Tham khảo tài liệu 'sổ tay tiêu chuẩn thiết kế máy p45', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | _CHAPTER 38__ VIBRATION AND CONTROL OF VIBRATION_ T. S. Sankar . Eng. Professor and Chairman Department of Mechanical Engineering Concordia University Montreal Quebec Canada R. B. Bhat . Associate Professor Department of Mechanical Engineering Concordia University Montreal Quebec Canada INTRODUCTION SINGLE-DEGREE-OF-FREEDOM SYSTEMS I SYSTEMS WITH SEVERAL DEGREES OF FREEDOM VIBRATION ISOLATION REFERENCES INTRODUCTION Vibration analysis and control of vibrations are important and integral aspects of every machine design procedure. Establishing an appropriate mathematical model its analysis interpretation of the solutions and incorporation of these results in the design testing evaluation maintenance and troubleshooting require a sound understanding of the principles of vibration. All the essential materials dealing with various aspects of machine vibrations are presented here in a form suitable for most design applications. Readers are encouraged to consult the references for more details. SINGLE-DEGREE-OF-FREEDOM SYSTEMS Free Vibration A single-degree-of-freedom system is shown in Fig. . It consists of a mass m constrained by a spring of stiffness k and a damper with viscous damping coefficient c. The stiffness coefficient k is defined as the spring force per unit deflection. The coef- STANDARD HANDBOOK OF MACHINE DESIGN FIGURE Representation of a single-degree-of-freedom system. ficient of viscous damping c is the force provided by the damper opposing the motion per unit velocity. If the mass is given an initial displacement it will start vibrating about its equilibrium position. The equation of motion is given by nix ex kx 0 where x is measured from the equilibrium position and dots above variables represent differentiation with respect to time. By substituting a solution of the form x es into Eq. the characteristic equation is obtained ms2 cs k
