Modal analysis
Encyclopedia
Modal analysis is the study of the dynamic properties of structures under vibration
Vibration
Vibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.Vibration is occasionally "desirable"...

al excitation.

Modal analysis is the field of measuring and analysing the dynamic response of structures and or fluids when excited by an input. Examples would include measuring the vibration of a car's body when it is attached to an electromagnetic
Electromagnetic
Electromagnetic may refer to:* Electromagnetism* Electromagnetic field* Electromagnetic force* Electromagnetic radiation* Electromagnetic induction* Electromagnetic spectrum...

shaker, or the noise pattern in a room when excited by a loudspeaker.

Modern day modal testing
Modal testing
Modal testing is a form of vibration testing of an object whereby the natural frequencies, modal masses, modal damping ratios and mode shapes of the object under test are determined.A modal test consists of an acquisition phase and an analysis phase...

systems are composed of transducer
Transducer
A transducer is a device that converts one type of energy to another. Energy types include electrical, mechanical, electromagnetic , chemical, acoustic or thermal energy. While the term transducer commonly implies the use of a sensor/detector, any device which converts energy can be considered a...

s (typically accelerometer
Accelerometer
An accelerometer is a device that measures proper acceleration, also called the four-acceleration. This is not necessarily the same as the coordinate acceleration , but is rather the type of acceleration associated with the phenomenon of weight experienced by a test mass that resides in the frame...

A load cell is a transducer that is used to convert a force into electrical signal. This conversion is indirect and happens in two stages. Through a mechanical arrangement, the force being sensed deforms a strain gauge. The strain gauge measures the deformation as an electrical signal, because the...

s), or non contact via a
Laser vibrometer, an analog-to-digital converter frontend (to digitize analog
Analog signal
An analog or analogue signal is any continuous signal for which the time varying feature of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. It differs from a digital signal in terms of small fluctuations in the signal which are...

instrumentation signals) and a host PC (personal computer
Personal computer
A personal computer is any general-purpose computer whose size, capabilities, and original sales price make it useful for individuals, and which is intended to be operated directly by an end-user with no intervening computer operator...

) to view the data and analyze it.

Classically this was done with a SIMO (single-input, multiple-output) approach, that is, one excitation point, and then the response is measured at many other points. In the past a hammer survey, using a fixed accelerometer and a roving hammer as excitation, gave a MISO (multiple-input, single-output) analysis, which is mathematically identical to SIMO, due to the principle of reciprocity
Reciprocity (engineering)
Reciprocity in linear systems is the principle that a response Rab, measured at a location a, when the system has an excitation signal applied at a location b, is exactly equal to Rba which is the response at location b, when that same excitation is applied at a...

. In recent years MIMO (multi-input, multiple-output) has become more practical, where partial coherence analysis identifies which part of the response comes from which excitation source.

Typical excitation signals can be classed as impulse, broadband
The term broadband refers to a telecommunications signal or device of greater bandwidth, in some sense, than another standard or usual signal or device . Different criteria for "broad" have been applied in different contexts and at different times...

, swept sine
Sine
In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....

, chirp, and possibly others. Each has its own advantages and disadvantages.

The analysis of the signals typically relies on Fourier analysis. The resulting transfer function
Transfer function
A transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant system. With optical imaging devices, for example, it is the Fourier transform of the point spread function i.e...

will show one or more resonances, whose characteristic mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

, frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

and damping
Damping
In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator.In mechanics, friction is one such damping effect...

can be estimated from the measurements.

The animated display of the mode shape is very useful to NVH (noise, vibration, and harshness)
Noise, Vibration, and Harshness
Noise, vibration, and harshness , also known as noise and vibration , is the study and modification of the noise and vibration characteristics of vehicles, particularly cars and trucks...

engineers.

The results can also be used to correlate with finite element analysis normal mode solutions.

## Structures

In structural engineering
Structural engineering
Structural engineering is a field of engineering dealing with the analysis and design of structures that support or resist loads. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right....

, modal analysis uses a structure's overall mass and stiffness to find the various periods that it will naturally resonate at. These periods of vibration are very important to note in earthquake engineering
Earthquake engineering
Earthquake engineering is the scientific field concerned with protecting society, the natural and the man-made environment from earthquakes by limiting the seismic risk to socio-economically acceptable levels...

, as it is imperative that a building's natural frequency does not match the frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

of expected earthquakes in the region in which the building is to be constructed. If a structure's natural frequency matches an earthquake's frequency, the structure could continue to resonate and experience structural damage.

Although modal analysis is usually carried out by computers, it is possible to hand-calculate the period of vibration
Vibration
Vibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.Vibration is occasionally "desirable"...

of any high-rise building by idealizing it as a fixed-ended cantilever with lumped masses. For a more detailed explanation, see "Structural Analysis" by Ghali, Neville, and Brown, as it provides an easy-to-follow approach to idealizing and solving complex structures by hand.

## Electrodynamics

The basic idea of a modal analysis in electrodynamics is the same as in mechanics. The application is to determine which electromagnetic wave modes can stand or propagate within conducting enclosures such as waveguide
Waveguide
A waveguide is a structure which guides waves, such as electromagnetic waves or sound waves. There are different types of waveguides for each type of wave...

s or resonator
Resonator
A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonant frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical...

s.

• Frequency analysis
Frequency analysis
In cryptanalysis, frequency analysis is the study of the frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers....

• Modal analysis using FEM
Modal analysis using FEM
The goal of modal analysis in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during free vibration. It is common to use the finite element method to perform this analysis because, like other calculations using the FEM, the object being...

• Mode shape
• Eigenanalysis
• Structural dynamics
Structural Dynamics
Structural dynamics is a subset of structural analysis which covers the behaviour of structures subjected to dynamic loading. Dynamic loads include people, wind, waves, traffic, earthquakes, and blasts. Any structure can be subject to dynamic loading. Dynamic analysis can be used to find dynamic...

• Vibration
Vibration
Vibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.Vibration is occasionally "desirable"...

• Modal testing
Modal testing
Modal testing is a form of vibration testing of an object whereby the natural frequencies, modal masses, modal damping ratios and mode shapes of the object under test are determined.A modal test consists of an acquisition phase and an analysis phase...

• Seismic performance analysis