Vibrations and explanations (original) (raw)
Fundamentals of vibrations: Basic Concepts and definitions. Vibration Analysis, Harmonic Motion. Single degree-of-freedom systems: Equation of motion; Lagrange’s equation; free vibration of undamped and damped systems; logarithmic decrement; other forms of damping. Forced vibration: Equation of motion; response to harmonic excitation; resonance; rotating unbalanced; base motion excitation; response to general non-periodic excitation; impulse response function. Design for vibration control: Vibration isolation; critical speeds of rotating shafts; practical isolation design. Multiple degree-of-freedom systems: Equations of motion; Lagrange’s equations; free vibration, natural frequencies and mode shapes; forced vibration; response to harmonic excitation and normal-mode approach. Continuous systems: Introduction to continuous systems. Vibration absorption: Balancing of rotating machines.
Vibrations are mechanical oscillations about an equilibrium position. There are cases when vibrations are desirable, such as in certain types of machine tools or production lines. Most of the time, however, the vibration of mechanical systems is undesirable as it wastes energy, reduces efficiency and may be harmful or even dangerous. For example, passenger ride comfort in aircraft or automobiles is greatly affected by the vibrations caused by outside disturbances, such as aeroelastic effects or rough road conditions. In other cases, eliminating vibrations may save human lives, a good example is the vibration control of civil engineering structures in an earthquake scenario. All types of vibration control approaches—passive, semi-active and active— require analyzing the dynamics of vibrating systems. Moreover, all active approaches, such as the model predictive control (MPC) of vibrations considered in this book require simplified mathematical models to function properly. We may acquire such mathematical models based on a first principle analysis, from FEM models and from experimental identification. To introduce the reader into the theoretical basics of vibration dynamics, this chapter gives a basic account of engineering vibration analysis. There are numerous excellent books available on the topic of analyzing and solving problems of vibration dynamics. This chapter gives only an outline of the usual problems encountered in vibration engineering and sets the ground for the upcoming discussion. For those seeking a more solid ground in vibration mechanics, works concentrating rather on the mechanical view can be very valuable such as the work of de Silva [10] and others [4, 22]. On the other hand, the reader may get a very good grip of engineering vibrations from the books discussing active vibration control such as the work of Inman [21] and others [15, 18, 37, 38]. The vibration of a point mass may be a simple phenomenon from the physical viewpoint. Still, it is important to review the dynamic analysis beyond this phenomenon , as the vibration of a mass-spring-damper system acts as a basis to understand more complex systems. A system consisting of one vibrating mass has one natural frequency, but in many cases, in a controller it is sufficient to replace a continuous G. Takács and B. Rohal'-Ilkiv, Model Predictive Vibration Control, 2 5
A Modular Approach To Vibrations
2001 Annual Conference Proceedings
An undergraduate vibration course has been presented in a modular form to improve student participation and understanding. The new modular format highlights the key concepts and tools required to perform vibration analysis on both single (SDOF) and multiple degree-of-freedom (MDOF) systems. The traditional approach, placing MDOF late in the semester, emphasizes the SDOF model and leaves the students with an oversimplified view of vibrations. A reorganization of the material found in most vibration texts encourages the students to strengthen their system analysis skills. Module 1 covers the modeling of systems, both SDOF and MDOF. This has been a stumbling block for students thus needing a more focused approach. An early introduction of Lagrange's equations has strengthened students' ability to model complex engineering systems mathematically. Module 2 presents the tools required to carry out future analysis, such as matrix methods, complex notation, and MATLAB. Module 3 encourages physical understanding of the dynamic response of 1 and 2 DOF systems using an air-track demonstration unit. Observing and measuring actual system response motivates the students to understand the upcoming mathematical development. Module 4, the analytical heart of the course, presents free and forced responses for SDOF and MDOF systems. Equations are more easily understood because they correlate to observations made during Module 3. The course ends with Module 5, practical applications. Lack of interest in the subject Modeling concepts, real systems transformed into SDOF/MDOF models Application of dynamic principles to obtain equations of motion Mathematical ability to deal with solution of differential equations Getting lost in the details