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Free vibration analysis of beams and shafts
432 the special problems of isolating torsional vibrations between machinery components is tllso provided. Chapter 3, "Principles of Construction" (23 pp.) gives design guidelines and specific details of the forms in which rubber springs are used and manufactured. The last chapter (69 pp.) covers "Examples of Applications". These include examples for the design of machines (pumps, compressors, engines, etc.), machine tools (lathes, presses, shapers, etc.), vehicles, couplings, panel instruments, bridges, piping and in noise abatement. It is an excellent compilation. In an appendix, comparable British, U.S. and German Standard Test Methods are given. A seven-page bibliography is provided, sectionalized so as to agree in content with the four chapters. The 117 references are distributed between the chapters, 17, 12, 5 and 83, respectively, thus showing the practical-example bent of the material presented. Unfortunately, most American readers will have difficulty finding specific bibliographic references, much less translating their language and terminology to those familiar to them. In summary, this reviewer recommends Rubber Spring Design to interested practicioners and educators in the field of vibration, shock and noise control. Despite the faults of unfamiliar terms and language, it is the "only game in town". D. MUSTER,
Brown and Root Professor, Dept. of Mechanical Engineering, University of Houston, Houston, TX 77004, U.S.A.
D. J. Gorman: Free Vibration Analysis of Beams and Shafts, Wiley, New York, 1975, 386 pp.
THIS book presents a rather thorough study of free vibration frequencies for straight beams and shafts governed by classical fourth order, Euler-Bernoulli deflection theory. Extensive tabular results are given for frequencies. Mode shapes and bending stresses corresponding to these frequencies are ignored, except in Chap. 6. The effects of shear deformation and rotary inertia of beams are not included. Chapters 1-6 deal with small deflection, transverse vibrations of homogeneous beams having uniform cross-section and no axial loading. In the first chapter the classical eigenvalues for beams having clamped, simply-supported or free boundary conditions are presented. The second chapter extends the types of boundary conditions to include translational or rotational springs and lumped masses. In Chaps. 3-6 a valiant effort is made to extend the analyses of the first two chapters to beams having 2, 3, 4 and more than 4 spans, respectively, although the number of combinations of end and intermediate support conditions becomes, of course, unmanageable and completeness of results must be sacrificed in favor of some of the more interesting and useful possible combinations. Chapter 7 is a brief interlude dealing with the classical, second-order, one dimensional wave equation applied to the torsional vibration of rods having various combinations of clamped, free, elastic, or lumped mass boundary conditions to which is appended 66 pp. of tabulated numerical results for frequency parameters. The author returns to the classical beam theory in Chap. 8 to consider beams made up of two or more segments, each having uniform thickness. Chapter 9 serves as a very brief introduction to the effects of constant axial force, variable thickness, or an elastic foundation upon the vibration frequencies of beams. No consideration is given to coupling between bending and torsion, thus limiting the analyses to transverse motion in only Certain planes or to cross-sections having two or more symmetry axes.
433 For the designer or analyst desiring to have extensive tables of free vibration frequencies for rods and beams, the book is highly recommended. However, for a thorough understanding of the behavior of rods and beams undergoing vibration (mode shapes, stresses, forces transmitted to foundations, effects of axial force, shear deformation, beam rotary inertia, etc.), there are better places to look. A. LEISSA, Professor, Engineering Mechanics, The Ohio State University, Columbus, Ohio, U.S.A.
J. L. Meriam: Statics, SI Version, Second Edition, J. Wiley, New York, 1975, 381 pp. "WIDESPREADadoption of the International System of Units (abbreviated SI after the French 'Le Syst6me International d'Unit6s') by technology throughout the world is an accomplished fact;;. With this statement, Prof. Meriam opens the SI version of the second edition of his text Statics published in 1971. Except for the discussion of systems of units and the law of gravitation, the original second edition and the new SI version are identical. Thus, the SI version retains the clarity of exposition, detailed illustrations, and highly realistic exercise problems of its predecessor. SI is used exclusively, and the controversy over the appropriate unit for pressure or stress is nicely handled by simply stating that the basic unit is the Newton per square metre, which is also called a pascal. Conversion charts in the form of parallel scales showing the corresponding values of common mechanical quantities (length, force, mass, pressure, torque, etc.) in both SI and U.S.-British units are given. These should be a real help to those new to SI in developing a feeling for the amounts represented by the various units involved. The text presents a full vector treatment of three-dimensional statics. Vector methods are not overly emphasized, however, and a scalar approach is used wherever practical. The material is organized into eight chapters, with Appendices on vector analysis, tables of useful properties and mathematical relations, and review problems. Basic concepts are presented in Chap. l, and the concept of force, moment, couple, and equipollent force systems are discussed in Chap. 2. Equilibrium is covered in Chap. 3 and is applied to the force analysis of structures in Chap. 4. Chapter 5 deals with distributed forces, and includes an introduction to fluid statics and stress. Friction, virtual work, and area moments of inertia are covered in Chap. 6-8, respectively. There is more material than is covered in the usual statics course. However, the organization is such that topics can be easily deleted without interrupting the continuity of the presentation. This is a very good text and will undoubtedly find wide acceptance. It should be particularly welcomed by educators in the United States whose desire to use SI in their classes has been hampered by a lack of suitable textbooks. The range of topics covered and the emphasis on the solution of practical problems also make this an excellent reference book for practicing engineers. A companion volume on dynamics is available. K. K. STEVENS,
Professor, The Ohio State University, Columbus, Ohio, U.S.A.
Brown and Root Professor, Dept. of Mechanical Engineering, University of Houston, Houston, TX 77004, U.S.A.
D. J. Gorman: Free Vibration Analysis of Beams and Shafts, Wiley, New York, 1975, 386 pp.
THIS book presents a rather thorough study of free vibration frequencies for straight beams and shafts governed by classical fourth order, Euler-Bernoulli deflection theory. Extensive tabular results are given for frequencies. Mode shapes and bending stresses corresponding to these frequencies are ignored, except in Chap. 6. The effects of shear deformation and rotary inertia of beams are not included. Chapters 1-6 deal with small deflection, transverse vibrations of homogeneous beams having uniform cross-section and no axial loading. In the first chapter the classical eigenvalues for beams having clamped, simply-supported or free boundary conditions are presented. The second chapter extends the types of boundary conditions to include translational or rotational springs and lumped masses. In Chaps. 3-6 a valiant effort is made to extend the analyses of the first two chapters to beams having 2, 3, 4 and more than 4 spans, respectively, although the number of combinations of end and intermediate support conditions becomes, of course, unmanageable and completeness of results must be sacrificed in favor of some of the more interesting and useful possible combinations. Chapter 7 is a brief interlude dealing with the classical, second-order, one dimensional wave equation applied to the torsional vibration of rods having various combinations of clamped, free, elastic, or lumped mass boundary conditions to which is appended 66 pp. of tabulated numerical results for frequency parameters. The author returns to the classical beam theory in Chap. 8 to consider beams made up of two or more segments, each having uniform thickness. Chapter 9 serves as a very brief introduction to the effects of constant axial force, variable thickness, or an elastic foundation upon the vibration frequencies of beams. No consideration is given to coupling between bending and torsion, thus limiting the analyses to transverse motion in only Certain planes or to cross-sections having two or more symmetry axes.
433 For the designer or analyst desiring to have extensive tables of free vibration frequencies for rods and beams, the book is highly recommended. However, for a thorough understanding of the behavior of rods and beams undergoing vibration (mode shapes, stresses, forces transmitted to foundations, effects of axial force, shear deformation, beam rotary inertia, etc.), there are better places to look. A. LEISSA, Professor, Engineering Mechanics, The Ohio State University, Columbus, Ohio, U.S.A.
J. L. Meriam: Statics, SI Version, Second Edition, J. Wiley, New York, 1975, 381 pp. "WIDESPREADadoption of the International System of Units (abbreviated SI after the French 'Le Syst6me International d'Unit6s') by technology throughout the world is an accomplished fact;;. With this statement, Prof. Meriam opens the SI version of the second edition of his text Statics published in 1971. Except for the discussion of systems of units and the law of gravitation, the original second edition and the new SI version are identical. Thus, the SI version retains the clarity of exposition, detailed illustrations, and highly realistic exercise problems of its predecessor. SI is used exclusively, and the controversy over the appropriate unit for pressure or stress is nicely handled by simply stating that the basic unit is the Newton per square metre, which is also called a pascal. Conversion charts in the form of parallel scales showing the corresponding values of common mechanical quantities (length, force, mass, pressure, torque, etc.) in both SI and U.S.-British units are given. These should be a real help to those new to SI in developing a feeling for the amounts represented by the various units involved. The text presents a full vector treatment of three-dimensional statics. Vector methods are not overly emphasized, however, and a scalar approach is used wherever practical. The material is organized into eight chapters, with Appendices on vector analysis, tables of useful properties and mathematical relations, and review problems. Basic concepts are presented in Chap. l, and the concept of force, moment, couple, and equipollent force systems are discussed in Chap. 2. Equilibrium is covered in Chap. 3 and is applied to the force analysis of structures in Chap. 4. Chapter 5 deals with distributed forces, and includes an introduction to fluid statics and stress. Friction, virtual work, and area moments of inertia are covered in Chap. 6-8, respectively. There is more material than is covered in the usual statics course. However, the organization is such that topics can be easily deleted without interrupting the continuity of the presentation. This is a very good text and will undoubtedly find wide acceptance. It should be particularly welcomed by educators in the United States whose desire to use SI in their classes has been hampered by a lack of suitable textbooks. The range of topics covered and the emphasis on the solution of practical problems also make this an excellent reference book for practicing engineers. A companion volume on dynamics is available. K. K. STEVENS,
Professor, The Ohio State University, Columbus, Ohio, U.S.A.