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Mass and Elasticity
All systems possessing __________ are capable of free vibration, or vibration that takes place in the absence of external excitation.
Damping
It has little influence on the natural frequency and may be neglected in its calculation
Effect of Damping
It is mainly evident in the diminishing of the vibration amplitude with time.
Mass, Massless Spring, and Damper
The Basic Vibration Model of a Simple Oscillatory System
Viscous Damping
It is generally represented by a dashpot where force is proportional to the velocity.
Simple Undamped Spring-mass System
It moves only along the vertical coordinate x (1 DOF).
When at motion oscillation take place at the natural frequency fn.
Kinetic Energy
It is stored in the mass by virtue of its velocity.
Potential Energy
It is stored in the form of strain energy in elastic deformation or work done in a force field such as gravity.
Conservative System
The total energy is constant, and the differential equation of motion is established using the principle of conservation of energy.
Effective Mass: Rayleigh Method
In a systems in which masses are joined by rigid links, levers, or gears, the motion of the various masses can be expressed in terms of the motion of x* some specific point and the system is simply one of a single DOF, because one coordinate is necessary.
Springs and Beams
In distributed mass system as ________, distribution of vibration amplitude is necessary before calculating the kinetic energy.
Rayleigh’
It showed that with a reasonable assumption for the shape of the vibration amplitude., it is possible to take into account previously ignored masses and arrive at a better estimate for the fundamental frequency.
Forced Harmonic Vibration
When a system is subjected to harmonic excitation, it is forced to vibrate at the same frequency as that of the excitation.
Resonance
It is to be avoided in most cases, and to prevent large amplitudes from developing, dampers and absorbers are often used.
Rotating Unbalance
Unbalance in rotating machines is a common source of vibration excitation.
Counter-rotating Eccentric Weight Exciter
It is used to produce the forced oscillation for a spring supported mass.
Static Unbalance
When the unbalanced masses all lie in a single plane, the resultant unbalance can be detected by a static test in which the wheel-axle assembly is placed on a pair of horizontal rails.
Dynamic unbalance
When the unbalance appears in more than one plane, the resultant is a force and a rocking moment.
180 Degrees
If the two unbalanced masses are equal and _____ apart, the rotor will be statically balanced about the axis of the shaft.
Rotor Balancing Machine
Machines to detect and correct the rotor unbalance, essentially, the balancing machine consists of supporting bearings that are spring-mounted so as to detect the unbalanced forces by their motion.
Thin Disk
It can be balanced statically; it can also be balanced dynamically.
Disk
It is supported on a spring-restrained bearings that can move horizontally.
Whirling
When the rotation of the plane made by the bent shaft and the line of centers of the bearings. The phenomenon results from various causes as; mass unbalance, hysteresis damping in the shaft, gyroscopic forces, fluid friction in bearings, etc.
Vibration
It is a mechanical phenomenon in which the oscillations occur about an equilibrium point.
Critical Speed
If the speed of rotating shaft reaches its Natural Frequency, Resonance occurs in the shaft which causes the shaft to vibrate violently in transverse vibration with very high amplitude and this ultimately leads to failure of shaft. That is why the Resonance speed of the shaft is called as ________.
Mode of Vibration
In vibrational analysis, it is the different types in which the system tries to oscillate naturally, i.e. without any excitation force.
Mode Shape
It is the frequency of oscillation is termed as modal frequency (or natural frequency) and the shape made by the system.
Modal Analysis
It is a technique to study the dynamic characteristics of a structure under vibration excitation. Natural frequencies, mode shapes and mode vectors of a structure can be determined using modal analysis workbench.
Resonance Frequencies
Modal is the simplest analysis and the only thing it does is finding out what are the _________ of the geometry.
Modal Analysis Workbench
It shows the nature of deformation at different modes of vibration. The end conditions and geometry of shaft decide the shape of vibration and critical frequency
Theoretical Calculations or Experimental data
It is always advisable to go through it before the Simulation in ANSYS. The meshing and solver settings are to be modified to minimize the error
Viscous Damping
It is damping that is proportional to the velocity of the system. That is, the faster the mass is moving, the more damping force is resisting that motion. Fluids like air or water generate viscous drag forces.
Under Earthquake Excitation
It is the pistons of the viscous damper installed in the structure generates a reciprocating motion, which will force the viscous fluid to flow through the orifices, and then the damping force is generated and the structural dynamic responses are reduced.
Vibration Forces
It is generated by machines and other causes are often unavoidable; however, their effects on a dynamical system can be minimized by proper isolator design.
Isolation System
It attempts either to protect a delicate object from excessive vibration transmitted to it from its supporting structure or to prevent vibratory forces generated by machines from being transmitted to its surroundings.
Conservation of Energy
It is the term used to describe the physics phenomenon that energy cannot be created or destroyed. It can only be converted from one form into another.
Energy Dissipation
It helps us to understand more about physical interactions. By applying the concept of energy dissipation, it can be predicted how systems will move and act.
Single-Object System
It can only have kinetic energy; this makes perfect sense because energy is usually the result of interactions between objects.
Kinetic Energy
It only relies on the mass and velocity of an object or system; it does not require interaction between two or more objects.
A system involving the interaction between conservative forces can have both ______ and ______
Kinetic, Potential Energy
Potential Energy
It can result from the interaction between an object and the earth's gravitational force.
Damping
It is present in all oscillatory systems. Its effect is to remove energy from the system.
Energy in a Vibrating System
It is either dissipated into heat or radiated away.
Dissipation of Energy into Heat
It can be experienced simply by bending a piece of metal back and forth a number of times.
Energy Dissipation
It is usually determined under conditions of cyclic oscillations.
Hysteresis Loop
The force-displacement curve will enclose an area, that is proportional to the energy lost per cycle.
Solid Damping or Structural Damping
When materials are cyclically stressed, energy is dissipated internally within the material itself. Experiments by several investigators indicate that for most structural metals, such as steel or aluminum, the energy dissipated per cycle is independent of the frequency over a wide frequency range and proportional to the square of the amplitude of vibration. Internal damping fitting this classification is called _______.
Five Types of Stress
Torsion, Bending, Tension, Shear, & Compression
Fuselage
It is the central body of an airplane and is designed to accommodate the crew, passengers, and cargo. It also provides the structural connection for the wings and tail assembly.
Damping
It is a phenomenon that makes any vibrating body/structure to decay in amplitude of motion gradually by means of energy dissipation through various mechanisms. In other words, gradual transformation of energy within the vibrating system.
Dampers
It is strategically placed in the building structure to control floor vibrations and building displacement, cater for occupancy comfort and mitigate against major seismic events.
Aerodynamic damping
It prevents oscillations from occurring indefinitely. It is damping provided by the aerodynamic resistance acting upon the oscillation movement of the airplane.
Amplitude of Stress, Number of Cycles, and Geometry
The energy dissipation is caused by material damping which basically depends on three factors:
Decreases
As damping increases, the peak value _______
Dynamic Response and Transmissibility of a Structure
They are essentially determined by their mass and rigidity properties, responsible for the energy remaining in the system, and by the damping, which determines energy loss in the system.
Vicious Damping, Coulomb Damping, Solid Damping, Slip Damping, Magnetic Damping
Types of Damping
Static Structural Analysis of the Wing
It is done to find deformation, stress, and strain induced in the wing structure.
Modal Analysis
It is done to find the natural frequency of the wing to reduce the noise and avoid vibration
Loads on the Wing
They are the sum of the aerodynamic lift and drag forces, as well as concentrated and distributed weight of wing- mounted engines, fuel stored and structural elements. The resulting load factor will vary within the airplane's flight envelope
Two essential part of the wing
Internal Wing and External Wing Structure
Ribs
It gives the shape to the wing section, support the skin (prevent buckling), and act to prevent the fuel flowing around as the aircraft maneuvers.
Damping
It is of primary importance in controlling vibration response amplitudes under conditions of steady-state resonance and stationary random excitation. Also plays a crucial role in fixing the borderline between stability and instability in many dynamical systems.
decreases vibrations by removing energy through resistance to motion. For rotating equipment, this is necessary to control vibrations and prevent them from damaging the rotor, bearings or other components in the machine.
Complex Stiffness
It is used when the calculating the flutter speeds of airplane wings and tail surfaces
Stiffness
It is defined as the deflection resulting from a force load. An aircraft in straight steady flight has an upwards aerodynamic lift, bending the wing upwards.
Shear Stiffness & Torsional Stiffness
Two Type of Stiffness
Shear Stiffness
It is the ratio of applied shear force to shear deformation.
Torsional Stiffness
It is the ratio of applied torsion moment to the angle of twist
Axial Stiffness
It is the resistance towards axial deformation due to the applied tension (or compression).
Rotational Stiffness
It is the ability of a material to resist rotation by applied Moment.
Lateral Stiffness
It is the ability of a body to resist lateral deflection when a lateral force is applied. Also called as Storey Stiffness
Torsional Stiffness
It is the ratio of applied Torsional moment to the angle of twist.
Bending Stiffness
It is the resistance of a member against bending.
Strength
It is hard to be broken.
Stiffness
It is hard to be deformed.
Complex Airplane
It means an airplane that has a retractable landing gear, flaps, and a controllable pitch propeller, including airplanes equipped with an engine control system consisting of a digital computer and associated accessories for controlling the engine and propeller, such as a Full Authority Digital Engine Computer (FADEC).
In-Plane Bending
If the member is bending in its own plane.
Out of Plane Bending
If it is bending out of its plane
Forced Vibration
There is a quantity Q related to damping that is a measure of the sharpness of resonance.
Transducer
It is a device that transforms changes in mechanical quantities (such as displacement, velocity, acceleration, or force) into changes in electrical quantities (such as voltage or current).
Motion (or Dynamic Force) of the Vibrating Body
It is converted into an electrical signal by the vibration transducers or pickup.
Signal Conversion Instrument
When the output signal (voltage or current) of a transducer is too small to be recorded directly, it is used to amplify the signal to the required value.
The output from this instrument can be presented on a display unit for visual inspection, or recorded by a recording unit, or stored in a computer for later use. The data can then be analyzed to determine the desired vibration characteristics of the machine or structure.
Vibrometer (Velocity Meter, Accelerometer, Phase Meter, or Frequency Meter)
A vibration measuring instrument.
Graph
If the instrument is designed to record the measured quantity, then, suffix meter is to be replaced by a ______.
Electrodynamic Vibrators, Electrohydraulic Vibrators, and Signal Generators (oscillators)
In some applications, there is a need to vibrate a machine or a structure to find its resonance characteristics.
Mechanical motion
It produces a change in electrical resistance (of a rheostat, strain gage or a semiconductor), leading to a change in the output voltage or current.
Electrical Resistance Strain Gage
It consists of a fine wire whose resistance changes when it is subjected to mechanical deformation.
Strain Gage
When it is bonded to a structure, it experiences that same motion (strain) as the structure and hence its resistance change gives the strain applied to the structure.
It is bonded to the surface where the strain is to be measured.
Wire
It is sandwiched between two sheets of thin paper.
Piezoelectric Transducers
It generates electrical charge when subjected to a deformation or mechanical stress. The electrical charge disappears when the mechanical loading is removed. Such a material is called piezoelectric materials and the transducers, which take advantage of the piezoelectric effect, are known as ________
Inductive Transducer
It measures linear displacement
Secondary windings
It has an equal number of turns placed identically on either side of the primary winding.
Primary Winding
it is connected to an alternating current (AC) source. A movable soft iron core is placed inside the bobbin.
It is excited by the AC source, which produces an alternating magnetic field which in turn induces alternating current voltages in the two secondary winding.
Rod
it is slotted longitudinally to reduce eddy current losses
Measured Voltage
It is proportional to the relative movement of the core versus the coils
Vibration Exciter
Used for determining the dynamic characteristics of machines and structures
For fatigue testing of materials
Examples are: Mechanical, electromagnetic/electrodynamic, hydraulic, etc. they are also known as “Shakers”
Direct drive
It can be used either as a reaction exciter or a vibration shake table.
An exciter consists of a table guided to have rectilinear motion, driven by either a crank slider, scotch yoke or a cam type mechanism
Rotating unbalance
An exciter which is used only as a reaction type exciter.
Two unbalance masses rotate in opposite directions in order to generate a dynamic reaction force that acts only in the y-direction
Reaction Exciter
It develops it excitation force through ac inertial loading caused by accelerating a reaction mass
Electrodynamic Exciter
A reverse of electrodynamic transducer
Vibration Pickups
It is when a transducer is used in conjunction with another device to measure vibrations.
Note
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