Arashigore The country you have selected will result in the following: Approximate and numerical methods All instructor resources are now available on our Instructor Hub. The Bookshelf application offers access: In February Dr. The key assets of the book include comprehensive coverage of both the traditional and state-of-the-art numerical techniques of response analysis, such as the analysis by numerical integration of the equations of motion and analysis through frequency domain. Dynamics of Structures 3rd Edition J. Please accept our apologies for any inconvenience this may cause.

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Structural dynamics. Title TA6S4. Typesetting: Macmillan India Ltd. Nature of exciting forces : Dynamic forees caused by rotating machinery 1. Blast loads. Periodic and nonperiodic loads Systems with localized mass but distributed stiffness 2. Systems with distributed mass but localized stiffness 2.

Formulation of the equations of motion 84 3. Transformation of coordinates 3. Finite element method : iil 3. Selection of shape functions 3. Mass matrix of a beam element. Static condensation of stiffness matrix 3. Free vibrations with viscous damping 5. Overdamped system 5. Underdamped system 5. Damped free vibration with Coulomb damping 5.

Response to general dynamic loading. Response to a step function load : 7. Response to shock loading : Triangular pulse 7. Response to a periodically applied load Properties of standard eigenvalues and eigenvectors Implicit integration Self-adjointness of operators in the eigenvalue problem Simply supported beam Uniform cantilever beam Uniform beam clamped at both ends. The book attempts to explain the mathematical basis for the concepts presented, mostly in physically motivated terms or through heuristic argument, No special mathematical background is required of the reader, except for a basic knowledge of college algebra and calculus and engineering mechanics.

The essential steps in the dynamic analysis of a system are: a mathematical modeling b formulation of the equations of motion, and c solution of the equations. Modeling techniques can be divided into two broad categories. In one technique, the system is modeled as an assembly of rigid body masses and massless deformable elements, Systems modeled in this manner are referted to as discrete parameter systems.

In the other technique of modeling, both mass and deformabilty are assumed 0 be distributed throughout the extent of the system which is treated as continuous. Systems modeled in this manner are called continuous or distributed parameter systems.

In general, a continuous model will better represent the behavior of a dy- namical system. However, in most practical situations, the equations of motion of a continuous system are t00 difficult or impossible to solve, Therefore, in 4 majority of cases, dynamic analysis of engineering structures must rely on a representation of the structure by a discrete parameter model. The contents of the book reflect this emphasis on the use of discrete models. The first three parts of the book are devoted to the analysis of response of discrete systems.

Part 1, consisting of Chapters 2 through 4, deals with the formulation of equa- tions of motion of discrete parameter systems. XVI Humar Part 2 of the book, covering Chapters 5 through 9, deals with the solution of equation of motion for a single-degree-of-freedom system.

Part 3, consisting of Chapters 10 through 13, discusses the solution of equations of motion for multi degree-of-freedom systems. Part 4 of the book, covering Chapters 14 through 17, is devoted to the analysis of continuous system. Again, the subject matter is organized so that the formulation of equations of motion is presented first followed by a discussion of the solution techniques.

Many readers may prefer to complete a study of the single-degree-of-freedom systems, from formulation of equation to their solu- tion, before embarking on a study of multi-degree-of-freedom systems. This can be easily achieved by selective reading. The book chapters have been planned so that Chapters 3 and 4 relating to the formulation of equations of motion of a general system need not be studied prior to studying the material in Chapters 5 through 9 on the solution of equations of motion for a single-degree-of-freedom system.

A development that has had a profound effect in the recent times on proce- dures for the analysis of engineering systems is the advent of digital computers. Chapter 8 on single-degree-of-freedom systems and Chapter 13 on multi-degree-of-freedom systems, are devoted exclusively to numerical techniques of solution.

A fairly detailed treatment of the frequency domain analysis is included in Chapters 9 and 13, in recognition of the effi ciency of this technique in the numeric computation of response.

Also, a detailed treatment of the solution of discrete eigenproblems which plays a central role in the numerical analysis of response is included in Chapter 11 It is recognized that the field of computer hardware as well as software is undergoing revolutionary development. Program listings or detailed algorithms have not therefore been included in the book. Some of it has now become a part of the historical development of structural dynamics, other is more recent. The author offers his apologies to all researchers who have not been adequately recognized.

Refer- cences have been omitted from the text to avoid distracting the reader. However, where appropriate, a brief list of suitable material for further reading is provided at the end of each chapter. In preparing this second edition, the errors that had inadvertently crept into the first edition have been corrected.

Also included are additional end-of-chapter exercises for the benefit of the reader. All symbols, includ- ing those listed here, are defined at appropriate places within the text, usually at the time of their first occurrence. Occasionally, the same symbol may be tused to represent more than one parameter, but the meaning should be quite unambiguous when read in context.

An overdot signi- fics differential with respect to time and a prime stands for differentiation with respect to the argument of the function. The response of physical objects to dynamic or time-varying loads is an im- portant area of study in physics and engineering.

The physical object whose response is sought may cither be treated as rigid-body or considered to be deformable, The subject of rigid-body dynamics treats the physical objects as rigid bodies that undergo motion without deformation when subjected to dy- namic loading.

The study of rigid-body motion has many applications, including, for example, the movement of machinery, the flight of an aircraft or a space vehicle, and the motion of earth and the planets. In many instances, however, dynamic response involving deformations, rather than simple rigid-body motion, is of primary concem. This is particularly so in the design of structures and structural frames that support manufactured objects.

Structural frames form a part of a wide variety of physical objects created by human beings: for exam- ple, automobiles, ships, aircraft, space vehicles, offshore platforms, buildings, and bridges. Such equilibrium configuration may be static, that is, time invariant, or it may be dynamic involving rigid-body motion, Consider, for example, the vibrations ofa building under the action of wind.

In the absence of wind, the building structure is in a state of static equilibrium under the loads acting on it, such as those due to gravity, earth pressure, and so on. The aircraft can be ideatized as consisting of rigid-body masses of fuselage and the engines con- nected by flexible wing structure Fig.

When in flight, the whole system moves as a rigid body and may, in addition, be subjected to oscillatory motion transverse to the fight plane. Motions involving deformation are caused by dynamic forces or dynamic disturbances. Dynamic forces may, for example, be induced by rotating 2 Humar Figure 1. Oscillatory motion of a building fame under wind losd. Engine Engine Engine Engine Figure 1. A dynamic disturbance may result from an earthquake during which the motion of the ground is transmitted to the supported structure.

Later in this chapter, we discuss briefly the nature of some of the dynamic forces and disturbances. Whatever be the cause of excitation, the resulting oscillatory motion of the structure induces displacements and stresses in the latter.

An analysis of these displacements and stresses is the primary objective of a study of the dynamics of structures, 1. Under certain sit- uations, vibrations may cause large displacements and severe stresses in the structure. As we shall see later, this may happen when the frequency of the exciting force coincides with a natural frequency of the structure, Also, fluctu- ating stresses, even of moderate intensity, may cause material failure through Introduction 3 fatigue if the number of repetitions is large enough.

Oscillatory motion may at times cause wearing and malfunction of machinery. Also, the transmission of vibrations to connected structures may lead to undesirable results.

Vibrations induced by rotating of reciprocating machinery may, for example, be transmit- ted through the supporting structure to delicate instruments mounted elsewhere oon it, causing such instruments to malfunction.

Finally, when the structure is designed for human use, vibratory motion may result in severe discomfort to the occupants.

With progress in engineering design, increasing use is being made of light- weight, high strength materials. This is as true of mechanical structures as of buildings and bridges. This is in general true except for certain mechanical ma- chinery which relies on controlled vibration for its functioning.

In any case, whether or not the vibrations arise from natural causes or are induced on purpose, the structure subjected to such vibrations must be designed for the resultant displacements and stresses. The exciting forces may also be classified according to the nature of their variation with time as periodie, nonpe- riodic, ot random. It is also useful to classify dynamic forces as deterministic, being specified as a definite funetion of time, or nondererministic, being known only in a statistical sense.

In the following, we discuss briefly each of these classifications. Both forces depend on the wind velocity, the wind profile along the height of the structure, and the characteristics of the structure. Winds close to the surface of the earth are affected by turbulence and hence vary with time.

Estimates of design wind speeds are obtained by measurements of wind in an open exposure, often at an airport, at a standard height, usually 10m or 30f. Records are kept of maximum daily time-averaged mean wind speeds Obviously, the mean wind will depend on the time used for the purpose of averaging. Design codes generally specify the use of a maximum mean wind with given recurrence period.

A typical value of recurrence period for strength design of buildings subjected to wind loads is 30 years. The corresponding design wind is usually obtained by a statistical analysis of the recorded data on hourly mean winds, The variation of wind along the height, called wind profile, is determined on the basis of analytical studies and experimental observation.

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