natural frequencies 
The forward problem is to solve the natural frequencies through a cracked structural model and the inverse problem is to quantitatively determine the crack parameters using the experimental testing frequencies.


Contour plots of normalized crack location versus normalized crack size were plotted by using the first three natural frequencies as the inputs.


The estimations of natural frequencies and damping coefficients of the platform found as a result of data processing of microacceleration measurements made during its free oscillations are obtained.


Determining the natural frequencies of fluid oscillations in complex pipelines


Below we formulate the problem of the natural frequencies of small oscillations of a liquid for the general case of an equilibrium liquid surface in a weak potential mass force field.


It is shown that the natural frequencies and the corresponding eigenfunctions of this problem may be found by the Ritz method.


Dynamic stability of lattice blades with slight mismatch of natural frequencies


Natural frequencies and forms of small oscillations of an ideal liquid in a spherical vessel in a weak force field


The plane problem of determination of the natural frequencies of small oscillations of a viscous liquid rotating in a partially filled cylindrical vessel under conditions of weightlessness is examined.


A numerical method is proposed for determining the natural frequencies and modes of the small oscillations of an ideal fluid in a halfspace bounded above by a rigid plane with an aperture of arbitrary shape.


For the five lowest oscillation modes the natural frequencies and shapes are determined with high accuracy over a wide range of variation of the eccentricity.


The first natural frequencies are determined for elliptic basins with different eccentricities and angular velocities and certain characteristic natural shapes demonstrating the distinctive features of tidal flows in elliptic basins are constructed.


The shift produced by the resonator in the natural frequencies of the room is calculated.


The problem of determining the type of fastening of a circular plate inaccessible to direct observation from the natural frequencies of its symmetric flexural vibrations is considered.


An approximate formula for the determination of unknown boundary conditions from three natural frequencies is obtained.


It is assumed that the natural frequencies can be given approximately, within a certain accuracy.


Identification of the boundary conditions of a rectangular membrane from its natural frequencies


The first method allows one to identify the elastic constraint on each of the sides of the rectangular membrane from its four natural frequencies.


Identification of the type and parameters of fastening from the natural frequencies of a fastened rod


In this connection, a possible statement of the problem is as follows: to identify the type and parameters of fastening on both ends of a homogeneous rod from its natural frequencies.

