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Noise and Vibration Analysis is a complete and practical guide that combines both signal processing and modal analysis theory with their practical application in noise and vibration analysis.It provides an invaluable, integrated guide for practicing engineers as well as a suitable introduction for students new to the topic of noise and vibration.

With Over 60 tables, most with graphic illustration, and over 1000 formulas, this book will provide an invaluable time-saving source of concise solutions for mechanical, civil, nuclear, petrochemical and aerospace engineers and designers. Marine engineers and service engineers will also find it useful for diagnosing their machines that can slosh, rattle, whistle, vibrate, and crack under dynamic loads.

Since Lord Rayleigh introduced the idea of viscous damping in his classic work \"The Theory of Sound\" in 1877, it has become standard practice to use this approach in dynamics, covering a wide range of applications from aerospace to civil engineering. However, in the majority of practical cases this approach is adopted more for mathematical convenience than for modeling the physics of vibration damping. Over the past decade, extensive research has been undertaken on more general \"non-viscous\" damping models and vibration of non-viscously damped systems. This book, along with a related book Structural Dynamic Analysis with Generalized Damping Models: Analysis, is the first comprehensive study to cover vibration problems with general non-viscous damping. The author draws on his considerable research experience to produce a text covering: parametric senistivity of damped systems; identification of viscous damping; identification of non-viscous damping; and some tools for the quanitification of damping. The book is written from a vibration theory standpoint, with numerous worked examples which are relevant across a wide range of mechanical, aerospace and structural engineering applications.

This book by the late R D Mindlin is destined to become a classic introduction to the mathematical aspects of two-dimensional theories of elastic plates. It systematically derives the two-dimensional theories of anisotropic elastic plates from the variational formulation of the three-dimensional theory of elasticity by power series expansions. The uniqueness of two-dimensional problems is also examined from the variational viewpoint. The accuracy of the two-dimensional equations is judged by comparing the dispersion relations of the waves that the two-dimensional theories can describe with prediction from the three-dimensional theory. Discussing mainly high-frequency dynamic problems, it is also useful in traditional applications in structural engineering as well as provides the theoretical foundation for acoustic wave devices.

This introductory book covers the most fundamental aspects of linear vibration analysis for mechanical engineering students and engineers. Consisting of five major topics, each has its own chapter and is aligned with five major objectives of the book. It starts from a concise, rigorous and yet accessible introduction to Lagrangian dynamics as a tool for obtaining the governing equation(s) for a system, the starting point of vibration analysis. The second topic introduces mathematical tools for vibration analyses for single degree-of-freedom systems. In the process, every example includes a section called Exploring the Solution with MATLAB. This is intended to develop student’s affinity to symbolic calculations, and to encourage curiosity-driven explorations. The third topic introduces the lumped-parameter modeling to convert simple engineering structures into models of equivalent masses and springs. The fourth topic introduces mathematical tools for general multiple degrees of freedom systems, with many examples suitable for hand calculation, and a few computer-aided examples that bridges the lumped-parameter models and continuous systems. The last topic introduces the finite element method as a jumping point for students to understand the theory and the use of commercial software for vibration analysis of real-world structures.

This paper proposes a dynamic model to investigate the vibration response of a cylindrical roller bearing considering skidding. This model considers the frictional forces and the contact forces between rolling elements and races simultaneously. The interactions between the frictional forces and the dynamic responses of rolling bearing when skidding happens are also included in the model. It improves previous quasi-dynamic models in which the contact forces and frictional forces between races and rolling elements were determined by a separate load distribution model via the static force and moment equilibrium equations for races. The variations of the friction forces in a rotational period are elaborated, and the generating mechanism is also explained. It is found that the existence of skidding may lead to fluctuations and a significant increase of the friction force. The effect of skidding on the bearing vibration is studied by comparing the simulated results with those predicted by previous models under the pure rolling assumption. The results show that the friction forces will increase the vibration level and introduce impact components into the vibration response. It is necessary to consider the influence of skidding on the bearing vibration response using the proposed model, especially for high-speed bearings.

VIBROACOUSTIC SIMULATION Learn to master the full range of vibroacoustic simulation using both SEA and hybrid FEM/SEA methods Vibroacoustic simulation is the discipline of modelling and predicting the acoustic waves and vibration of particular objects, systems, or structures.

In this paper, the material nonlinearity is introduced in the dynamic modeling of fiber-reinforced composite thin plates, and a new nonlinear vibration model of such composite plate structures with amplitude-dependent property is established with the consideration of the nonlinear stiffness and damping characteristics, which is observed and confirmed in the nonlinear vibration characterization experiment. In this new model, the elastic moduli and loss factors are expressed as the function of strain energy density on the basis of Jones–Nelson material nonlinear model. By using the identified parameters under different excitation amplitudes, these elastic moduli and loss factors are characterized as the function of the maximum dimensionless strain energy density. Then, the power function fitting technique is used to determine the nonlinear stiffness and damping parameters in the model, and the nonlinear natural frequencies, vibration responses and damping ratios of a TC300 carbon/epoxy composite thin plate are calculated and measured in a case study. The comparisons between the theoretical and experimental results show that the maximum calculation error of natural frequencies with consideration of amplitude-dependent property is less than 4.3%, and the maximum calculation errors of resonant response and damping results are no more than 12.5 and 9.6% in the 3rd mode and the 6th mode, respectively. Therefore, the practicability and reliability of the proposed model have been verified.

In the drilling process of ultra-HPHT oil & gas wells, the drill string is more susceptive to tends to stick slip, whirl, jump and other harmful movements, which will lead to a decrease in drilling efficiency. Therefore, a multiple nonlinear vibration model of drilling string system in ultra-HPHT oil & gas wells is established using energy method and Lagrange equation, which considers multiple nonlinear factors including the nonlinearity of drill string geometry, contact collision of drill string-casing, and high temperature and high pressure on drill string viscous resistance. The correctness of the model is verified by the field test data and the simulation test results. Based on the mechanism of the torsion impact acceleration tool, corresponding motion equations are established and the main ways of acceleration are determined. Based on this, the influence of the impact tool on the vibration characteristics and stick slip characteristics of the drill string are explored. It is found that, firstly, applying constant torque can effectively improve the mechanical drilling speed of the drill bit. The sine wave torque excitation can effectively improve the mechanical drilling speed. Secondly, with the increase of torque amplitude, the peak speed decreases significantly, and the torsional vibration of the drill string becomes more stable. The viscosity time of stick slip vibration also decreases significantly. Under the premise of meeting the safety of the acceleration tool, a torque amplitude of 4000 N m can be used for acceleration, which has a better acceleration effect. Thirdly, the torque frequency increases, the peak speed and the viscosity time shows a trend of first decreasing and then increasing. The optimal acceleration effect is achieved when the frequency of acceleration tool is selected as 20 Hz. The research results provide a theoretically guidance for designing and practically sound approach for effectively improving the mechanical speed in ultra-HPHT oil & gas wells.

Cardiovascular diseases pose a long-term risk to human health. This study focuses on the rich-spectrum mechanical vibrations generated during cardiac activity. By combining Fourier series theory, we propose a multi-frequency vibration model for the heart, decomposing cardiac vibration into frequency bands and establishing a systematic interpretation for detecting multi-frequency cardiac vibrations. Based on this, we develop a small multi-frequency vibration sensor module based on flexible polyvinylidene fluoride (PVDF) films, which is capable of synchronously collecting ultra-low-frequency seismocardiography (ULF-SCG), seismocardiography (SCG), and phonocardiography (PCG) signals with high sensitivity. Comparative experiments validate the sensor’s performance and we further develop an algorithm framework for feature extraction based on 1D-CNN models, achieving continuous recognition of multiple vibration features. Testing shows that the recognition coefficient of determination (R2), mean absolute error (MAE), and root mean square error (RMSE) of the 8 features are 0.95, 2.18 ms, and 4.89 ms, respectively, with an average prediction speed of 60.18 us/point, meeting the re-quirements for online monitoring while ensuring accuracy in extracting multiple feature points. Finally, integrating the vibration model, sensor, and feature extraction algorithm, we propose a dynamic monitoring system for multi-frequency cardiac vibration, which can be applied to portable monitoring devices for daily dynamic cardiac monitoring, providing a new approach for the early diagnosis and prevention of cardiovascular diseases.