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Vibration for the Engineer

Vibration for the Engineer December, 1942 A I RC R A F T EN G I N E E R I N G 341 Fundamental s of Vibration Study. By felt that a very lucid and easily understood makes very clear, these factors may become section is slightly marred by leaving too much importan t features. It is noted that the R.G . Manley. [Chapman & Hall. 13s. 6d.] t o the imagination—particularly in the mathe­ description of I values in this chapter is given REVIEWE D BY C. WHITTINGHAM matics dealing with the resonant magnification as polar moment of area, whereas in the original List of Symbols this is referred to as second Available literature dealing with vibration is of page 27. moment of area—a small bu t important point. generally confined to ambitious volumes and Following this is a discussion on the relations tex t which presuppose a certain basic knowledge between resonance and natural frequency, a An interesting and enlightening three pages of the subject and which must often baffle the table of some interest showing th e error involved is devoted to the mathematics of Dynamic student reader. Stiffnesses related to frequencies of heavy in frequency calculations if damping is neg­ shafts. The author, in this book, has attempted to lected. Two practical examples which enhance bridge the gap which contains the basic mathe­ th e work of this chapter deal with the problem So far in thi s book we hav e not really touched matical principles. That such a book is needed of insulation from vibration of a machine by upon the mathematics of Flexural Vibration of th e use of flexible spring supports; the second beams but here the author gives ten pages is certain, in order to show, particularly to the example describes the mathematics involved in devoted to a very satisfying analysis of the young engineer, some point from which he can properly commence his study of a subject a n elementary vibrograph. fundamentals of this branch of the subject, daily becoming more insistent for recognition amongst which we find the first reference to Chapter Three introduces the problem of an d understanding because of the demand for tha t early classical mathematician Rayleigh. systems having two natural frequencies, such higher speeds and less massive proportions of Hi s energy methods for heavy beams have been as for instance a 3-mass two-shaft torsional machinery. gone into quite thoroughly and the chapter is arrangement ; a most useful description is completed with a list of th e mathematical con­ We find in the early pages of the book a list given of the basic principles of vibration absorbers, which as the author states, are ditions for th e three types of beam—cantilever, of the mathematical symbols t o be used and an simply supported and cncastr6 ends. often incorrectly named dampers. This chap­ indication of the first page on which these appear ; it would seem that, in general, British te r concludes with a very clear discussion on The Sixth and final chapter of the actual Standard Symbols have been retained—this is a comparative newcomer to vibration—the tex t deals adequately with the essentials of tha t a good beginning and augurs well for a methodi­ problem of coupled frequencies made possible importan t but often neglected aspect, Fourier cal development. from the movements of two coincident modes Series and Analysis, particularly but not solely of vibration ; brief reference is also made to useful for the resolution of harmonic com­ The author's preface states tha t no previous a system having the normal six degrees of ponents of a forcing torque diagram such as is knowledge of differential calculus is necessary bu t after a perusal of the early pages it is sug­ freedom. obtained for an internal combustion engine ; gested that this is a slight over-statement; it th e method of applying thi s analysis is very well The Fourt h Chapter commences by remarking is not felt tha t the early pages of Chapter One tha t the mathematics employed to describe an and thoroughly developed. could, for instance, be thoroughly understood elementary system having one and two degrees For those of its readers who are further without some knowledge of this branch of of freedom become cumbersome when used on interested the book has three Appendix Chap­ mathematics . Some further elementary pre­ systems having several degrees of freedom ters on pure fundamentals ; the first of these paration would, perhaps, have been an advant­ such as are developed in the next twenty deals with the pure mathematics that concern age at this important stage. pages. The calculation of natural frequencies th e earlier work and spans the subject from Use has been made by the author of the would henceforth be the object, instead of the Vectors and Exponential Functions to Ele­ differential operator method for simplifying more abstract resonances as heretofore. mentar y Calculus formula;. Th e second appendix such mathematical expressions. This has been The multi-mass shaft systems tha t suffer from covers the ground of elementary dynamics and developed in a clear and concise manner and it torsional vibration are dealt with in the early applied mechanics ; while the final of these does, without doubt, provide an easier method pages of Chapter Five and it is here that the chapters concerns itself with frequency equa­ tions and methods of handling variables that of understanding the fundamental equations. autho r introduces his " effective inertia" occur in expressions of vibrating systems. I t should, as is suggested on page 3, eliminate method, which allows a simple method of much of the guesswork often associated with frequency determination and, additionally, A further few examples and the answers to th e solution of differential calculus equations. conclusions ma y be drawn concerning the phase those inevitably found at the end of each Linear and torsional systems having a single displacements of masses and the relations of chapter; together with a short Bibliography, degree of freedom and their equations of motions frequencies having zero and lightly damped complete th e book. systems. are dealt with in a very thorough but simple To summarize; particularly must it be manner. It is, however, considered to be a Furthe r work includes a simple definition of remarked on the novel and extremely useful mistake to leave, as a n exercise, the solution of relative amplitudes and " swinging forms", method of numbering equations—one might a condition of motion ; it appears to bring the th e shape of which in the investigation of almost say that the mathematical appearance book t o the level of a school textbook. practical problems tell the expert quite a good of this method is in very natural surroundings. The use of the mass term of Slugs, noted in deal. Discussion on relative amplitudes logic­ The book will fill what has been a vacant Chapter One, may be regarded as an influence ally leads to considerations of that old and place on the shelves of all those interested in from the modern aeronautical engineer, to sometimes laborious, but nevertheless very vibration problems ; it deals essentially, as its convenient method, of frequency calculation whom at least, this unit is familiar ; it seems title implies, with the mathematical funda­ known as Frequency Tabulation. Every calcu­ t o be a pity tha t the general adoption of a more mentals of vibration. There is considerable appropriate name could not be instituted for lator of T.V. systems must at some time come evidence of much thought and hard work which such an important unit. across and make use of this method. The is deserving of the full attention of all who theory is very clearly explained and well worth wish to delve into the mathematics of an all A discussion of energy dissipation and ele­ th e study that the subject merits. important subject. mentar y damping of a linear system commences Chapter Two ; the mathematics of this section The final section of this chapter is devoted Wit h the exception of one or two minor de­ are admirably developed. If. damping is t o a description of the term " Dynamic Stiff­ tails, it is thorough, concise and complete, and present, as it must be in some form, then a ness " and the pages concerned with this ther e is no evidence of " padding". system can only be maintained in a state of matte r very considerably clarify the difference A final seal is set upon the book by that vibration by the application of some forced between Static and. Dynamic torsional stiff­ expert on the subject. Dr. W . Ker Wilson, who motion, and the theory of this is followed by nesses. has written a foreword. several pages devoted to one of the most I n Chapter Five we are introduced to more For a wartime publication its price of 13s. 6d. importan t aspects of vibration, namely, Reson­ advanced work arising out of the consideration is very good value for the 128 pages and its ance. The author states that most vibration of inertia due to heavy shafts and flexibilities production by Chapman and Hall well up to problems are concerned with detecting and of masses. These are sometimes ignored in their standard. avoiding resonances ; here again, however, it is normal practical problems but, as the text Professional Publications Uruler this heading are given each month the principal articles of S.A.E . Journal Quarterl y Transactions of the aeronautical interest appearing in the current issues of the Journals of Vol. 50, No. 10, October, 1942. Institute of Welding the leading professional societies an>l institutions. Synthetic Rubber Development: Discussion at the Cleveland Vol. V, No. 3, July, 1942. Section's Meeting. Th e Journal of the Royal Aeronautical Society " Examination of Stress Distribution in Spot Welded Joints in " The Testing of Heavy-Duty Motor Oils." H. C. Mougey and Light Alloys by the Brittle Lacquer Process." R. F. Tylecote. J . A. Moller. Vol. XLVI, No. 333, November, 1942. "Recent Development of Steel St.52 for Steel Structures." "Production Testing Facilities of Allison Division of General Motors." H.J. Buttner. (Translation.) E. II. Schulz and D. W. Bischof. " Fundamentals of Fighter Design." F. H. M. Lloyd. "A n Estimation of the Distribution of Shear Stress in Spot "Th e Role of Surface Chemistry and Profile in Boundary Abstracts from the Scientific and Technical Press. Lubrication." J. T, Burwell. Welds." K. F. Tyelcotc. Titles and References of Articles and Papers. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Aircraft Engineering and Aerospace Technology Emerald Publishing

Vibration for the Engineer

Aircraft Engineering and Aerospace Technology , Volume 14 (12): 1 – Dec 1, 1942

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Emerald Publishing
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Copyright © Emerald Group Publishing Limited
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0002-2667
DOI
10.1108/eb030973
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Abstract

December, 1942 A I RC R A F T EN G I N E E R I N G 341 Fundamental s of Vibration Study. By felt that a very lucid and easily understood makes very clear, these factors may become section is slightly marred by leaving too much importan t features. It is noted that the R.G . Manley. [Chapman & Hall. 13s. 6d.] t o the imagination—particularly in the mathe­ description of I values in this chapter is given REVIEWE D BY C. WHITTINGHAM matics dealing with the resonant magnification as polar moment of area, whereas in the original List of Symbols this is referred to as second Available literature dealing with vibration is of page 27. moment of area—a small bu t important point. generally confined to ambitious volumes and Following this is a discussion on the relations tex t which presuppose a certain basic knowledge between resonance and natural frequency, a An interesting and enlightening three pages of the subject and which must often baffle the table of some interest showing th e error involved is devoted to the mathematics of Dynamic student reader. Stiffnesses related to frequencies of heavy in frequency calculations if damping is neg­ shafts. The author, in this book, has attempted to lected. Two practical examples which enhance bridge the gap which contains the basic mathe­ th e work of this chapter deal with the problem So far in thi s book we hav e not really touched matical principles. That such a book is needed of insulation from vibration of a machine by upon the mathematics of Flexural Vibration of th e use of flexible spring supports; the second beams but here the author gives ten pages is certain, in order to show, particularly to the example describes the mathematics involved in devoted to a very satisfying analysis of the young engineer, some point from which he can properly commence his study of a subject a n elementary vibrograph. fundamentals of this branch of the subject, daily becoming more insistent for recognition amongst which we find the first reference to Chapter Three introduces the problem of an d understanding because of the demand for tha t early classical mathematician Rayleigh. systems having two natural frequencies, such higher speeds and less massive proportions of Hi s energy methods for heavy beams have been as for instance a 3-mass two-shaft torsional machinery. gone into quite thoroughly and the chapter is arrangement ; a most useful description is completed with a list of th e mathematical con­ We find in the early pages of the book a list given of the basic principles of vibration absorbers, which as the author states, are ditions for th e three types of beam—cantilever, of the mathematical symbols t o be used and an simply supported and cncastr6 ends. often incorrectly named dampers. This chap­ indication of the first page on which these appear ; it would seem that, in general, British te r concludes with a very clear discussion on The Sixth and final chapter of the actual Standard Symbols have been retained—this is a comparative newcomer to vibration—the tex t deals adequately with the essentials of tha t a good beginning and augurs well for a methodi­ problem of coupled frequencies made possible importan t but often neglected aspect, Fourier cal development. from the movements of two coincident modes Series and Analysis, particularly but not solely of vibration ; brief reference is also made to useful for the resolution of harmonic com­ The author's preface states tha t no previous a system having the normal six degrees of ponents of a forcing torque diagram such as is knowledge of differential calculus is necessary bu t after a perusal of the early pages it is sug­ freedom. obtained for an internal combustion engine ; gested that this is a slight over-statement; it th e method of applying thi s analysis is very well The Fourt h Chapter commences by remarking is not felt tha t the early pages of Chapter One tha t the mathematics employed to describe an and thoroughly developed. could, for instance, be thoroughly understood elementary system having one and two degrees For those of its readers who are further without some knowledge of this branch of of freedom become cumbersome when used on interested the book has three Appendix Chap­ mathematics . Some further elementary pre­ systems having several degrees of freedom ters on pure fundamentals ; the first of these paration would, perhaps, have been an advant­ such as are developed in the next twenty deals with the pure mathematics that concern age at this important stage. pages. The calculation of natural frequencies th e earlier work and spans the subject from Use has been made by the author of the would henceforth be the object, instead of the Vectors and Exponential Functions to Ele­ differential operator method for simplifying more abstract resonances as heretofore. mentar y Calculus formula;. Th e second appendix such mathematical expressions. This has been The multi-mass shaft systems tha t suffer from covers the ground of elementary dynamics and developed in a clear and concise manner and it torsional vibration are dealt with in the early applied mechanics ; while the final of these does, without doubt, provide an easier method pages of Chapter Five and it is here that the chapters concerns itself with frequency equa­ tions and methods of handling variables that of understanding the fundamental equations. autho r introduces his " effective inertia" occur in expressions of vibrating systems. I t should, as is suggested on page 3, eliminate method, which allows a simple method of much of the guesswork often associated with frequency determination and, additionally, A further few examples and the answers to th e solution of differential calculus equations. conclusions ma y be drawn concerning the phase those inevitably found at the end of each Linear and torsional systems having a single displacements of masses and the relations of chapter; together with a short Bibliography, degree of freedom and their equations of motions frequencies having zero and lightly damped complete th e book. systems. are dealt with in a very thorough but simple To summarize; particularly must it be manner. It is, however, considered to be a Furthe r work includes a simple definition of remarked on the novel and extremely useful mistake to leave, as a n exercise, the solution of relative amplitudes and " swinging forms", method of numbering equations—one might a condition of motion ; it appears to bring the th e shape of which in the investigation of almost say that the mathematical appearance book t o the level of a school textbook. practical problems tell the expert quite a good of this method is in very natural surroundings. The use of the mass term of Slugs, noted in deal. Discussion on relative amplitudes logic­ The book will fill what has been a vacant Chapter One, may be regarded as an influence ally leads to considerations of that old and place on the shelves of all those interested in from the modern aeronautical engineer, to sometimes laborious, but nevertheless very vibration problems ; it deals essentially, as its convenient method, of frequency calculation whom at least, this unit is familiar ; it seems title implies, with the mathematical funda­ known as Frequency Tabulation. Every calcu­ t o be a pity tha t the general adoption of a more mentals of vibration. There is considerable appropriate name could not be instituted for lator of T.V. systems must at some time come evidence of much thought and hard work which such an important unit. across and make use of this method. The is deserving of the full attention of all who theory is very clearly explained and well worth wish to delve into the mathematics of an all A discussion of energy dissipation and ele­ th e study that the subject merits. important subject. mentar y damping of a linear system commences Chapter Two ; the mathematics of this section The final section of this chapter is devoted Wit h the exception of one or two minor de­ are admirably developed. If. damping is t o a description of the term " Dynamic Stiff­ tails, it is thorough, concise and complete, and present, as it must be in some form, then a ness " and the pages concerned with this ther e is no evidence of " padding". system can only be maintained in a state of matte r very considerably clarify the difference A final seal is set upon the book by that vibration by the application of some forced between Static and. Dynamic torsional stiff­ expert on the subject. Dr. W . Ker Wilson, who motion, and the theory of this is followed by nesses. has written a foreword. several pages devoted to one of the most I n Chapter Five we are introduced to more For a wartime publication its price of 13s. 6d. importan t aspects of vibration, namely, Reson­ advanced work arising out of the consideration is very good value for the 128 pages and its ance. The author states that most vibration of inertia due to heavy shafts and flexibilities production by Chapman and Hall well up to problems are concerned with detecting and of masses. These are sometimes ignored in their standard. avoiding resonances ; here again, however, it is normal practical problems but, as the text Professional Publications Uruler this heading are given each month the principal articles of S.A.E . Journal Quarterl y Transactions of the aeronautical interest appearing in the current issues of the Journals of Vol. 50, No. 10, October, 1942. Institute of Welding the leading professional societies an>l institutions. Synthetic Rubber Development: Discussion at the Cleveland Vol. V, No. 3, July, 1942. Section's Meeting. Th e Journal of the Royal Aeronautical Society " Examination of Stress Distribution in Spot Welded Joints in " The Testing of Heavy-Duty Motor Oils." H. C. Mougey and Light Alloys by the Brittle Lacquer Process." R. F. Tylecote. J . A. Moller. Vol. XLVI, No. 333, November, 1942. "Recent Development of Steel St.52 for Steel Structures." "Production Testing Facilities of Allison Division of General Motors." H.J. Buttner. (Translation.) E. II. Schulz and D. W. Bischof. " Fundamentals of Fighter Design." F. H. M. Lloyd. "A n Estimation of the Distribution of Shear Stress in Spot "Th e Role of Surface Chemistry and Profile in Boundary Abstracts from the Scientific and Technical Press. Lubrication." J. T, Burwell. Welds." K. F. Tyelcotc. Titles and References of Articles and Papers.

Journal

Aircraft Engineering and Aerospace TechnologyEmerald Publishing

Published: Dec 1, 1942

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