Skip to main content

Mode of vibration .

      What is meant by modes of vibration? Can anyone explain the ...

                In physics and engineering, for a dynamical system according wave theory, a mode is a standing wave state of excitation, in which all the components of the system will be affected sinusoidally under a specified fixed frequency. Because no real system can perfectly fit under the standing wave framework, the mode concept is taken as a general characterization of specific states of oscillation, thus treating the dynamic system in a linear fashion, in where linear superposition of states can be performed. As classical examples, there are: 

* In a mechanical dynamical system, a vibrating rope is the most clear example of a mode, in which the rope is the medium, the stress on the rope is the excitation, and the displacement of the rope with respect to its static state is the modal variable. 

* In an acoustic dynamical systems, a single sound pitch is a mode, in which the air is the medium, the sound pressure in the air is the excitation, and the displacement of the air molecules is the modal variable. * In a structural dynamical systems, a high tall building oscillating under its most flexural axis is a mode, in which all the material of the building -under the proper numerical simplifications- is the medium, the seismic/wind/environmental solicitations are the excitations and the displacements are the modal variable. 

* In an electrical dynamical systems, a resonant cavity made of thin metal walls, enclosing a hollow space, for a particle accelerator is a pure standing wave system, and thus an example of a mode, in which the hollow space of the cavity is the medium, the RF source (a Klystron or another RF source) is the excitation and the electromagnetic field is the modal variable.

 * When relating to music, normal modes of vibrating instruments (strings, air pipes, drums, etc.) are called "harmonics" or "overtones". 

* The concept of normal modes also finds application in optics, quantum mechanics, and molecular dynamics. Most dynamical system can be excited under several modes. Each mode is characterized by one or several frequencies, according the modal variable field. For example, a vibrating rope in the 2D space is defined by a single-frequency (1D axial displacement), but a vibrating rope in the 3D space is defined by two frequencies -2D axial displacement-. For a given amplitude on the modal variable, each mode will store an specific amount of energy, because of the sinusoidal excitation. From all the modes of a dynamical system, the normal or dominant mode of a system, will be the mode storing the minimum amount of energy, for a given amplitude of the modal variable. Or equivalently, for a given stored amount of energy, will be the mode imposing the maximum amplitude of the modal variable

Labels

Labels:

Comments

Post a Comment

Popular posts from this blog

The manufacture of Biodiesel from used cooking oil

ABSTRACT                      The increasing awareness of the depletion of fossil fuel resources and the environmental benefits of biodiesel fuel has made it more attractive in recent times. Its primary advantages deal with it being one of the most renewable fuels currently available and it is also non-toxic and biodegradable. It can also be used directly in most diesel engines without requiring extensive engine modifications. However, the cost of biodiesel is the major hurdle to its commercialization in comparison to petroleum-based diesel fuel. The high cost is primarily due to the raw material, mostly neat cooking oil. Used cooking oil is one of the economical sources for biodiesel production. However, the products formed during frying, can affect the transesterification reaction and the biodiesel properties.     The production of biodiesel from waste cooking oil offers a triple-facet solution: economic, environmen...
9 comments
Read more

Mechanical and durability Behavior of fiber reinforced concrete incorporating deferent types of natural, pp and steel fibers

  1. Introduction As an important building material, concrete has been widely used in civil engineering applications such as bridges and roads engineering, and the related experimental study of the mechanical properties of concrete was also fruitful . With the vigorous development of engineering construction, high-performance concretes such as fiber-reinforced concrete was applied gradually in important engineering structures . Among these high-performance concretes, for the advantages of low cost, easy fabrication, and performance improvements, obviously, steel fiber-reinforced concrete was used widely in the current engineering field . However, the study showed that uneven incorporation of steel fiber would affect the fluidity and uniformity of concrete mixing and even result in fiber bonding, which eventually affects the reinforcement effect of mechanical properties. Up to now, most research paid attention on the improvement effect of different types of fiber or optimum fiber co...
Post a Comment
Read more

Chemical reaction and equation

  Chemical reactions -   The transformation of chemical substance into a new chemical substance by making and breaking of bonds between different atoms is known as Chemical Reaction.  Signs of a chemical reaction These factors denote that a chemical reaction has taken place- change of state of substance, change of color of substance,evolution of heat, absorption of heat, evolution of gas and evolution of light. Chemical Equation:   The representation of chemical reaction by means of symbols of substances in the form of formulae is called chemical equation.  E.g. - H 2  + O 2  ⇒ H 2 O                        Balanced Chemical Equation:   A balanced chemical equation has number atoms of each element equal on both left and right sides of the reaction.                                    *No...
1 comment
Read more