Matrix Computer Methods of Vibration Analysis is an eight-chapter introductory text to a particular technique that combines vibration analysis, matrix algebra, and computational methods. This book is emerged from a series of lectures presented at the North-East London Polytechnic. Chapters 1 and 2 introduce the basic concepts of matrix algebra, followed by a discussion on the facilities and methods of use of the computer in Chapter 3. Chapter 4 deals with the synthesis and manipulation of the system matrix for a vibrating system consisting of a number of lumped parameters, each of these being either a point mass or a massless spring. Chapter 5 describes the concept of separate matrices for the stiffnesses and masses of beams or shafts, while Chapter 6 evaluate the systems subjected to forced vibration due to varying frequencies of excitation and damping. Chapters 7 considers the different types of element that can be encountered in the analysis of a shaft or beam for natural frequencies, with an emphasis on the algorithm for dealing with massless shaft elements and point masses. Chapter 8 covers the analysis and computational requirements of torsional vibration. This work is an invaluable source for mathematicians and computer programmers and researchers.

Understanding and controlling vibration is critical for reducing noise, improving work environments and product quality, and increasing the useful life of industrial machinery and other mechanical systems. Computer-based modeling and analytical tools provide fast, accurate, and efficient means of designing and controlling a system for improved vibr

Vibration problems arise in the design of almost all engineering machinery and structures. Many of these problems are extremely complex but their solution is essential if a safe and satisfactory design is to be achieved. The equations of motion are often insoluble by the classical methods of the calculus and so it is necessary to approximate on order to reduce them to a set of linear equations. The use of matrices simplifies the solution of sets of linear equations. This book describes the matrix formulation of the equations of motion and techniques for the solution of matrix equations. The book describes some typical computer methods and also includes a large number of problems (with solutions) which may conveniently be solved by using a desk calculating machine.

The Finite Element Method in Engineering, Fifth Edition, provides a complete introduction to finite element methods with applications to solid mechanics, fluid mechanics, and heat transfer. Written by bestselling author S.S. Rao, this book provides students with a thorough grounding of the mathematical principles for setting up finite element solutions in civil, mechanical, and aerospace engineering applications. The new edition of this textbook includes examples using modern computer tools such as MatLab, Ansys, Nastran, and Abaqus.This book discusses a wide range of topics, including discretization of the domain; interpolation models; higher order and isoparametric elements; derivation of element matrices and vectors; assembly of element matrices and vectors and derivation of system equations; numerical solution of finite element equations; basic equations of fluid mechanics; inviscid and irrotational flows; solution of quasi-harmonic equations; and solutions of Helmhotz and Reynolds equations. New to this edition are examples and applications in Matlab, Ansys, and Abaqus; structured problem solving approach in all worked examples; and new discussions throughout, including the direct method of deriving finite element equations, use of strong and weak form formulations, complete treatment of dynamic analysis, and detailed analysis of heat transfer problems. All figures are revised and redrawn for clarity.This book will benefit professional engineers, practicing engineers learning finite element methods, and students in mechanical, structural, civil, and aerospace engineering. - Examples and applications in Matlab, Ansys, and Abaqus - Structured problem solving approach in all worked examples - New discussions throughout, including the direct method of deriving finite element equations, use of strong and weak form formulations, complete treatment of dynamic analysis, and detailed analysis of heat transfer problems - More examples and exercises - All figures revised and redrawn for clarity

Illustrates theories and associated mathematical expressions with numerical examples using various methods, leading to exact solutions, more accurate results, and more computationally efficient techniques This book presents the derivations of the equations of motion for all structure foundations using either the continuous model or the discrete model. This mathematical display is a strong feature of the book as it helps to explain in full detail how calculations are reached and interpreted. In addition to the simple 'uniform' and 'straight' beams, the book introduces solution techniques for the complicated ‘non uniform’ beams (including linear or non-linear tapered beams), and curved beams. Most of the beams are analyzed by taking account of the effects of shear deformation and rotary inertia of the beams themselves as well as the eccentricities and mass moments of inertia of the attachments. Demonstrates approaches which dramatically cut CPU times to a fraction of conventional FEM Presents "mode shapes" in addition to natural frequencies, which are critical for designers Gives detailed derivations for continuous and discrete model equations of motions Summarizes the analytical and numerical methods for the natural frequencies, mode shapes, and time histories of straight structures rods shafts Euler beams strings Timoshenko beams membranes/thin plates Conical rods and shafts Tapered beams Curved beams Has applications for students taking courses including vibration mechanics, dynamics of structures, and finite element analyses of structures, the transfer matrix method, and Jacobi method This book is ideal for graduate students in mechanical, civil, marine, aeronautical engineering courses as well as advanced undergraduates with a background in General Physics, Calculus, and Mechanics of Material. The book is also a handy reference for researchers and professional engineers.

Discusses in a concise but through manner fundamental statement of the theory, principles and methods of mechanical vibrations.