As has been mentioned above the second chapter of the article is dedicated to the consideration of the systems with more than one degree of freedom. These systems also have more than one natural frequency and conditions of forced vibration they also have more than one resonant frequency.
In this chapter such tasks have been described as orthogonality of principal modes (planar and non-planar systems); static and dynamic coupling; systems with rigid body degrees of freedom and geared systems. Lagrange’s equations of motion are a central point of the part, in which forced vibration has been considered. The practical application of Lagrange’s equations is a central point of the whole work under review in turn.
GLOSSARY
- A-
- an increase of speed or velocity; angular acceleration; initial acceleration
- the process of doing, acting| the working of one thing on another;
balancing action; brake action
- the act of admitting;
chararacteristic admittance; complex admittance.
- the maximum numerical value attained by a periodically varying quantity measured from its mean value taken as zero and giving a measure of a vibratory or oscillatory disturbance;
peak-to-peak amplitude; resonance amplitude
- the extent of a surface as measured by the number of squares it contains each with side 1 unit long or by another standard measure;
per unit area; moment area
- decrease in intensity of a signal, beam, or wave; attenuation per unit length; dissipative attenuation
- the force, due to gravitational, electric, magnetic or other effects, causing or tending to cause two bodies to a approach one another;
gravitational attraction
-
the line, real or imaginary, around which a thing
rotates; axis of revolution; axis of symmetry
- B -
- to weight in a balance; balance of couples; back balance
- the action of carrying; carriage expansion bearing; free bearing
- manners, deportment; the way in which a machine works frictional behavior; viscoelastic behavior
- to make curved or crooked; bending rigidity; elastic bending
- C-
- an axis, pivot or point around which an object moves; center of attraction; center of rotation
- a quality typical of a person, place or object; amplitude characteristic; kinetic characteristic
- any one of a set of numbers specifying the position of a point on a line, a surface or in space; orthogonal coordinates
- a pair of parallel forces of equal magnitude but acting in opposite directions on the same body; centrifugal couple; turning couple
- to fracture without complete separation; fatigue crack; stress crack
- the act or pace of creeping; initial creep; total creep
- a line or direction subject to continuous deviation from the straight;
compression curve; decay curve
-D-
- decreasing the amplitude of vibration or oscillation of a body or a wave motion;
critically damped; exponentially damped
- a known fact;
frequency-response data; design data
- a deviation, a turning or bending aside or down; sagging deflection; static deflection
- the limit of the ratio of the increment of a function to the increment in the independent variable as the latter increment tends to zero;
partial derivative
- a figure or sketch designed to give a broad explanation; diagram of strains; constitutional diagram
- the vector, drawn between two successive points on the trajectory of a moving object, representing the magnitude and direction of the motion;
longitudinal displacement; shear displacement
- the interval for any range of values;
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