Wiley Analytical and Numerical Methods for Vibration Analyses

Illustrates theories and associated mathematical expressions with numerical examples using various methods, leading to exact solutions, more accurate results, and more computationally efficient techniquesThis 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 FEMPresents "mode shapes" in addition to natural frequencies, which are critical for designersGives detailed derivations for continuous and discrete model equations of motionsSummarizes the analytical and numerical methods for the natural frequencies, mode shapes, and time histories ofstraight structuresrodsshaftsEuler beamsstringsTimoshenko beamsmembranes/thin platesConical rods and shaftsTapered beamsCurved beamsHas applications for students taking courses including vibration mechanics, dynamics of structures, and finite element analyses of structures, the transfer matrix method, and Jacobi methodThis 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. From the Inside Flap ANALYTICAL AND NUMERICAL METHODS FOR VIBRATION ANALYSESJONG-SHYONG WUNational Cheng-Kung University, TaiwanIllustrates theories and associated mathematical expressions with numerical examples using various methods, leading to exact solutions, more accurate results, and more computationally efficient techniquesThis 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. Numerous 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. For some cases, the effects of axial loads and elastic foundations are also investigated. Furthermore, for the uniform and straight beams in various boundary conditions, their lowest fi ve (instead of fundamental) critical buckling loads and associated buckled mode shapes are introduced from the viewpoint of vibrations. Demonstrates approaches which dramatically cut CPU times to a fraction of conventional FEMPresents "mode shapes" in addition to natural frequencies, which are critical for designersGives detailed derivations for continuous and discrete model equations of motionsSummarizes the analytical and numerical methods for the natural frequencies, mode shapes, and/or time histories ofstraight structuresrods ??? Euler beams ??? Timoshenko beamsshafts ??? strings ??? membranes/thin platesConical rods and shaftsTapered beamsCurved beamsHas applications for students taking courses including vibration mechanics, dynamics of structures, and finite element analyses of structures, the transfer matrix method, and Jacobi methodThis bo