A Seminar On Vibration Analysis And Damping In Structures Submitted to: Submitted By: Mr Rahul Bhaiji Divya Lattoo Utkarsh Tiwari
A Seminar On Vibration Analysis And Damping In Structures
Submitted to: Submitted By:Mr Rahul Bhaiji Divya Lattoo
Utkarsh Tiwari
IntroductionStructure –
A structure is a combination of parts fastened together to create a supporting framework, which may be part of a building, ship, machine, space vehicle, engine or some other system.
Vibrations –
THE CAUSES AND EFFECTS OF STRUCTURAL VIBRATION
Cause
Effect
THE REDUCTION OF STRUCTURAL VIBRATION
THE ANALYSIS OF STRUCTURAL VIBRATION
Stage I. Devise a mathematical or physical model of the structure to be analysed.
Stage II. From the model, write the equations of motion.
Stage III. Evaluate the structure response to
a relevant specific excitation.
The Vibration Of Structures With One Degree Of FreedomFREE UNDAMPED VIBRATION
Translation vibration
Torsional vibration
Energy methods for analysis• For undamped free vibration the total energy in the
vibrating system is constantthroughout the cycle. Therefore the maximum potential energy V(max), is equal to the maximum kinetic energy T(max) , although these maxima occur at different times during the cycle of vibration. Furthermore, since the total energy is constant,
• T + V = constant, • d(T + V)/dt = 0
• ω = (k/m)1/2 • Condition of stability –
.
FREE DAMPED VIBRATIONThe most common types of damping are
Viscousdry frictionhysteretic
Vibration with viscous Damping• Case 1 ζ less than 1, that is, damping less than critical• The motion of the body is therefore an exponentially
decaying harmonic oscillation
• Case 2 ζ = 1; that is, critical damping• Critical damping represents the limit of periodic motion;
hence the displaced body isrestored to equilibrium in the shortest possible time, and without oscillation or overshoot.
• Case 3 ζ greater than critical,• Since both values of s are negative the motion is the
sum of two exponential decays
Vibration with Coulomb (dry friction) damping
Equation Of Motion - mẍ = Fd – kx
Vibration with hysteretic dampingExperiments on the damping that occurs in
solid materials and structures that have been subjected to cyclic stressing have shown the damping force to be independent of frequency internal, or material, damping is referred to as hysteretic damping.
the induced stress is σ = σ0sin (Vt+ α)
FORCED VIBRATIONThe equation of motion is
X/Xs is known as the dynamic magnification factor
ResonanceThe phenomenon known as resonance occurs
when the forcing frequency is equal to the natural frequency, that is when v/ω = 1.
The maximum value of X/Xs actually occurs at values of v/ω less than unity:
Response of a viscous damped Structure supported on a foundation subjected to harmonic vibration
Equation Off Motion
Vibration IsolationThe force transmitted to the foundation is the
sum of the spring force and the damperforce. Thus the transmitted force = kx + cẋ
and Fx the amplitude of the transmitted force is given by –
Response of a Coulomb damped structure to a simple harmonic exciting force with constant amplitudeThe equation of motion is non-linear because
the constant friction force F, always opposes the motion:
Response of a structure to a suddenly applied ForceThe equation of motion can be written
If the structure possesses viscous damping of coefficient c, the solution to the equation of motion is
Shock excitationSome structures are subjected to shock or
impulse loads arising from suddenly applied, non-periodic, short-duration exciting forces.
X(t) =
Wind- or current-excited oscillationA structure exposed to a fluid stream is
subjected to a harmonically varying force in a direction perpendicular to the stream. This is because of eddy, or vortex, shedding on alternate sides of the structure on the leeward side.
Damping In Structures• Sources of damping
– Inherent damping– Hysteretic or material damping– Damping in structural joints– Acoustic radiation damping– Air pumping– Aerodynamic damping
• Added damping – High damping alloys– Composite materials– Viscoelastic materials– Constrained layer damping– Vibration dampers and absorbers
Vibration IsolationThe force transmitted to the foundation is the
sum of the spring force and the damper force. Motion Transmission TR = X/A =
BIBLIOGRAPHY•
Structural Vibration and DampingBy C. E Beards
www.howstuffwork.com
Theory Of Machine
By R.S.Khurmi
Questions And Query Are Welcome