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Theory of Vibrations. Dr. Suhad Dawood Salman Mechanical Engineering Department Faculty of Engineering, Mustansiriyah University, Baghdad, Iraq. Definitions : Period : The time elapsed in repeating a periodic motion once.
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Theory of Vibrations Dr. Suhad Dawood Salman Mechanical Engineering Department Faculty of Engineering, Mustansiriyah University, Baghdad, Iraq
Definitions : Period : The time elapsed in repeating a periodic motion once. If a vibratory motion if a vibratory motion repeats itself in equal intervals of time, it is called a periodic motion. The time elapsed in repeating the motion, once is called as period. Cycle : Motion completed during a period is referred to as a cycle. This vibratory motion it repeats its motion after equal intervals of time. So, after this much of time capital T, the motion is again repeating the same motion is getting repeated. So, this time to repeat it once is called the time period or period of the vibratory motion and what is called cycle in this context.
Frequency : The number of cycles of motion in a unit of time. It is the number of cycles of motion in unit time it is called frequency of vibration. So, frequency f can be written by 1 by T, that is number of cycles of motion in unit time. • Natural frequency: The frequency with which an elastic system vibrates under the action of forces inherent in the system. The natural frequency of vibration of an elastic system is the vibration the natural frequency of an elastic system, which vibrates under the action of its inherent forces. In absence of any externally applied force the frequency with which it vibrates is known as natural frequency.
Forced vibrations: Vibrations that occur under the excitation of external forces. • Forced vibrations occur at the frequency of the exciting force. • • Degrees of freedom: The number of independent coordinates necessary to describe the motion of a system. • Generally, it is denoted by this abbreviation DOF; DOF means degrees of freedom, it is defined as a number of independent coordinates, for example, it can be displacement, required to define the displaced position of all the masses relative to their original positions or all positions are defined as degrees of freedom.
Principal modes of vibration: In a principal mode, each point in the system vibrates with the same frequency. The vibration of a multi degree freedom system can always be represented by the superposition of principal modes. Harmonic motion • The simplest form of periodic motion, occurring under the influence of elastic restoring force in the absence of all friction, which is represented by sine or cosine functions • (Phase plane representation of a harmonic motion)
