types of dynamic loads

TYPES OF DYNAMIC LOADS,
TYPES OF VIBRATIONS
Speaker
Mondrus Vladimir Lvovich
Professor
1
Definition
Dynamic loads are called the loads acting on
the structure, the magnitude, direction, and
position of which change over a short period of
time.
The purpose of the structural dynamic
calculation is to determine the law of the
masses motion of the deforming system and the
magnitude of the inertial forces
• Allow to check the system for resonance
• Give an assessment of the strength and
stiffness of the calculated structure
Dynamic loads
• Vibration load - periodic vibrational effects from the movement of
unbalanced parts of machines and mechanisms, in particular, electric
motors, looms, etc.
Simple harmonic load
Complex load
Dynamic loads
• The impact load created by the falling parts of the mechanisms
(hammers, copres, etc.).
• These loads are characterized by a short duration of action.
• The maximum value of the load and the time of its action depend on the
elastic and inertial properties of the structures that perceive the impact.
Dynamic loads
• Movable load, the position of which changes in time, for example, the
load from the movement of railway trains, bridge cranes, etc.
Dynamic loads
• Impulse load: explosion, wave load, causing a sharp change in pressure
on the surface of the structure
Dynamic loads
• Seismic load on buildings and structures caused by an earthquake,
causing the occurrence of base movements, changing in time according to
a complex law - a seismogram and, as a result, causing vibrations of the
structure.
• The parameters of the seismic impact cannot be accurately set in
advance.
Dynamic loads
Wind load is the load, in pounds per square foot,
placed on the exterior of a structure by wind.
This will depend on:
• The angle at which the wind strikes the structure
• The shape of the structure (height, width, etc.)
Wind exerts three types of forces on a structure:
• Uplift load - Wind flow pressures that create a strong lifting effect,
much like the effect on airplane wings. Wind flow under a roof
pushes upward; wind flow over a roof pulls upward.
• Shear load – Horizontal wind pressure that could cause racking of
walls, making a building tilt.
• Lateral load – Horizontal pushing and pulling pressure on walls that
could make a structure slide off the foundation or overturn.
VIBRATIONS
у
у0
free
vibrations
Т
А
φ0/ω
To start free vibrations only,
the force is required initially
The frequency of free
vibrations depends on the
natural frequency
t
А
Free vibrations are produced
when body is disturbed from its
equilibrium position and released
Energy of body remains constant in the
absence of friction, air resistance, etc. Due
to damping forces, total energy decreases.
Graph of free non-extinguishing harmonic oscillations
Amplitude of vibrations
decreases with time
у
R
J
=1
External load action
P(t)
forced
vibrations
Forced vibrations are produced
by an external periodic force of
any frequency
Continuous external periodic force is
required. If external periodic force is stopped
then forced vibrations also stop
The frequency of forced
vibrations depends on the
frequency of the external periodic
force
Energy of the body is maintained
constant by the external periodic
force acts on it
Amplitude is small but remains
constant as long as external
periodic force acts on it
Vibrations stop as soon as
external periodic force is stopped
VIBRATIONS
VIBRATIONS
impulse
(impact)
processes
deterministic processes
periodic
harmonic
complex
periodic
nonperiodic
almost
periodic
random processes
transient
stationary
ergodic
nonergodic
nonstationary
VIBRATIONS
• Deterministic processes are
oscillatory processes that can be
described by specific mathematical
expressions.
• They can be periodic or non-periodic.
periodic
complex
periodic
• In turn, periodic processes are divided
into harmonic and complex.
almost
periodic
• The dependence of the maximum
amplitude of oscillations on the
frequency of oscillations is called the
spectrum.
damped
process
 The spectrum of periodic and almost periodic
processes is characterized by discrete distributions
in the coordinate system "Amplitude-frequency of
oscillations"
VIBRATIONS
• Complex harmonic processes - a periodic oscillatory process
that has the same frequency at different times, but different
amplitudes
𝑢 𝑡 = 𝑢(𝑡 + 𝑛𝑇0 )
Complex harmonic processes can be expanded in a Fourier series according to the formula:
∞
𝑎0
𝑢 𝑡 =
+
𝑎𝑛 cos 2𝜋𝑛𝑓1 𝑡 + 𝑏𝑛 sin 2𝜋𝑛𝑓1 𝑡
2
2
𝑇0
2
𝑏𝑛 =
𝑇0
𝑛=1
𝑇0
𝑎𝑛 =
𝑢 𝑡 cos 𝜔1 𝑛𝑡 𝑑𝑡
0
𝑇0
0
𝑢(𝑡) sin 𝜔1 𝑛𝑡 𝑑𝑡, 𝑤ℎ𝑒𝑟𝑒 𝑓1 =
𝜔1 = 2𝜋𝑓1
𝑇0 - period
1
𝑇0
VIBRATIONS
• Transient processes are such processes for which in most
cases the spectral distribution is continuous and can be
represented as a Fourier transform.
∞
𝑈 𝑓 =
𝑢 𝑡 𝑒 −𝑖𝜔𝑡 𝑑𝑡 ,
−∞
wℎ𝑒𝑟𝑒 𝜔 = 2𝜋𝑓 − 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
VIBRATIONS
• A random function is a function that,
as a result of an experiment, can take
on some unknown form.
• All realizations of a specific random
event (earthquake, wind gusts, voltage
on the transformer winding, pressure
distribution during explosions and
vibrations, etc.) over a finite
observation interval is called a
random or stochastic process.
VIBRATIONS
• Random processes are divided into stationary and nonstationary.
• Stationary processes can be represented as ergodic or nonergodic processes.
A random process is called stationary if the probability distribution laws of two value
groups:
𝑋 𝑡1 , 𝑋 𝑡2 , … , 𝑋 𝑡𝑛
𝑎𝑛𝑑 𝑋 𝑡1 + 𝜏 , 𝑋 𝑡2 + 𝜏 , … , 𝑋 𝑡𝑛 + 𝜏
are identical to each other, and the quantities 𝑛, 𝑡1 , 𝑡2 … 𝑡𝑛 and 𝜏 are chosen arbitrarily → the distribution functions
do not depend on the choice of the origin of time
VIBRATIONS
• A random process is called ergodic if any of its realizations has
the same statistical properties, i.e. the statistical characteristic
obtained by averaging over a set of realizations is equal to the
statistical characteristic obtained by averaging the process over
time.
Non-ergodic process
Ergodic process
VIBRATIONS
• Among the oscillatory processes that are
not stationary, in particular, there are
damped and divergent oscillations.
• Damping is an influence within or upon an
oscillatory system that has the effect of
reducing or preventing its oscillation.
THANK YOU FOR YOUR ATTENTION
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