Numerical Analysis of Vibrations of Structures under Moving Inertial Load

Numerical Analysis of Vibrations of Structures under Moving Inertial Load
اسم المؤلف
Czeslaw I. Bajer and Bartlomiej Dyniewicz
التاريخ
27 نوفمبر 2017
المشاهدات
التقييم
Loading...

Numerical Analysis of Vibrations of Structures under Moving Inertial Load
Czeslaw I. Bajer and Bartlomiej Dyniewicz
Contents
1 Introduction .
1.1 Literature Review
1.2 Solution Methods
1.3 Approximate Methods
1.4 Review of Analytical-Numerical Methods in Moving Load
Problems .
1.4.1 d’Alembert Method
1.4.2 Fourier Method
1.4.3 Lagrange Formulation
1.5 Examples .
2 Analytical Solutions
2.1 A Massless String under a Moving Inertial Load .
2.1.1 Case of ? = 1 .
2.1.2 Case of ? = 1 .
2.2 Discontinuity of the Solution .
2.3 Conclusions .
3 Semi-analytical Methods
3.1 String
3.1.1 Fourier Analysis .
3.1.2 The Lagrange Equation .
3.2 Bernoulli–Euler Beam
3.2.1 Fourier Solution .
3.2.2 The Lagrange Equation of the Second Kind
3.2.3 Conclusions .
3.3 Timoshenko Beam
3.3.1 Fourier Solution .
3.3.2 The Lagrange Equation .
3.3.3 Examples .
3.3.4 Conclusions and Discussion .
3.4 Bernoulli–Euler Beam vs. Timoshenko Beam .
3.5 Plate .
3.6 The Renaudot Approach vs. The Yakushev Approach
3.6.1 The Renaudot Approach
3.6.2 The Yakushev Approach
4 Review of Numerical Methods of Solution
4.1 Oscillator .
4.1.1 String Vibrations under a Moving Oscillator
4.1.2 Beam Vibrations under a Moving Oscillator
4.2 Inertial Load .
4.2.1 A Bernoulli–Euler Beam Subjected to an Inertial Load .
4.2.2 A Timoshenko Beam Subjected to an Inertial Load
5 Classical Numerical Methods of Time Integration .
5.1 Integration of the First Order Differential Equations
5.2 Single-Step Method SSpj
5.3 Central Difference Method .
5.3.1 Stability of the Method .
5.3.2 Accuracy of the Method
5.4 The Adams Methods
5.4.1 Explicit Adams Formulas (Open) .
5.4.2 Implicit Adams Formulas (Closed) .
5.5 The Newmark Method
5.6 The Bossak Method
5.7 The Park Method .
5.8 The Park–Housner Method
5.8.1 Stability of the Park–Housner Method .
5.9 The Trujillo Method
6 Space–Time Finite Element Method
6.1 Formulation of the Method—Displacement Approach .
6.1.1 Space–Time Finite Elements in the Displacement
Description .
6.2 Properties of the Integration Schemes
6.2.1 Accuracy of Methods .
6.3 Velocity Formulation of the Method .
6.3.1 One Degree of Freedom System
6.3.2 Discretization of the Differential Equation of String
Vibrations
6.3.3 General Case of Elasticity .
6.3.4 Other Functions of the Virtual Velocity
6.4 Space–Time Element Method and Other Time Integration
Methods
6.4.1 Convergence
6.4.2 Phase Error .
6.4.3 Non-inertial Problems
6.5 Space–Time Finite Element Method vs. Newmark Method
6.6 Simplex Elements
6.6.1 Property of Space Division
6.6.2 Numerical Efficiency .
6.7 Simplex Elements in the Displacement Description
6.7.1 Triangular Element of a Bar Vibrating Axially .
6.7.2 Space–Time Finite Element of the Beam of Moderate
Height .
6.7.3 Tetrahedral Space–Time Element of a Plate
6.8 Triangular Elements Expressed in Velocities
7 Space–Time Finite Elements and a Moving Load
7.1 Space–Time Finite Element of a String
7.1.1 Discretization of the String Element Carrying a Moving
Mass .
7.1.2 Numerical Results .
7.1.3 Conclusions .
7.2 Space–Time Elements for a Bernoulli–Euler Beam Carrying
a Moving Mass
7.2.1 Numerical Results .
7.3 Space–Time Element of Timoshenko Beam Carrying a Moving
Mass .
7.3.1 Conclusions .
7.4 Space–Time Finite Plate Element Carrying a Moving Mass .
7.4.1 Thin Plate
7.4.2 Thick Plate .
7.4.3 Plate Placed on an Elastic Foundation .
7.5 Problems with Zero Mass Density .
8 The Newmark Method and a Moving Inertial Load
8.1 The Newmark Method in Moving Mass Problems .
8.2 The Newmark Method in the Vibrations of String
8.3 The Newmark Method in Vibrations of the Bernoulli–Euler
Beam
8.4 The Newmark Method in Vibrations of a Timoshenko Beam
8.5 Numerical Results
8.6 Accelerating Mass—Numerical Approach
8.6.1 Mathematical Model .
8.6.2 The Finite Element Carrying the Moving Mass Particle
8.6.3 Accelerating Mass—Examples .
8.7 Conclusions .
9 Meshfree Methods in Moving Load Problems
9.1 Meshless Methods (Element-Free Galerkin Method)
9.2 Results
10 Examples of Applications
10.1 Dynamics of the Classical Vehicle–Track System .
10.2 Dynamics of the System Vehicle—Y-Type Track .
10.3 Dynamics of Subway Track .
10.4 Vibrations of Airport Runways
Appendix .
A Computer Programs .
A.1 String—Space–Time Element Method
A.2 Timoshenko Beam—Newmark Method .
A.3 Mindlin Plate—Space–Time Element Method
A.4 Kirchhoff Plate — Space-Time Element Method .
References
Index
كلمة سر فك الضغط : books-world.net
The Unzip Password : books-world.net

تحميل

يجب عليك التسجيل في الموقع لكي تتمكن من التحميل
تسجيل | تسجيل الدخول

التعليقات

اترك تعليقاً