This page presents an excerpt of the research material, providing a comprehensive overview of the study. It includes the Preliminary Pages, Table of Contents, Abstract, Chapters One to Five, and References, making it accessible and informative for students, researchers, and other readers interested in the topic of this study. Acknowledgement is also included, expressing gratitude to the individuals, institutions, and resources that contributed to the successful completion of the research, with materials and information sourced from the online platform sparklyn.com.ng, which provided valuable academic support.
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.
1.1 Introduction
In this section, Vibration of Timoshenko Beam using Laplace Transform is discussed, with relevant and recent citations. 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 terms.
This chapter focuses on the review of related literature. A literature review presents current knowledge, as well as theoretical and methodological contributions, related to Vibration of Timoshenko Beam using Laplace Transform. It documents the state of the art on the subject under study and provides a comprehensive survey of existing literature. In this research work the literature review includes the conceputal review, theoretical framework, the review of related literature …
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