TAILIEUCHUNG - Ebook Engineering vibrations: Part 2

(BQ) Part 2 book "Engineering vibrations" has contents: Free Vibration of multi degree of freedom systems, forced vibration of multi degree of freedom systems, dynamics of one-dimensional continua, free vibration of one-dimensional continua, forced vibration of one-dimensional continua. | 7 Free Vibration of Multi-Degree of Freedom Systems In this chapter we consider the behavior of discrete multi-degree of freedom systems that are free from externally applied dynamic forces. That is, we examine the response of such systems when each mass of the system is displaced and released in a manner that is consistent with the constraints imposed on it. We are thus interested in the behavior of the system when is left to move under its own volition. As for the case of single degree of freedom systems, it will be seen that the free vibration response yields fundamental information and parameters that define the inherent dynamical properties of the system. THE GENERAL FREE VIBRATION PROBLEM AND ITS SOLUTION It was seen in Chapter 6 that the equations that govern discrete multi-degree of freedom systems take the general matrix form of Eq. . We shall here consider the fundamental class of problems corresponding to undamped systems that are free from applied (external) forces. For this situation, Eq. reduces to the form mu + ku = 0 () where, for an N degree of freedom system, m and k are the N × N mass and stiffness matrices of the system, respectively, and u is the corresponding N × 1 displacement matrix. To solve Eq. (), we parallel the approach taken for solving the correspond341 342 Engineering Vibrations ing scalar problem for single degree of freedom systems. We thus assume a solution of the form () u = Ueiω t where U is a column matrix with N, as yet, unknown constants, and ω is an, as yet, unknown constant as well. The column matrix U may be considered to be the spatial distribution of the response while the exponential function is the time dependence. Based on our experience with single degree of freedom systems, we anticipate that the time dependence may be harmonic. We therefore assume solutions of the form of Eq. (). If we find harmonic forms that satisfy the governing equations then such forms are, by definition, .

• Cơ khí - Chế tạo máy
• Engineering vibrations
• Freedom systemsc
• One dimensional continua
• Forced vibration
• Multi degree
• Second order systems
• Freedom systems
• Forced vibration of single degree
• Nonperiodic excitation
• Periodic excitation
• Operational methods
• Dynamics of multi degree of freedom systems
• Torsional vibrations
• Damping coefficient
• Relative and absolute damping coefficients
• Elastic torque
• Marine engineering
• Nuclear engineering and technology
• Two way fluid structure interaction simulation
• Steady state vibration of a slender rod
• URANS and LES turbulence models
• The steady state Flow Induced Vibrations
• Computational Fluid Dynamics
• Electronic Engineering
• Active magnetic bearing
• Assault block
• Dynamic stiffness
• Rotor vibration
• Lecture Automatic control systems technology
• Bài giảng Công nghệ hệ thống điều khiển tự động
• Automatic control systems technology
• Second order lag processes
• Second order system responses
• Second order mechanical system
• Vietnam Journal of Mechanics
• A selection of parameters
• Tuned mass damper for multi degree of freedom systems subjected
• Second order coloured noise excitation
• Optimal tuned mass damper
• Lecture Introduction to Circuits for ECE
• Bài giảng Tổng quan mạch điện ECE
• Introduction to Circuits for ECE
• Second order systems in frequency domain
• Parallel L C circuit
• Series L C circuit
• Second order narrow band colored noises
• Non linear random vibrations
• Lightly nonlinear systems
• Stochastic averaging method
• Advanced engineering mathematics
• First Order ODEs
• Second Order linear ODEs
• Higher order linear ODEs
• Systems of ODEs
• Phase plane
• Qualitative methods
• Asymptotic stability
• Nonautonomous second order stochastic delay
• Differential equation
• Lyapunov functional
• Engineered systems
• Analysis and design of control systems using Matlab
• Transientresponse analysis
• Response to initial condition
• Root locus plots
• Bode diagrams
• Signals systems
• Lecture Signals systems
• Time invariant system models
• System models in continuous
• Linear system models
• State–space models
• Correlation coefficient
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• kiến thức toán học
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• Physical modeling in MATLAB
• Optimization and interpolation
• Ordinary differential equations
• Zero finding
• Non linearity on random vibrations
• The classical first prder stochastic averaging method
• Non linear random vibration systems
• Journal of Chemistry
• Cu(II) ions
• Alizarin red S
• Binary system
• Pseudo second order model
• X ray diffraction
• High resolution transmission electron microscopy