In the Name of Allah, the Gracious, the Merciful

By Muhammad Ishfaq Khan Engineering Dynamics By Muhammad Ishfaq Khan

Thesis Defense Worskhop Lecture 1 UTSI-NSBE Thesis Defense Worskhop

Course Content B-Tech Vibration: Revision of matrix algebra: Introduction, types of vibration, basic concepts and terminologies Revision of matrix algebra: Characteristic equations, solution methods, free vibration, equation of motion, energy methods, series and parallel combination, viscously damped free vibration, logarithmic decrement, coulomb damping. Harmonically excited vibration: Forced harmonic vibration, rotating unbalanced, and vibration measuring instruments.

Physical stiffness of elements: Eigen value analysis of: Mechanical system: Gravity pendulum, spring-mass vibrating system, compound gravity pendulum, stiffness, potential energy, stability, torsional pendulum, free vibration and resonance. Physical stiffness of elements: Rods, beams, stiffness coefficients as matrix elements. Eigen value analysis of: Two degree of freedom problems, three degree of freedom problems, determination of modes of vibration. Rayleigh’s method and its applications Books Recommended: 1. Vibration theory and applications – William, T. and Thompson. 2. Fundamentals of mechanical vibrations by Kelly. 3. Mechanical Vibration by S. S. Rao

Thesis Defense Worskhop Lab Outline 1. Demonstration on simple spring mass system and related calculation. 2. Demonstration simulation of beams and rod vibration. 3. Demonstration on damped vibration and analysis. 4. Computer simulation of whole range of vibrating components. 5. Application of computer for solving set of equations. UTSI-NSBE Thesis Defense Worskhop

Thesis Defense Worskhop History first musical instruments 4000 B.C. with 1st Musical Instument Pythagoras’s Monotone (582 507 B.C.) 1st Scientific Investigation! UTSI-NSBE Thesis Defense Worskhop

Zhang Heng measured earthquakes Time of Occurrence & Direction Galileo Galilei (1564 1642) From a Lamp in a Church in Pisa: Time Period was Independent of Amplitude Frequency of vibration on the length of a simple pendulum Phenomenon of sympathetic vibrations i.e. resonance Newton’s 2nd Law J.B. Fourier Transformation Charles Coulomb Discovered the period of oscillation is independent of the angle of twist E. F. F. Chladni (1756 1824) mode shapes of a Plate

Importance of Vibrations Tacoma Narrows bridge during wind-induced vibration Aero planes Vanished due to fatigue caused by wind on the wing and chassis vibrations UTSI-NSBE Thesis Defense Worskhop

Thesis Defense Worskhop Introduction What is Vibration? Any motion that repeats itself after an interval of time is called vibration or oscillation. Any movement w.r.t. reference position Vibration of road surface! Earth Quakes Excited Tuning Fork Speaking Singing UTSI-NSBE Thesis Defense Worskhop

Basic Concepts & Terminologies Means for Storing Potential Energy Spring or Elasticity a means for storing kinetic energy mass or inertia a means by which energy is gradually lost damper the transfer of its potential energy to kinetic energy and of kinetic energy to potential energy, alternately! some energy is dissipated in each cycle of vibration due to damping An external source if a state of steady vibration is to be maintained for damped system

Thesis Defense Worskhop Bob of mass m be released at angle θ At 1, K.E. 0, P.E. = mgl(cosθ-1) a torque mglsinθ about the point O, the bob starts swinging to the left from position 1 At position 2, all of its potential energy will be converted into kinetic energy Due to Inertia it wont stop! mglsinθ now acts till pendulum stops at 3 So on and so forth UTSI-NSBE Thesis Defense Worskhop

Thesis Defense Worskhop DOFs The minimum number of independent coordinates required to determine completely the positions of all parts of a system at any instant of time defines the number of degrees of freedom of the system Pendulum is 1 DOF System! Why? UTSI-NSBE Thesis Defense Worskhop

Thesis Defense Worskhop External Force Types of Mechanical Vibrations Free vibration If a system, after an initial disturbance, is left to vibrate on its own Any Example? Forced vibration If a system is subjected to an external force (often, a repeating type of force) resonance UTSI-NSBE Thesis Defense Worskhop

Thesis Defense Worskhop Resistance Un-Damped no energy is lost or dissipated in friction or other resistance during oscillation Any Example? Damped UTSI-NSBE Thesis Defense Worskhop

Thesis Defense Worskhop Component Behavior Linear the basic components of a vibratory system behave linearly Non-Linear the basic components of a vibratory system behave non-linearly UTSI-NSBE Thesis Defense Worskhop

Thesis Defense Worskhop Predictability Deterministic the value or magnitude of the excitation (force or motion) is known Random the value or magnitude of the excitation (force or motion) is not known UTSI-NSBE Thesis Defense Worskhop