -3- A CKNOW LEDGEMENTS I wish to express my thanks to my supervisor, Dr.M.Redwood, for his help and guidance throughout the course of this work. This project was carried out under a Ministry of Defence Contract and the test transducer was constructed and tested at the Admiralty Underwater Weapons Establishment. I should also like to acknowledge the advice and assistance afforded by a number of individuals at this Establishment, in particular Dr.D.Stansfield, Mr.G.Bromfield and Mr. D. Evans. Thanks are also due to Lynn Parry who typed this thesis. CO NTENTS Page ABSTRACT 2 ACKNOWLEDGEMENTS 3 CONTENTS 14 LIST OF MAIN SYMBOLS 6 CHAPTER ONE: INTRODUCTION 9 1.1. Aims and Scope of Study 9 1.2. Use of Equivalent Circuits 9 1.3. Analysis 13 1.14. Design Theory 15 1.5. Experimental Verification of Theory 17 CHAPTER TWO: PRELIMINARY CONSIDERATIONS 19 2.].. Piezoelectric Materials for Sonar 19 Transducers 2.2. Electromechanical Analogies 22 2.3. Derivation of the Equivalent Circuit 25 of a Longitudinally Poled Piezo- electric Bar for Parallel Excitation 2.4. Elementary Theory of Conventional 29 Composite Transducers 2.5. Construction of the Ceramic Stack 37 CHAPTER THREE: EQUIVALENT CIRCUITS 140 3.1. Mechanical Elements 42 3.2. Equivalent Circuit of a Tubular Ceramic 45 Segment 3.3. Equivalent Circuit of the Ceramic Stack 50 3.14. Effect of Bonds on the Equivalent 58 Circuit of a Ceramic Stack 3.5. Lateral Effects and Losses 614 3.6. Radiation Impedance of a Single 66 Piston Source 3.7. Average Radiation Impedance of Piston 71 Sources in Regular Plane Arrays CHAPTER FOUR: DESIGN OF PIEZOELECTRIC SONAR 8]. TRANSDUCERS 4.1. Generalized Equivalent Circuit of a 81 Piezoelectric Sonar Transducer -5- Page 4.2. Properties of the Generalized 85 Equivalent Circuit 4.3. Canonic Bandpasa Circuits 89 4.4. Coupled Resonator Bandpass Circuits 95 4.5. Properties of the Alternative 103 Broadband Circuits 4.6. Transducer Design in Lead Zirconate 111 Titanate Type Ceramic CHAPTER FIVE: ANALYSIS 123 5.1. Formulation of the Complete 123 Equivalent Circuit 5.2. Computation of the Frequency 130 Characteristics 5.3. Evaluation of the Time Responses 135 5.4. Analysis of Ladder Networks 147 CHAPTER SIX: EXPERIMENTAL RESULTS AND 150 CONCLU SI ON S 6.1. Characteristics of the Test 150 Transducer 6.2. Comparison of the Measured and 159 Computed Characteristics 6.3. Summary and Conclusions 162 APPENDIX I: Radiated Power and Bandwidth of 166 Shunt Tuned Elementary Transducer APPENDIX II: Program for the Determination 171 of the Average Radiation Impedance in a Regular Array APPENDIX III: Program for the Analysis of a 173 Piezoelectric Sonar Transducer APPENDIX IV: Program for the Analysis of 178 Ladder Networks REFERENCES 183 -6- LIST OF MAIN SYMBOLS a Radius of radiating face A Cross-sectional area normal to the direction of propagation of longitudinal waves B Inverse of the bandwidth s c Velocity of longitudinal waves Ce c(l-k3); effective velocity in a ceramic stack C Generic symbol for electrical capacitance and mechanical compliance in the impedance analogy Cb Bond compliance CC Low frequency compliance of a ceramic stack Co Electrical capacitance of a ceramic segment d33 Effective component of the piezoelectric tensor (strain/field at constant stress) D Electric flux density E Electric field f Frequency centre frequency f=0 Cut-off frequency at lower half-power point Cut-off frequency at upper half-power point Frequency of resonance F Complex representation of force g33 Effective component of the piezoelectric tensor (electric field/stress at constant D) G Electrical conductance 1 Instantaneous value of current I Complex representation of current I k 2w/A; wave number -7- E T k 33 = d 33 /(S 33 . £33) k Effective electromechanical coupling factor e ff Coupling factors associated with filter circuits K = keff/Ci - k ff ); measure of effective coupling K Low frequency value of K 0 L Gqneric symbol for electrical inductance and mass in the impedance analogy L Mass of the radiating head M correction factor for bonding p Number of segments in a ceramic stack P Power radiated or absorbed from the supply by a transducer Maximum power that can be delivered from a given supply (see equation ('4.2)) q Quality factors associated with filter circuits Output or mechanical Q of a transducer r Terminating resistance of normalized filter circuits R Generic symbol for electrical and mechanical resistance and in particular radiation resistance R Generator resistance g R Radiation resistance r 8 Laplace transform variable S33D Effective component of the elastic compliance tensor at constant D - effective component of the elastic 33 - compliance tensor at constant E t Time T Stress U Instantaneous velocity v Instantaneous voltage -8- V Complex representation of voltage V Supply voltage g x: 2 ak x Length in the direction of propagation of longitudinal waves X Radiation reactance Y Generic symbol for admittance Y Young's modulus Z Generic symbol for electrical and mechanical impedance Z0 pAc; mechanical characteristic impedance Zr Radiation impedance fractional bandwidth Dirac delta function T £33 Free dielectric constant A Wavelength of longitudinal waves Ii Function of coupling (see equation ('.'4O)) Particle displacement p Density Electromechanical transformation ratio x Packing factor of a transducer array w = 2irf; angular frequency corresponding frequency (see above) tIo W etc. (I, Actual centre frequency of a normalized filter network -9- CHAPTER I INTRODUCTION 1.1. Aims and Scope of Study The objectives of this study are twofold. First the development of a general technique of analysis applicable to piezoelectric sonar transducers, based on electrical equivalent circuits which accurately represent t1 transducer in the sonic range. Second, the investigation of the possibility of extending the bandwidth of piezoelectric sonar transducers, by a systematic design technique based on equivalent circuits. The scope of the study is restricted to the commonly used extensional type transducers, which employ longitudinal mode operation of the main constituent mechanical elements. 1.2. Use of Equivalent Circuits The analysis of complex electromechanical systems, by means of the direct solution of the intrinsic differential equations, is fraught with difficulties. The preferred and well-established method of attack is to formulate the related 'steady-state' or frequency domain problem in terms of an analogous electrical circuit. The latter problem is generally much more tractable on account of the powerful and well-developed techniques of electrical circuit theory. The recently developed method of modern systems theory, employing the state-space formulation, is advantageous in that it finds the time domain solution directly, while -1 - simultaneously tracing all the variables. At present, however, its scope is severely limited in comparison with the equivalent circuit technique. A further advantage of the equivalent circuit method is that once the basic analogies are set up, it is usually much easier to form the equivalent circuit than to derive the intrinsic system equations. Thus in sonar transducer design and analysis in general and in this study in particular, the equivalent circuit method is used. Where required, the time domain solutions are obtained from the steady state responses by inverse Fourier transformation. In the
Load more

Recommended publications
  • Analysis and Measurement of Anti-Reciprocal Systems By
    ANALYSIS AND MEASUREMENT OF ANTI-RECIPROCAL SYSTEMS BY NOORI KIM DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2014 Urbana, Illinois Doctoral Committee: Associate Professor Jont B. Allen, Chair Professor Stephen Boppart Professor Steven Franke Associate Professor Michael Oelze ABSTRACT Loudspeakers, mastoid bone-drivers, hearing-aid receivers, hybrid cars, and more – these “anti-reciprocal” systems are commonly found in our daily lives. However, the depth of understanding about the systems has not been well addressed since McMillan in 1946. The goal of this study is to provide an intuitive and clear understanding of the systems, beginning from modeling one of the most popular hearing-aid receivers, a balanced armature receiver (BAR). Models for acoustic transducers are critical in many acoustic applications. This study analyzes a widely used commercial hearing-aid receiver, manufactured by Knowles Electron- ics, Inc (ED27045). Electromagnetic transducer modeling must consider two key elements: a semi-inductor and a gyrator. The semi-inductor accounts for electromagnetic eddy cur- rents, the “skin effect” of a conductor, while the gyrator accounts for the anti-reciprocity characteristic of Lenz’s law. Aside from the work of Hunt, to our knowledge no publications have included the gyrator element in their electromagnetic transducer models. The most prevalent method of transducer modeling evokes the mobility method, an ideal transformer alternative to a gyrator followed by the dual of the mechanical circuit. The mobility ap- proach greatly complicates the analysis. The present study proposes a novel, simplified, and rigorous receiver model.
    [Show full text]
  • ELEC-E5650 Electroacoustics
    ELEC-E5650ELECElectroacoustics-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 Lecture 2: SteadyRaimundo -GonzalezState Analysis / Dynamic Analogies Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering Raimundo2 2GonzalezFebruary 2018 Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering March 7, 2019 ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez 1 Aalto, Signal Processing & Acoustics ELEC-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 LectureRaimundo Gonzalez 2: Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering 22 February 2018 I. Steady State Analysis ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez 2 Aalto, Signal Processing & Acoustics Steady state sinusoidal response When designing Electroacoustics systems we are usually more interestedELEC in the-E5650 steady state behavior of the system. This will ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 lead into Raimundomostly Gonzalez working in the frequency domain. Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering 22 February 2018 ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 3 Phasors to represent sinusoidal signals ELEC-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements
    [Show full text]
  • Modeling of the Electroacoustic Coupling of Electrostatic Microphones Including the Preamplifier Circuit
    Electroacoustics and Audio Engineering: Paper ICA2016-193 Modeling of the electroacoustic coupling of electrostatic microphones including the preamplifier circuit Bernardo Henrique Pereira Murta(a), Eric Brandão(b), Julio Cordioli(c), William D’A. Fonseca(d), Paulo H. Mareze(e) (a, b, d, e)Federal University of Santa Maria, Acoustical Engineering, Santa Maria, RS, Brazil, [email protected], [email protected] (c)Universidade Federal de Santa Catarina, Florianópolis, Brazil, [email protected] Abstract: This research aims to study tools to model and design electrostatic microphones coupled with its preamplifier circuits. The outcome is the access to their combined sensitivities curves, which allows the design of microphones with a wider and flat bandwidth. Analytical and numerical mod- eling techniques are explored and compared. On one hand, the lumped parameters approach is the basis of the analytical modeling of acoustic transducers. That is, this technique allows the engineer to design the transducer and its preamplifier circuit by predicting its sensitivity changes due to variations of model properties with low computational cost. On the other hand, numerical analysis is carried out using the Finite Element Method with a multiphysics approach, which is able to solve both the transducer model and the coupled electrical circuit. Two microphones with different complexities and constructive characteristics are studied. For validation of the proposed techniques, the behavior of a commercial measurement microphone model that has been well studied in the literature is considered. Once the validation of the modeling approach is satisfac- tory, one can use the same methodology to study a piezoelectric microphone for hearing aid applications, for instance.
    [Show full text]
  • ETD Template
    DESIGN ISSUES IN ELECTROMECHANICAL FILTERS WITH PIEZOELECTRIC TRANSDUCERS by Michael P. Dmuchoski B.S. in M.E., University of Pittsburgh, 2000 Submitted to the Graduate Faculty of School of Engineering in partial fulfillment of the requirements for the degree of Master of Science University of Pittsburgh 2002 UNIVERSITY OF PITTSBURGH SCHOOL OF ENGINEERING This thesis was presented by Michael P. Dmuchoski It was defended on December 11, 2002 and approved by Dr. Jeffrey S. Vipperman, Professor, Mechanical Engineering Department Dr. Marlin H. Mickle, Professor, Electrical Engineering Department Dr. William W. Clark, Professor, Mechanical Engineering Department Thesis Advisor ii ________ ABSTRACT DESIGN ISSUES IN ELECTROMECHANICAL FILTERS WITH PIEZOELECTRIC TRANSDUCERS Michael P. Dmuchoski, MS University of Pittsburgh, 2002 The concept of filtering analog signals was first introduced almost one hundred years ago, and has seen tremendous development since then. The majority of filters consist of electrical circuits, which is practical since the signals themselves are usually electrical, although there has been a great deal of interest in electromechanical filters. Electromechanical filters consist of transducers that convert the electrical signal to mechanical motion, which is then passed through a vibrating mechanical system, and then transduced back into electrical energy at the output. In either type of filter, electrical or electromechanical, the key component is the resonator. This is a two-degree-of-freedom system whose transient response oscillates at its natural frequency. In electrical filters, resonators are typically inductor-capacitor pairs, while in mechanical filters they are spring-mass systems. By coupling the resonators correctly, the desired filter type (such as bandpass, band-reject, etc.) or specific filter characteristics (e.g.
    [Show full text]
  • Application Notes
    Application Note Accurate Determination of Loudspeaker Parameters using Audio Analyzer Type 2012 and Laser Velocity Transducer Type 3544 by Søren Jønsson, Brüel & Kjær, Denmark A method to determine the parame- ters characterising low frequency, mid- range and high frequency loudspeaker units is presented. A laser velocity transducer is used to detect the veloc- ity of the diaphragm. All measure- ments are made with the loudspeaker in free air. The method uses an im- proved model of the loudspeaker and takes into account the frequency de- pendent behaviour of some of the ele- ments. It produces accurate results and is easy to implement compared with conventional methods. The proce- dure is fully automated using an au- tosequence program for the analyzer. The process of automation is discussed and results of a typical driver are in- cluded. 1. Introduction Over the last two decades, it has be- The method presented here is a ance. From these functions the loud- come almost an industrial standard compilation of the traditional method speaker parameters can be calculated. to measure the parameters of a loud- and the method introduced by Applying the post-processing capa- speaker by the method introduced by J. N. Moreno [6]. It uses an improved bilities of the analyzer to the meas- A.N. Thiele and Dr. Richard Small [1 model of the loudspeaker and takes ured data, it is shown how to correct & 2]. various non-linearities in frequency the loudspeaker parameters and ex- Since the method was introduced, into account. The method produces tract information about the frequency more research in loudspeaker model- accurate results regardless of the dependent behaviour of some of the ling has been made, (e.g., [3, 4 & 5], components in the equivalent circuit type of driver used.
    [Show full text]
  • Analysis and Measurement of Anti-Reciprocal Systems
    University of Illinois, Urbana-Champaign Electrical and Computer Engineering Department The Doctoral Preliminary Examination Document Analysis and measurement of anti-reciprocal systems Committee: Associate Professor Jont B. Allen Author: (Advisor, Chair) Noori Kim Professor Stephen Boppart (UIN:677205530) Professor Steven Franke Associate Professor Michael Oelze October 12, 2014 1 Abstract 2 Loudspeakers, mastoid bone-drivers, hearing-aid receivers, hybrid cars, and more - these 3 “anti-reciprocal” systems are commonly found in our daily lives. However, the depth of un- 4 derstanding about the systems has not been well addressed since McMillan in 1946. The goal 5 of this study is to guide an intuitive and clear understanding of the systems, beginning from 6 modeling one of the most popular hearing-aid receivers, a balanced armature receiver (BAR). 7 Models for acoustic transducers are critical in many acoustic applications. This study ana- 8 lyzes a widely used commercial hearing-aid receiver ED series, manufactured by Knowles Elec- 9 tronics, Inc. Electromagnetic transducer modeling must consider two key elements: a semi- 10 inductor and a gyrator. The semi-inductor accounts for electromagnetic eddy-currents, the 11 “skin effect” of a conductor (Vanderkooy, 1989), while the gyrator (McMillan, 1946; Tellegen, 12 1948) accounts for the anti-reciprocity characteristic [Lenz’s law(Hunt, 1954, p. 113)]. Aside 13 from Hunt (1954), to our knowledge, no publications have included the gyrator element in their 14 electromagnetic transducer models. The most prevalent method of transducer modeling evokes 15 the mobility method, an ideal transformer alternative to a gyrator followed by the dual of the 16 mechanical circuit (Beranek, 1954).
    [Show full text]
  • Electrical Schematic of the Earth and Solar System
    Fundamental Journal of Modern Physics ISSN: 2249-9768 Volume 13, Issue 2, 2020, Pages 121-139 This paper is available online at http://www.frdint.com/ Published online June 22, 2020 ELECTRICAL SCHEMATIC OF THE EARTH AND SOLAR SYSTEM GREG POOLE Industrial Tests, Inc. Rocklin, CA USA e-mail: [email protected] Abstract By visualizing the Sun and Earth coupled together by a mechanical spring, I have shown how gravity is like spring tension. This rotating spring coupler example is then exchanged for an analogous rotating electrical capacitor which leads to an improved electrical circuit diagram of the solar system. The series capacitive coupled circuit is the electrical transmission system for the solar system. Low frequency electrical energy is transferred from the Sun to the planets via flux transfer events. A capacitive coupled system inherently develops torque which provides rotation and centripetal/centrifugal force or what we call gravity. The paralleling of electricity generating Suns indicates that the power of the universe is virtually unlimited as James Clerk Maxwell inferred. Harnessing the power of the universe is one step closer to reality by virtue of the electrical schematic of the solar system. Keywords and phras :es flux transfer events, gravity, Newton’s cradle, spring coupler, series capacitive coupling, wireless transmission system. Received May 28, 2020; Accepted June 2, 2020 © 2020 Fundamental Research and Development International 122 GREG POOLE 1. Introduction In 1686, a controversy arose when the first book of Newton’s Principia was presented to the Royal Society. Robert Hooke accused Newton of plagiarism by claiming that he had taken from his paper “System of the World” [1].
    [Show full text]
  • Modeling of MEMS Piezoelectric Energy Harvesters Using Electromagnetic and Power System Theories
    Modeling of MEMS piezoelectric energy harvesters using electromagnetic and power system theories Mahmoud Al Ahmad1, Amro M. Elshurafa2, Khaled N. Salama2 and H. N. Alshareef1,* 1 Material Sciences and Engineering, Physical Sciences and Engineering Division, King Abdullah University of Science & Technology (KAUST), Thuwal, Saudi Arabia, 23955-6900. 2 Electrical Engineering, Physical Sciences and Engineering Division, King Abdullah University of Science & Technology (KAUST), Thuwal, Saudi Arabia, 23955-6900. *Corresponding author: [email protected] Abstract This work proposes a novel methodology for estimating the power output of piezoelectric generators. An analytical model that estimates, for the first time, the loss ratio and output power of piezoelectric generators, based on the direct mechanical-to-electrical analogy, electromagnetic theory, and power system theory, is developed and takes into account the dimensions and material properties of the generator. The mechanical-to-electrical analogy and power system theory allow deriving an equivalent input impedance expression for the network. Further, electromagnetic theory allows deducing the equivalent electromechanical loss of the piezoelectric generator. By knowing the mechanical input power and the loss of the network, calculating the output power of the piezoelectric device becomes a straightforward procedure. Experimental results based on published data are also presented to validate the analytical solution. Moreover, and to fully benefit from the well established electromagnetic and electric circuit theories, further analysis efforts on the resonant frequency, bandwidth, and sensitivity are presented. Compared to conventional modeling methods currently being adopted in the literature, the proposed method provides, relatively easily, significant additional information that is crucial for enhanced device operation. Finally, and with the study provided in this paper, optimizing piezoelectric harvesters is simplified.
    [Show full text]
  • Lstl Ter Tional
    FINITE ELEMENT MODELING OF FLUID SYSTEMS USING THE MOBILITY ANALOGY APPROACH Ronald J. Gaines* Rajendra Singh Research Assistant Assistant Professor Department of Mechanical Engineeri ng The Ohio State University 206 West 18th Avenue Columbus, Ohio 43210 Proceedings of the lstl ter tional •International Mo alAn...... ysis Modal Analysis Co...... nee 1ft·Exhibit November 8-10, 1982 Holiday Inn, International Driv~ Orlando, Florida FINITE ELEMENT MODELING OF FLUID SYSTEMS USING THE MOBILITY ANALOGY APPROACH Ronald J. Gaines* Rajendra Singh Research Assistant Assistant Professor Department of Mechanical Engineering The Ohio State University 206 West 18th Avenue Columbus, Ohio 43210 *Currently with Toledo Scale Div., Reliance Electric, Worthington, Ohio 43D85 ABSTRACT obtained good agreement between SUPERB and WAVENET (a fluid transients computer program based on the One-dimensional fluid systems can be analyzed for method of characteristics [9] ) . However, in order natural frequencies and modes using an available to establish the mobility analogy solution tech­ structural finite element program, wi th the aid of nique, a sufficient number of example cases must the mobility analogy. In this paper, the be analyzed, and an adequate error analysis should methodology, strength and limitation of the be performed. Thi s i s the focu s of this paper as solution technique are discussed . Th i s method is we will consider several one-dimensional fluid validated by considering several example cases and systems and compare the computed results, using comparing results with theory, experiment or other the mobility analogy-finite element analysis, with numerical techniques. the solutions obtained by theory, experiment, or other numerical techniques. INTRODUCTION SCOPE The physical variables of a dynamic system could be classified either according to the dynamic and We are interested in obtaining an eigenvalue kinematic variables (impedance approach) , or solution (i .e.
    [Show full text]
  • Section 2.2 : Electro-Mechanical Analogies
    Section 2.2 : Electro- mechanical analogies PHILIPE HERZOG AND GUILLAUME PENELET Paternité - Pas d'Utilisation Commerciale - Partage des Conditions Initiales à l'Identique : http://creativecommons.org/licenses/by-nc-sa/2.0/fr/ Table des matières I - Introduction 5 A. Objective.....................................................................................................5 B. Test your knowledge.....................................................................................5 C. Context........................................................................................................7 II - Elementary phenomena 9 A. Mechanical elements.....................................................................................9 1. Mechanical elements..........................................................................................................9 2. Inertia of an object............................................................................................................9 3. Deformation of an object..................................................................................................10 4. Damping........................................................................................................................10 5. Mechanical lever.............................................................................................................10 III - Electro-mechanical analogies 13 A. Electro-mechanical analogies........................................................................13 B. Direct analogy............................................................................................13
    [Show full text]
  • Experience Teaching Electrical Energy Systems to Non-Electrical Engineering Students
    EXPERIENCE TEACHING ELECTRICAL ENERGY SYSTEMS TO NON-ELECTRICAL ENGINEERING STUDENTS Federico Milano University College Dublin (IRELAND) Abstract This paper describes the author's experience in teaching modules on electrical energy systems to Civil and Mechanical Engineering students at University of Castilla-La Mancha, Spain, and University College Dublin, Ireland, respectively. Teaching electrical energy systems to non-electrical engineering students presents several didactic and methodological challenges. These are originated mainly due to the lack of knowledge of circuit theory and electrical machines as well as to the little motivation of the students to learn and understand concepts apparently not related to their programmes. The paper describes the teaching approach adopted by the author through several practical examples. Keywords: Electrical energy systems; mechanical engineering; civil engineering; impedance analogy. 1 INTRODUCTION Teaching electrical energy systems to non-electrical engineering students presents several didactic and methodological challenges. First, when they attend such modules, the students have only a very basic knowledge of circuit theory and lack fundamental concepts of electrical machine modelling and control theory. Then, since the students are not going to specialize in electrical energy systems, they often have little motivation to learn and understand concepts related to power systems. It is thus crucial that the matter of the module is delivered in an appealing way. Including examples where the students can see the similarities and differences with respect to other disciplines that are better known or more interesting to them appears a sensible way to deliver the module. This paper describes the author's experience in teaching modules on electrical energy systems to two different groups of non-electrical engineering students, as follows.
    [Show full text]
  • The Vibration of a Struck String (Acoustical Research on the Piano, Part 1)
    J. Acoust. Soc. Jpn.(E) 13, 5 (1992) The vibration of a struck string (Acoustical research on the piano, Part 1) Isao Nakamura Teikyo University of Technology, 2289, Uruido, Ichihara, 290-01 Japan (Received 11 December 1991) [English translation of the same article in J. Acoust. Soc. Jpn. (J) 36, 504-512 (1980)] Vibrations of piano strings struck with an elastic hammer are studied by using equivalent circuitmodels based on the impedance analogy and the mobility analogy respectively. When the tension of a piano string alone is considered, neglecting its elasticity, the string and hammer system has an analogy with an electric transmission line, the hammer being represented by an inductance and a capacitance. An analogue simulator based on the models was designed and used for the study of the string and hammer system. Various waveformes, contact times, and the maximum contact force in each case were obtained by using the simulator. The reason for the appearance of even harmonics series in a high frequency region of piano keys, clearly shown in the simulator, is ex plained;and the method of their adjustment is suggested. A velocity waveform is de terminedby the resultant of two vertical tension waveforms in the simulator. The characteristics of these waveforms are shown compared with those from an actual piano. The contact forces, from which their vertical tensions can be reduced, are calculated from the equivalent circuits. Waveforms in all the cases become very similar to damped half sinusoidal waves. The energy transmission from a hammer to a string, including its efficiency at a low-frequency region, is discussed.
    [Show full text]