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2014 | Buch

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Structural Dynamics

verfasst von: Einar N. Strømmen

Verlag: Springer International Publishing

Buchreihe : Springer Series in Solid and Structural Mechanics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book introduces to the theory of structural dynamics, with focus on civil engineering structures that may be described by line-like beam or beam-column type of systems, or by a system of rectangular plates. Throughout this book the mathematical presentation contains a classical analytical description as well as a description in a discrete finite element format, covering the mathematical development from basic assumptions to the final equations ready for practical dynamic response predictions. Solutions are presented in time domain as well as in frequency domain. Structural Dynamics starts off at a basic level and step by step brings the reader up to a level where the necessary safety considerations to wind or horizontal ground motion induced dynamic design problems can be performed. The special theory of the tuned mass damper has been given a comprehensive treatment, as this is a theory not fully covered elsewhere. For the same reason a chapter on the problem of moving loads on beams has been included.

Inhaltsverzeichnis

Frontmatter

Basic Theory

Abstract

This text book focuses on the prediction of dynamic response of slender line-like civil engineering structures. It is a general assumption that structural behaviour is linear elastic and that any non-linear part of the relationship between load and structural displacements may be disregarded. It is taken for granted that the load direction throughout the entire span of the structure is perpendicular to the axis in the direction of its span.

Einar N. Strømmen

One and Two Degree of Freedom Systems

Abstract

While we in Chapter 1 focused on the basic mathematical methods of determining the structural properties of free vibrations, we shall now turn to the more realistic cases of including the effects of damping and the possibility of an external fluctuating force. However, in this chapter we limit ourselves to only consider the cases of single or two degrees of freedom systems, subject to a single harmonic force. Such a load case is virtually absent in the field of structural dynamics. Nonetheless, the case of a single harmonic force on simple systems is an illustrative overture to the ensuing chapters in this book. It is taken for granted that forces are rectilinear.

Einar N. Strømmen

Eigenvalue Calculations of Continuous Systems

Abstract

A simple beam is defined as a single span beam whose cross section is symmetric about the y - as well as the z - axis, i.e. its shear centre and its centre of pure linear bending coincides with its mass centre ( e _y = e _z = 0 ). It is homogenous and line-like in the sense that along the entire span it contains only one type of material, and the cross section is small as compared to the length of the beam such that it may mathematically be modelled as a single line through its shear centre.

Einar N. Strømmen

The Finite Element Method in Dynamics

Abstract

As linearity has been taken for granted, a formal finite element approach to the problem of structural dynamics will comply with the computational methods usually applied elsewhere in theory of elasticity. However, in dynamics it is necessary to add the effects of mass in motion as well as internal damping, which, for a line like system, will affect the shape of motion into a combination of harmonic and hyperbolic functions, see Chapter 3, and thus also the overall physical properties of the system.

Einar N. Strømmen

The Normal Mode Method

Abstract

In Chapter 4 we developed the equilibrium condition

M.r̈(t)+C.ṙ(t)+K.r(t)=R(t)

for a general discrete system with a chosen set of degrees of freedom r = [r ₁...r _p...r _Nr]^T and subject to a corresponding set of external loads R = [R ₁...R _p...R _Nr]^T.

Einar N. Strømmen

Frequency and Time Domain Response Calculations

Abstract

The relevant equilibrium equations that are necessary for the pursuit of a solution to the problem of dynamic load effects have been developed above, in Chapters 4 with respect to the original degrees of freedom (see Eq. 4.39) and in Chapter 5 with respect to the modal degrees of freedom (see Eq. 5.13 for a discrete system description and Eq. 5.32 for a continuous system description). In this chapter we shall present possible solution strategies. Basically, one is free to choose whichever approach is deemed most suitable solution strategy, e.g. with respect to efficiency or accuracy.

Einar N. Strømmen

Dynamic Response to Earthquake Excitation

Abstract

Earthquake excitation of civil engineering structures is in general a complex process. However, an idealised situation where the structure is subject to representative single component horizontal ground acceleration will usually suffice for design purposes. The problem of dynamic response calculations under such excitation is pursued in the present chapter. For simplicity, the focus of the theory below is limited to structures with main extension in the vertical direction (e.g. vertical frames or cantilevered type of tower buildings).

Einar N. Strømmen

Wind Induced Dynamic Response Calculations

Abstract

It is in the following taken for granted that the main wind direction throughout the entire span of the structure is perpendicular to the direction of its span. The wind velocity vector is split into three fluctuating orthogonal components, U in the main wind direction, and v and w in the across wind horizontal and vertical directions. Typical full scale recordings of U, v and w are illustrated in Figs. 8.1 and 8.2 above.

Einar N. Strømmen

Damping

Abstract

The introduction of small or moderate damping forces into the theory of structural dynamics is based on the simple observation that any linear elastic system set into a free unloaded motion will harmonically oscillate in a characteristic modeshape which gradually decays until the system again is at rest. The preference of a harmonic modeshape is usually associated with the characteristic largest period (i.e. the lowest eigenfrequency) of the system, as this is its slowest possible free motion, and therefore it requires the least amount of energy exchange between inertia and stress fluctuations. The reason for the decay of the motion (diminishing of kinetic energy) is ascribed to damping forces within the system or between the system and its surrounding air or water.

Einar N. Strømmen

Rectangular Plates

Abstract

The development below is limited to cover the theory of rectangular thin and plane plates. It is often referred to as the Kirchhoff-Love theory, as it was first presented by A.E.H. Love [45] based on basic assumptions outline by G.R.

Einar N. Strømmen

Moving Loads on Beams

Abstract

An investigation of the dynamic load effects of moving loads on beams may be required in cases of heavy vehicles or a train passing a flexible bridge, though the problem may not necessarily be that of the bridge, it may also involve uncomfortable vertical oscillations of the vehicle. The problem may also occur on moving hoisting forces on heavy cranes.

Einar N. Strømmen

Backmatter

Titel: Structural Dynamics
verfasst von: Einar N. Strømmen
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-01802-7
Print ISBN: 978-3-319-01801-0
DOI: https://doi.org/10.1007/978-3-319-01802-7

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