..Il mobily 14:01 Mechanical Vibration MENG 470 Homework ( 1 ) ibration Fundamen
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..Il mobily 14:01 Mechanical Vibration MENG 470 Homework ( 1 ) ibration Fundamentals 1. Define the following terminology and their units a) Degree of Freedom d) Resonance g) Cycle b) Natural Frequency e Physical system h) Amplitude k) Time period Free Vibration D Analysis i) Phase angle near frqency 2. Mention the conditions for the vibration motion to be occur 3. Mention four applications for desired vibration and four applications for undesired vibration. 4. Mention the difference between each of the following vibration systems with a given example of each of them A. The continuous and discrete systems, B. The linear and nonlinear systems. C. The deterministic excited and undeterministic excited systems. vibration? 6. How can you connect several springs to increase the overall stiffness? 7. What is the difference between harmonic and periodic motion? 8. The spring constant of a helical spring under axial load is given by G d4 8 N D3 Where G is the shear modulus, d is the wire diameter, D is the coil diameter and N is the number of tuns. Find the spring constant and the weight of aExplanation / Answer
1.
A. Degree of Freedom :- (for a vibration system) It is a number of independents coordinates required to describe a vibration system.
B. Natural Frequency:- natural frequency is the elastic vibrations when there is no friction and external forces after initial release of the body.
C. free vibrations :- elastic vibrations in which there are no friction and external forces after the initial release of the body is free vibration.
D. Resonance:- It is large amplitudes of vibration when the frequency of the external force is equal to the natural frequency of the system.
E. Physical System:- a physical system is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment .
F. Analysis:- A detailed examination of a material or component.
G. Cycle:- a series of event that are repeated at regular interval is cycle.
H. Amplitude:- the maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
I. Phase angle:- it is a phase difference expressed at an angle.
J. Linear Frequency:- the linear frequency is the number of periodic motions executed by a body per second.
K. Time period:- time needed for one complete cycle is time period.
2. the condition for vibration motion are:-
a. Inertial elements:- these are represented by lumped masses for rectilinear motion and by lumped moment of inertia for angular motion.
B. Restoring elements:- Massless linear or torsional springs represent the restoring elements for rectilinear and torsional motions respectively.
C. Damping elements :- Massless dampers of rigid elements may be considered for energy dissipation in a system.
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