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Vibration of Timoshenko Beam using Laplace Transform

Vibration of Timoshenko Beam using Laplace Transform

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DEDICATION

This research material, titled “Vibration of Timoshenko Beam using Laplace Transform” is dedicated to God for His boundless grace and guidance. It is also a tribute to all computer enthusiasts whose contributions made my research journey smoother and enriched my documentation process, making the experience truly fulfilling.



ACKNOWLEDGEMENT

I am profoundly grateful to everyone who contributed to the successful completion of this project. I am especially grateful to my Supervisor (Name), the Head of Department (Name), and the Lecturers in the Department of Mathematics for their invaluable guidance and support. I also acknowledge the contributions of authors and scholars whose works on Vibration of Timoshenko Beam using Laplace Transform provided essential insights. Special thanks go to my study area (and any funding organizations, if applicable) for their financial assistance. I am equally thankful to stakeholders, including mentors, teachers, and colleagues, for their encouragement and support. Finally, I deeply appreciate my family and friends for their patience and unwavering support throughout this journey. Your contributions have been instrumental in making this research a reality.



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 conceputal review, theoretical framework, the review of related literature …

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Defense Procedure for Mathematics Researchers

In preparation for defending a project or seminar on Vibration of Timoshenko Beam using Laplace Transform, it is imperative that as a nursing student, you demonstrate comprehensive knowledge of your research. The defense process is structured to include presenting your work, answering questions, and illustrating its pertinence. Initially, provide a succinct yet thorough introduction to your research topic, emphasizing its importance and the objectives, ensuring that both the audience and the External Examiner can understand the scope of your study.

Prior to your defense, be thoroughly acquainted with your research abstract and the critical elements of Chapter One, including motivation for embarking on this research, problem statement, objectives, and significance. In Chapter Two, be ready to cite at least two references from the literature review. For Chapter Three, you should be equipped to discuss the methodologies, tools, and techniques utilized. In Chapter Four, defend your research by justifying the findings and linking them to your research objectives.

Conclude your defense by succinctly summarizing the study and offering insightful, evidence-based recommendations. A professional dress code, such as wearing a suit and tie, is vital to create a favorable impression and elevate your presentation.

During the question and answer segment, the External Examiner may pose questions pertaining to your research. If confronted with a challenging or irrelevant question, respond diplomatically with, “Sorry, Sir/Madam, the question asked is beyond the scope of my study.” Whenever possible, direct your answers back to your research findings to reinforce your expertise.

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