SDV FINALS (Last update: Lecture 5-11(nd) )

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.