Finite Element Analysis of Vibration Problems in Engineering

                                 Course-1: Modal and Harmonic Analysis

Chapter

Topic

I

Introduction  

(a)  Preamble

      Definition of FEM

      Applications of FEM in the study of Vibration Problems

      Methodology of application of the technique

(b) Review of basic definitions and principles

      Definition of Vibration

      Periodic Motion – Simple Harmonic Motion (SHM)

      Equation of Motion of a particle

      Elements of Vibrating Systems (Spring, Mass, Damper)

      Degree of Freedom – SDFS, MDFS and Infinite DFS

      Classification of Vibration Problems

      Difference between Linear & Nonlinear Vibrations

      FEM formulation principles

      Consistent & Lumped Mass Matrix Formulations

      Units and Dimensions

II

Analysis of Truss Problems

   Introduction

   Study Problems

Project Problem – 1

Project Problem – 2

   Project Problem – 3

III

Analysis of Beam Problems

   Introduction

   Study Problems

Project Problem – 1

Project Problem – 2

   Project Problem – 3

IV

Analysis of Frame Problems

   Introduction

   Study Problems

Project Problem – 1

Project Problem – 2

   Project Problem – 3

V

Two-Dimensional Problems

   Introduction

   (a) Plane Stress Problems

   (b) Plane Strain Problems

Project Problem – 1

Project Problem – 2

   Project Problem – 3

VI

Analysis of Axisymmetric Problems

   Introduction

   Study Problems

Project Problem – 1

Project Problem – 2

   Project Problem – 3

VII

Plate and Shell Structures

  Introduction

   Study Problems

Project Problem – 1

Project Problem – 2

   Project Problem – 3

VIII

Three-dimensional Problems

   Introduction

   Study Problems

Project Problem – 1

Project Problem – 2

Project Problem – 3

IX

Composite Structures

   Introduction

   Study Problems

Project Problem – 1

Project Problem – 2

   Project Problem – 3

X

Fluid-Structure Interaction

   Introduction

   Study Problems

Project Problem – 1

Project Problem – 2

   Project Problem – 3

XI

Harmonic Analysis

   Introduction

   Study Problems

Project Problem – 1

Project Problem – 2

   Project Problem – 3

XII

Critical Speed Calculations

   Introduction

   Study Problems

XIII

Campbell Diagrams and their usage in Vibration Analysis

   Introduction

   Study Problems

XIV

Pre-Stress Effects on Vibration Characteristics

   Introduction

   Study Problems

XV

Classification of Finite Element Software

(a)     Classical and Commercial Software

(b)     General Purpose and Special Purpose Software

(c)  Standard FEM Modules

(d)     FEM Editors (Pre-/Post-Processors)

(e)     Solid Modelers

References:

1. Introduction to Finite Elements in Engineering

    T.R. Chandru Patla and A.D. Belegundu, Prentice Hall of India Pvt. Ltd., 1991

2. Mechanical Vibrations

    Singiresu S. Rao, McGraw -Hill International Edition, 1987

 3. Finite Element Hand Book

     H. Kardestuncer & D.H. Norrie (Editors), McGraw -Hill International Edition, 1987

 

                                                                       

 

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