A theorem on the representation of the field of forced vibrations of a composite elastic system

Bobrovnitskiĭ, Yu. I.

doi:10.1134/1.1403536

Cited by 23 publications

(18 citation statements)

References 4 publications

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“…This statement has been rigorously substantiated in the form of a theorem by Yu.I. Bobrovnitskii [11].…”

Section: Solution For a Simple Stiffened Structurementioning

confidence: 99%

“…We find that an arbitrary stiffened structure is determined by four matrices E pjm , F mpj and is described by four equations: (11) where the first equation is the dynamic equation of the main body, the second is the dynamic equation of the stiffening elements, and the third and fourth equations represent the kinematic and dynamic contact condi tions. From these equations, we obtain a single equation for the generalized displacements of the main body W m :…”

Section: A Universal Expression For Calculating the Displacements Of mentioning

confidence: 99%

“…Substituting them in the first equation (11) for the generalized displacements of the main body, we obtain (18) The resulting equation given by Eqs. (17) and (18) is universal and can be used for solving a wide range of problems.…”

Section: A Universal Expression For Calculating the Displacements Of mentioning

confidence: 99%

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Evaluation of the effect of stopping selected frames on noise in the cabin of a propeller airplane

Efimtsov

Lazarev

2015

Acoust. Phys.

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A unified approach is proposed to solve vibration problems for stiffened plates, shells, and other arbitrary stiffened structures. The approach is applicable under the condition that independent solutions for the stiffened structure and the stiffening elements are known in the form of explicit expressions determining generalized displacements through generalized forces. The proposed universal equation is used to solve the problem of deterministic vibrations of a closed cylindrical shell with "smeared" stringers and irregular dis crete frames. The solution is used to estimate the effect of noise suppression achieved in the cabin of a pro peller airplane by stopping some of the frames positioned near the propeller.

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“…This statement has been rigorously substantiated in the form of a theorem by Yu.I. Bobrovnitskii [11].…”

Section: Solution For a Simple Stiffened Structurementioning

confidence: 99%

Section: A Universal Expression For Calculating the Displacements Of mentioning

confidence: 99%

See 1 more Smart Citation

Evaluation of the effect of stopping selected frames on noise in the cabin of a propeller airplane

Efimtsov

Lazarev

2015

Acoust. Phys.

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“…As before we replace the excitation at b i with the equivalent excitation, i.e., the blocked force distribution f ðsÞ ðb i Þ applied to the interface. 13,14 The velocity at the same points as before can thus be re-expressed in terms of an integration over the interface…”

Section: B Extension To Continuous Interfaces and Arbitrary Sub-domainsmentioning

confidence: 99%

“…We now wish to generate an identical velocity field in substructure A but by applying a set of forces at the interface c rather than at b i . Bobrovnitskii 13 (see also Ref. 14) has shown that this occurs when the forces applied at c are equal and opposite to the "blocked forces," denoted f ðb i Þ bl , i.e., the reaction forces obtained at c under the action of f b i when c is blocked.…”

Section: A Theorymentioning

confidence: 99%

The “round trip” theory for reconstruction of Green's functions at passive locations

Moorhouse

Elliott

2013

The Journal of the Acoustical Society of America

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An expression for the Green's function at an arbitrary set of passive locations (no applied force) is derived and validated by experiment. Three sets of points are involved, the passive reconstruction points, c, which lie on a virtual boundary and two sets of auxiliary points, denoted a and b, located either side. The reconstruction is achieved using Green's functions forming a "round trip" from and to the reconstruction points via a and b. A two stage measurement procedure is described involving excitation at b and a but with no excitation required at the reconstruction points. A known "round trip" relationship is first introduced which is theoretically exact for points on a multi-point interface between two linear, time invariant subsystems. Experimental results for frequency response functions of a beam-plate structure show that this relationship gives good results in practice. It is then shown that the theory provides an Nth order approximation for the Green's function at arbitrary points, where N is the number of points at b. The expression is validated by reconstructing point and transfer frequency response functions at two passive points on an aluminum plate.

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A Patch Transfer Function Approach for Combined Computational-Experimental Analysis of Vibro-Porous-Acoustic Problems

Rejlek

Nijman

Veronesi

et al. 2015

SpringerBriefs in Applied Sciences and Technology

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A theorem on the representation of the field of forced vibrations of a composite elastic system

Cited by 23 publications

References 4 publications

Evaluation of the effect of stopping selected frames on noise in the cabin of a propeller airplane

Evaluation of the effect of stopping selected frames on noise in the cabin of a propeller airplane

The “round trip” theory for reconstruction of Green's functions at passive locations

A Patch Transfer Function Approach for Combined Computational-Experimental Analysis of Vibro-Porous-Acoustic Problems

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