This paper considers one computational method of the eigenvalues approximate value of the horizontal vibration problem of beam. The proof of our main result is based on the variational formula. First of all, Cauchy in...This paper considers one computational method of the eigenvalues approximate value of the horizontal vibration problem of beam. The proof of our main result is based on the variational formula. First of all, Cauchy inequality is used to obtain a basic inequality. Secondly, the functions of basis are made by Galerkin method, and the error estimates of eignevalues are obtained by Cauchy inequality. At last, the computational method of the approximate value of the eigenvalues turns out immediately, and acc...展开更多
In this paper,we deal with the nonlinear second-order differential equation with damped vibration term involving p-Laplacian operator.Of particular interest is the resolution of an open problem.An interesting outcome ...In this paper,we deal with the nonlinear second-order differential equation with damped vibration term involving p-Laplacian operator.Of particular interest is the resolution of an open problem.An interesting outcome from our result is that we can obtain the fast homoclinic solution with general superlinear growth assumption in suitable Sobolev space.To our knowledge,our theorems appear to be the first such result about damped vibration problem with p-Laplacian operator.展开更多
The tridiagonal coefficient matrix for the ＂fixed-fixed＂ spring-mass system was obtained by changing spring length. And then a new algorithm of the inverse problem was designed to construct the masses and the spring...The tridiagonal coefficient matrix for the ＂fixed-fixed＂ spring-mass system was obtained by changing spring length. And then a new algorithm of the inverse problem was designed to construct the masses and the spring constants from the natural frequencies of the ＂fixed-fixed＂ and ＂fixed-fres＂ spring-mass systems. An example was given to illustrate the results.展开更多
The end windings of generators are excited to vibrations due to electromagnetic forces which can cause severe damage （especially in case of resonance） and noise. To avoid this, it is important to predict the natural...The end windings of generators are excited to vibrations due to electromagnetic forces which can cause severe damage （especially in case of resonance） and noise. To avoid this, it is important to predict the natural frequencies and modes of the end windings with finite elements during the design process. Hence, a material model of the complete stator bar is necessary. This paper shows the development of such a material model. The composite structure of a stator bar is quite complex and makes it impossible to provide a quick calculation of the eigenvalues. That is the reason for using a suitable, homogeneously, geometry based solid model. Special attention was paid to the experimental determination of the material characteristics of the orthotropic composite space brackets. The numerical results have been evaluated against measurements. Eigenvalues, Young＇s modulus, and shear modulus have been experimentally investigated.展开更多
We formulate a coupled vibration between plate and acoustic field in mathematically rigorous fashion. It leads to a non-standard eigenvalue problem. A finite element approximation is considered in an abstract way, and...We formulate a coupled vibration between plate and acoustic field in mathematically rigorous fashion. It leads to a non-standard eigenvalue problem. A finite element approximation is considered in an abstract way, and the approximate eigenvalue problem is written in an operator form by means of some Ritz projections. The order of convergence is proved based on the result of Babugka and Osborn. Some numerical example is shown for the problem for which the exact analytical solutions are calculated. The results shows that the convergence order is consistent with the one by the numerical analysis.展开更多
A frequency equation for the vibration of an engine seating and an equation for pressure under the bottom of the engine are obtained.The present approach extends the so called Muravskii model possessing high practical...A frequency equation for the vibration of an engine seating and an equation for pressure under the bottom of the engine are obtained.The present approach extends the so called Muravskii model possessing high practical accuracy of the ground modeling with its simultaneous simplicity.展开更多
Aeroelastic vibration problems are commonly found in modern compressors operating in off-design conditions.Large amplitude vibration could lead to high cycle fatigue(HCF)of blade and usually occurs in front stages of ...Aeroelastic vibration problems are commonly found in modern compressors operating in off-design conditions.Large amplitude vibration could lead to high cycle fatigue(HCF)of blade and usually occurs in front stages of axial compressors.In this study,the influence of tip gap size on aeroelastic stability is analyzed in a 1.5 stage compressor with an in-house fluid-structure interaction code.A three-dimensional unstructured finite-volume compressible flow solver is applied in the fluid domain and a structure dynamic solver with the modal superimposition method for blade motion is used in the structure domain.Rotor tip clearances of 1%,2%and 3%of tip axial chord at maximum rotor loading conditions at off-design speeds are analyzed for aeroelastic stability.The tip leakage flow and vortex structure can be seen near the blade tip region at a larger tip gap size.The aeroelastic stability of rotor blade at different tip gap sizes is mainly influenced by the 1st torsion mode,and the variation of aerodynamic damping is not monotonous.The intensity of the tip vortex and shock wave are the key factors affecting the aeroelastic stability of rotor when tip gap size increases.展开更多
文摘This paper considers one computational method of the eigenvalues approximate value of the horizontal vibration problem of beam. The proof of our main result is based on the variational formula. First of all, Cauchy inequality is used to obtain a basic inequality. Secondly, the functions of basis are made by Galerkin method, and the error estimates of eignevalues are obtained by Cauchy inequality. At last, the computational method of the approximate value of the eigenvalues turns out immediately, and acc...
基金partially supported by Natural Science Foundation of Hubei Province of China(2021CFB473)。
文摘In this paper,we deal with the nonlinear second-order differential equation with damped vibration term involving p-Laplacian operator.Of particular interest is the resolution of an open problem.An interesting outcome from our result is that we can obtain the fast homoclinic solution with general superlinear growth assumption in suitable Sobolev space.To our knowledge,our theorems appear to be the first such result about damped vibration problem with p-Laplacian operator.
基金Project supported by the National Natural Science Foundation of China(Grant No.10271074)
文摘The tridiagonal coefficient matrix for the ＂fixed-fixed＂ spring-mass system was obtained by changing spring length. And then a new algorithm of the inverse problem was designed to construct the masses and the spring constants from the natural frequencies of the ＂fixed-fixed＂ and ＂fixed-fres＂ spring-mass systems. An example was given to illustrate the results.
文摘The end windings of generators are excited to vibrations due to electromagnetic forces which can cause severe damage （especially in case of resonance） and noise. To avoid this, it is important to predict the natural frequencies and modes of the end windings with finite elements during the design process. Hence, a material model of the complete stator bar is necessary. This paper shows the development of such a material model. The composite structure of a stator bar is quite complex and makes it impossible to provide a quick calculation of the eigenvalues. That is the reason for using a suitable, homogeneously, geometry based solid model. Special attention was paid to the experimental determination of the material characteristics of the orthotropic composite space brackets. The numerical results have been evaluated against measurements. Eigenvalues, Young＇s modulus, and shear modulus have been experimentally investigated.
文摘We formulate a coupled vibration between plate and acoustic field in mathematically rigorous fashion. It leads to a non-standard eigenvalue problem. A finite element approximation is considered in an abstract way, and the approximate eigenvalue problem is written in an operator form by means of some Ritz projections. The order of convergence is proved based on the result of Babugka and Osborn. Some numerical example is shown for the problem for which the exact analytical solutions are calculated. The results shows that the convergence order is consistent with the one by the numerical analysis.
文摘A frequency equation for the vibration of an engine seating and an equation for pressure under the bottom of the engine are obtained.The present approach extends the so called Muravskii model possessing high practical accuracy of the ground modeling with its simultaneous simplicity.
文摘Aeroelastic vibration problems are commonly found in modern compressors operating in off-design conditions.Large amplitude vibration could lead to high cycle fatigue(HCF)of blade and usually occurs in front stages of axial compressors.In this study,the influence of tip gap size on aeroelastic stability is analyzed in a 1.5 stage compressor with an in-house fluid-structure interaction code.A three-dimensional unstructured finite-volume compressible flow solver is applied in the fluid domain and a structure dynamic solver with the modal superimposition method for blade motion is used in the structure domain.Rotor tip clearances of 1%,2%and 3%of tip axial chord at maximum rotor loading conditions at off-design speeds are analyzed for aeroelastic stability.The tip leakage flow and vortex structure can be seen near the blade tip region at a larger tip gap size.The aeroelastic stability of rotor blade at different tip gap sizes is mainly influenced by the 1st torsion mode,and the variation of aerodynamic damping is not monotonous.The intensity of the tip vortex and shock wave are the key factors affecting the aeroelastic stability of rotor when tip gap size increases.
