Structural Dynamics

Yong Bai, Zhao-Dong Xu, Zhao-Dong Xu

• Publisher: Wiley-Scrivener
• Year: 2019
• ISBN:
  9781119605812
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

Written by two experts across multiple disciplines, this is the perfect reference on structural dynamics for veteran engineers and introduction to the field for engineering students.

Across many disciplines of engineering, dynamic problems of structures are a primary concern. Civil engineers, mechanical engineers, aircraft engineers, ocean engineers, and engineering students encounter these problems every day, and it is up to them systematically to grasp the basic concepts, calculation principles and calculation methods of structural dynamics. This book focuses on the basic theories and concepts, as well as the application and background of theories and concepts in engineering.

Since the basic principles and methods of dynamics are applied to other various engineering fields, this book can also be used as a reference for practicing engineers in the field across many multiple disciplines and for undergraduate and graduate students in other majors as well. The main contents include basic theory of dynamics, establishment of equation of motion, single degree of freedom systems, multi-degree of freedom systems, distributed-parameter systems, stochastic structural vibrations, research projects of structural dynamics, and structural dynamics of marine pipeline and risers.

Whether for the veteran engineer or student, this is a must-have for any scientific or engineering library.

Useful for students and veteran engineers and scientists alike, this is the only book covering these important issues facing anyone working with coastal models and ocean, coastal, and civil engineering in this area.

Chapter 1
Introduction

1.1 Overview of Structural Dynamics

Have you ever thought about the technology used in the Shenzhou spacecraft that we are all so proud of? Have you ever thought about what kind of marvelous power it takes to make planes which weigh tons fly while we enjoy them? What’s the reason for the collapse of Tacoma Narrows Bridge when it suffered 19m/s wind? Why are buildings with seismic resistance and isolation technology considered better in terms of seismic safety? All those subjects exist in nature, and are aspects of the subject of advanced dynamics as well.

The theoretical study of dynamics began in the seventeenth century, and the publication of Analytical Mechanics by Joseph Louis Lagrange (1736–1813) laid the foundation for the dynamic analysis in the linear system. With the development of science and technology, a variety of dynamic dives are applied to different engineering structures, which allows the theory of structural dynamics to move forward constantly. Up to now, we can already accomplish the dynamical analysis for huge complex structures with thousands of freedom degrees.

With regard to the design or analysis for a structure, static problems are always major areas which should be of primary concern. However, a structure often comes to failure when critically subjected to dynamic loading. Structural dynamic analysis thus frequently plays as the control function in a structure’s design, which may be far more critical than static load for the damages of a structure. Examples include seismic-induced structure collapse, wind-induced failure of bridges or other long-span flexible structures, deformation of pile and destabilization of foundation under impact loads. Thus, it’s indispensable to conduct the dynamic analysis for engineering structures’ study, design, and security evaluation. Despite the fact that numerous pseudo-static calculation methods are adopted in some specifications for structural design and structural dynamic analysis for simplicity, such as the response spectrum method in seismic design code or the equivalent statics wind stress which is used to substitutes the actual wind stress in wind-resistance design, their theoretical basis is still from structure dynamics. Hence, it’s still essential to conduct the dynamic analysis in these solution procedures, such as solving the structure’s natural period and modes in multi-degree-of-freedom system, all of which are necessary parameters involved in response spectrum method.

Structural dynamics is a theoretical and technical subject to study the dynamic characteristics of structural systems (mainly referring to the period, frequency, mode, and damping characteristics) and determine the dynamic responses of structures under dynamic loads (including internal force, strain, displacement, speed, acceleration etc.). The fundamental purpose of this discipline is to provide a solid theoretical basis for improving the safety and reliability of engineering structural systems in the dynamic environment.

1.2 Dynamic Loads

According to whether a load is time-varying or not, loads are divided into dynamic load and static load. For static load, its magnitude, direction, and action point of static loads don’t change or change with time slightly, such as dead weight of structure, snow load, ash load, etc. On the other hand, dynamic loads change with time. In addition, dynamic loads will also bring structure inertial forces, which cannot be neglected and must be taken into consideration. Typical dynamic loads include simple harmonic oscillation caused by working machinery, wind loads, seismic loads, etc.

1.2.1 Simple Harmonic Loads

Simple harmonic loads are the loads varying with time harmonically and periodically, which can be represented by harmonic function, such as P(t)=P₀sinθt and Ρ(t)=P₀cosθt. Analyses of structural response under the simple harmonic loads are of great importance, not only because these dynamic loads actually exist in engineering structures (centrifugal load caused by cam axial rotation), but also any nonharmonic periodic loads can be represented as a sum of a series of simple harmonic components. Thus, in principle, structural dynamic response caused by any periodic loading can be translated into a superposition of responses created by a series of simple harmonic components. Furthermore, the responses of a structure under simple harmonic loads can reflect its dynamic characteristics; therefore simple harmonic loads play a vast role in the structural dynamic analysis.

Figure 1.1 Classification of dynamic loads.

1.2.2 Nonharmonic Periodic Loads

Nonharmonic periodic loads are periodic functions of time, which vary with time periodically. They are different from simple harmonic functions. Examples include the hydrodynamic pressure of calm waves on dams and thrust generated by a propeller of a ship.

1.2.3 Impulsive Load

Magnitude of impulsive load can increase or decrease rapidly in short duration, for example, impact load produced by explosion or blast.

1.2.4 Irregular Dynamic Load

Irregular dynamic loads are difficult to be expressed by analytic expression because of the complexity and arbitrariness of its magnitude, direction, and position, such as earthquake action or wind load acting on the structure.

Four classifications of loads are shown in Figure 1.2.

Figure 1.2 Types of dynamic load.

1.3 Characteristics of a Dynamic Problem

A structural dynamic problem is intended to solve for the response of the structure under dynamic loads, which differs from its static loading counterpart in the following two important aspects.

The first is the time varying nature of the dynamic problem. Because the dynamic loads vary with time, the analyst must calculate a succession of solutions corresponding to all times in the response history when computing the dynamic responses of structure. Thus, a dynamic analysis is clearly more complex and time-consuming than a static analysis.

Secondly, the inertia force must be considered in the dynamic problem. Compared with the static problems, the inertial force brought in by acceleration due to rapid variation of displacement in the structural dynamic reaction will seriously influence the structural dynamic response, and the direction of inertia force oppose the direction of acceleration.

If a simple beam is subjected to a static load, F, as shown in Figure 1.3, forces acting on the simple beam are only external force, F, and support reactions. However, if F is a dynamic load, displacement of the beam will change rapidly. Therefore, in addition to external force F and support reactions, there is also an inertial force distributed along the beam’s central axis acting on the simple beam. Magnitude of the inertial force depends on motion of the beam, which is significantly influenced by the inertial forces themselves. Occurrence of inertial force makes analysis of structure responses more complex. Especially when the loading rate gets faster, the additional responses induced by inertial force may be far bigger than the corresponding responses caused by static force.

Figure 1.3 The difference between static and dynamic.

Dynamic calculations must be conducted in all time domain, while inertia force induced impact must be taken into consideration. Occurrence of inertial force makes analysis more complex, but understanding and effective treatment can significantly simplify the complexity of dynamic analysis.

Structural dynamics differs from statics due to the inclusion of inerti...

Table of contents

• Cover
• Title Page
• Copyright
• Preface
• About the Authors
• Chapter 1: Introduction
• Chapter 2: Establishment of the Structural Equation of Motion
• Chapter 3: Single Degree of Freedom Systems
• Chapter 4: Multi-Degree of Freedom System
• Chapter 5: Distributed-Parameter System
• Chapter 6: Stochastic Structural Vibrations
• Chapter 7: Research Topics of Structural Dynamics
• Chapter 8: Structural Dynamics of Marine Pipeline and Riser
• Answers to Exercises
• Index
• End User License Agreement