JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisites

Structural Analysis I & II, Mathematics

Course Objectives:

• 1. To know the fundamental concepts and theory of dynamic analysis
• 2. To understand the free vibrations concepts and the problem of determining the natural frequency of a system
• 3. To understand the free vibrations concepts of harmonically excited vibrations
• 4. To understand the free Vibrations of Multi -degree of freedom

Course Outcomes

After completion of the course, students should be able to

• 1. Apply the fundamental concepts and definitions used in structural dynamics
• 2. Calculate the natural frequency of a system using equilibrium or energy methods
• 3. Determine the effect of viscous damping on the response of a freely vibrating system
• 4. Determine the response of a system to a harmonic excitation

UNIT - I

Theory of Vibrations: Introduction - Elements of vibratory system - Degrees of Freedom - Continuous System - Lumped mass idealization - Oscillatory motion - Simple Harmonic motion - Vectorial representation of S.H.M. – Fundamental objectives of dynamic analysis -Types of prescribed loading - Methods of discretization - Formulation of equations of motion by different methods – Direct equilibration using Newton’s law of motion / D’Alembert’s principle, Principle of virtual work and Hamilton principle.

UNIT - II

Single Degree of Freedom Systems: Free vibrations of single degree of freedom system - undamped and damped vibrations - critical damping - Logarithmic decrement - Forced vibration of SDOF systems – Half Power (Band-Width) Method-Harmonic excitation - Vibration Isolation – Response to support motion-Force transmitted to the foundation-Transmissibility-Dynamic magnification factor – Phase angle. Response to General Dynamic Loading – Duhamel’s Integral-Constant Force, Rectangular load, Triangular load, Response to Periodic loading- Fourier series expression of periodic loading- Response to Fourier series loading

UNIT - III

Multi Degree of Freedom Systems: Selection of the degrees of Freedom - Evaluation of structural property matrices - Formulation of the MDOF equations of motion -Undamped free vibrations - Solutions of Eigen value problem for natural frequencies and mode shapes - Analysis of Dynamic response – Normal co-ordinates - Uncoupled equations of motion - Orthogonal properties of normal modes - Mode superposition procedure.

UNIT - IV

Practical Vibration Analysis: Introduction - Stodola method - Fundamental mode analysis - Analysis of second and higher modes - Holzer method - Basic procedure.

UNIT - V

Continuous Systems: Introduction - Flexural vibrations of beams - Elementary case – Derivation of governing differential equation of motion - Analysis of undamped free vibrations of beams in flexure - Natural frequencies and mode-shapes of simple beams with different end conditions.

REFERENCES:

• 1. Dynamics of Structures by Ray W.Clough & Joseph Penzien, Second Edition, CBS Publishers & Distributors
• 2. Dynamics of Structures by Anil K. Chopra, Pearson Education (Singapore), Delhi.
• 3. Structural Dynamics by Mario Paz and William Leigh, Fifth Edition, Springer
• 4. Theory of Vibrations by W.T. Thomson, Pearson
• 5. Fundamentals of Structural Dynamics by Roy. R. Craig, John wiley & sons M. Tech in COMPUTER AIDED STRUCTURAL ENGINEERING I YEAR II – SEMESTER