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Vibration of Timoshenko Beam using Laplace Transform

Vibration of Timoshenko Beam using Laplace Transform

Project / Seminar Material
Reference ID: PS-23890-TM

DEDICATION

This research material titled “Vibration of Timoshenko Beam using Laplace Transform” is dedicated to God for his enabling grace, and to all computer enthusiasts who contributed to make life a pleasant experience during my research documentation.

ACKNOWLEDGEMENT

I extend my sincere gratitude to all those who contributed to the completion of this project. Special thanks to my Supervisor (Name of your Supervisor), the Head of Department (Name of your HOD), the Lecturers in the department of Mathematics, Book Authors and Profound Scholars of existing or related project material on “Vibration of Timoshenko Beam using Laplace Transform” for their invaluable guidance, support, and expertise throughout the journey.

I am also grateful to your study area (mention any funding organizations, if applicable) for their financial assistance. This research would not have been possible without the encouragement and assistance of some stakeholders (mention any mentors, teachers, or colleagues). Additionally, I would like to acknowledge the understanding and patience of my family and friends during this endeavor. Your unwavering support has been a constant source of motivation. Thank you all for being part of this meaningful endeavor.

ABSTRACT

The study evaluates the Vibration of Timoshenko Beam using Laplace Transform, thereby eliminating the problems of the Vibration of Timoshenko Beam. The application of Laplace Transform to case of continuous beam vibration, it is quite necessary and encouraged to carry out related studies on the application method. The Laplace transform method provided the means to obtain a solution to a vibrating system subject to a set of general boundary conditions and to four different types of in-span attachments applied simultaneously. Boundary conditions related to the initial-boundary value problem under consideration were described by a proper differential equation of both or only one of those functions. Construction of the dynamic Green functions was proposed to solve the problem of forced vibration amplitudes of the beam, excited by an arbitrary function of time t and applied to a beam in an arbitrary way, as a function of the spatial coordinate x. This study will be of immense benefit to mathematician, statistician, and other researchers who intend to know more on this study and can also be used by non-researchers to build more on their research work. This study contributes to knowledge and could serve as a guide for other study.


Vibration of Timoshenko Beam using Laplace Transform

CHAPTER ONE

1.1 Introduction

… As a prelude to other parts of this study, this chapter will discuss the background upon which this study was initiated, the statement of problems that led to this study, the Aim and Objectives of the study. Others are Significance of the study, Scope of work, Research hypothesis and questions, Limitation of the study and Definition of technical terms.

CHAPTER TWO

2.0 Literature Review

2.1 Introduction

This chapter focuses on the review of related literature. A literature review includes the current knowledge as well as theoretical and methodological contributions to a particular topic. It documents the state of the art with respect to the topic you are writing. It surveys the literature in the topic selected. In this research work the literature review includes the …

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