Engineering vibration analysis : worked problems
著者
書誌事項
Engineering vibration analysis : worked problems
（Foundation of engineering mechanics）
Springer-Verlag, c2004
- v. 1
- v. 2
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注記
Vol. 2 translated by A.S. Lidvansky and R.A. Mukhamedshin
内容説明・目次
- 巻冊次
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v. 1 ISBN 9783540206583
内容説明
Theory of vibrations belongs to principal subjects needed for training mechani cal engineers in technological universities. Therefore, the basic goal of the mono graph "Advanced Theory of Vibrations 1" is to help students studying vibration theory for gaining experience in application of this theory for solving particular problems. Thus, while choosing the problems and methods to solve them, the close attention was paid to the applied content of vibration theory. The monograph is devoted to systems with a single degree of freedom and sys tems with a finite number of degrees of freedom. In particular, problems are for mulated associated with determination of frequencies and forms of vibrations, study of forced vibrations, analysis of both stable and unstable vibrations (includ ing those caused by periodic but anharmonic forces). The problems of nonlinear vibrations and of vibration stability, and those related to seeking probabilistic characteristics for solutions to these problems in the case of random forces are also considered. Problems related to parametric vibrations and statistical dynamics of mechanical systems, as well as to determination of critical parameters and of dy namic stability are also analyzed. As a rule, problems presented in the monograph are associated with particular mechanical systems and can be applied for current studies in vibration theory. Al lowing for interests of students independently studying theory of vibrations, the majority of problems are supplied with either detailed solutions or algorithms of the solutions.
目次
Problems and Examples in Vibration Theory.- 1 Vibrations of Systems with a Single Degree of Freedom.- 1.1 Free Vibrations.- 1.2 Free Vibrations of Systems with Allowance for Resistance Forces.- 1.3 Forced Vibrations.- 1.4 Critical States and Vibration Stability.- 1.5 Parametric Vibrations.- 1.6 Nonlinear Vibrations.- 2 Vibrations of Systems with Several Degrees of Freedom.- 2.1 Free Vibrations.- 2.2 Forced Vibrations.- 2.3 Critical States and Vibration Stability.- 2.4 Approximate Methods of Determining the Lowest Frequency.- 2.5 Random Vibrations.- Answers and Solutions.- 1 Vibrations of Systems with a Single Degree of Freedom.- 1.1 Free Vibrations.- 1.2 Free Vibrations of Systems with Allowance for Resistance Forces.- 1.3 Forced Vibrations.- 1.4 Critical States and Vibration Stability.- 1.5 Parametric Vibrations.- 1.6 Nonlinear Vibrations.- 2 Vibrations of Systems with Several Degrees of Freedom.- 2.1 Free Vibrations.- 2.2 Forced Vibrations.- 2.3 Critical States and Vibration Stability.- 2.4 Approximate Methods of Determining the Lowest Frequency.- 2.5 Random Vibrations.- References.- Appendices.
- 巻冊次
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v. 2 ISBN 9783540207825
内容説明
Constantly increasing attention is paid in the course 'Vibration 'Theory' to vibration of mechanical systems with distributed parameters, since the real elements of machines, devices, and constructions are made of materials that are not perfectly rigid. 'Therefore, vibrations of the objects including, for ex ample, rod elastic elements excite the vibrations of these elements, which can produce a substantial effect on dynamic characteristics of moving objects and on readings of instruments. For a mechanical engineer working in the field of design of new technolo gies the principal thing is his know-how in developing the sophisticated math ematical models in which all specific features of operation of the objects under design in real conditions are meticulously taken into account. So, the main emphasis in this book is made on the methods of derivation of equations and on the algorithms of solving them (exactly or approximately) taking into con sideration all features of actual behavior of the forces acting upon elastic rod elements. 'The eigen value and eigen vector problems are considered at vibrations of curvilinear rods (including the rods with concentrated masses). Also consid ered are the problems with forced vibrations. When investigating into these problems an approximate method of numerical solution of the systems of lin ear differential equations in partial derivatives is described, which uses the principle of virtual displacements. Some problems are more complicated than others and can be used for practical works of students and their graduation theses.
目次
1 Problems and Examples.- 2 Answers and solutions.- References.- A Statics of rods: basic equations.- A.1 Derivation of nonlinear equations of rod equilibrium.- A.2 Transformations of base vectors.- A.5 Vector equation of displacements of points of the rod axial line.- A.7 System of nonlinear equations of rod equilibrium.- A.8 Reduction of equations to dimensionless notation.- A.9 Boundary conditions.- A.10 External load and its behaviour under rod loading process.- A.11 Vector nonlinear equations of rod equilibrium in the bound coordinate system.- A.12 Equations of rod equilibrium in projections onto bound axes.- A.13 Special cases of equilibrium equations.- B Basic equations of rod kinematics.- B.2 Absolute and local derivatives of a vector with respect to time.- B.3 Velocity and acceleration of a point of the rod axial line.- C Basic equations a rod dynamics.- C.1 Nonlinear vector equations of motion of three-dimensional curvilinear rods.- C.2 Reduction of equations to dimensionless form.- C.3 Equations of small vibrations of rods (linear equations).- C.4 Equations of small vibrations in projections onto bound axes.- C.5 Equations of small vibrations of a rod whose axial line in the unloaded state is a plane curve.- D Exact numerical method of determining the frequencies and modes of rod vibrations.- D.1 Determination of eigen values (frequencies).- D.2 Determination of eigen functions for conservative problems.- E Approximate numerical determination of frequencies at small vibrations of rods.- F Approximate solution of equation of rod forced vibrations.
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