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論文
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永井, 健一 ; 荒井, 徳幸 ; 長屋, 幸助 ; 武田, 定彦
概要:
application/pdf<br />Journal Article<br />An analytical method is presented for free flexural vibrations of a cantilevered beam with a concentrated mass, introducing the new mode shape function to the Galerkin procedure. The mode
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shape function is expressed with the sum of the product of the trigonometrical function and the finite power series truncated with the fourth order. The trigonometrical function expresses the form of the higher mode of vibration. The coefficients of the power series are determined by solving the homogeneous equations for the boundary conditions of the beam. Applying the Galerkin method, the sets of differential equation in a time function are reduced. It is found that this method gives good accuracy to the natural frequencies and the natural modes of vibration within the limited number of terms for unknown time functions.
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| 2.
論文 |
論文
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永井, 健一 ; 笹井, 重俊 ; 長屋, 幸助 ; 武田, 定彦 ; 内山, 茂
概要:
application/pdf<br />Journal Article<br />This paper presents a method for the error compensation of measuring data in a two-dimensional length measuring device from lack of sufficient stiffness. Introducing the mode shape function
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which is expressed with the product of the finite power series truncated with fourth order and the trigonometric function to the least square approximation. Applying the method to the test device, the effects of compensation are clarified. It is found that this method gives good results to improve the measuring accuracy with the limited number of terms for unknown coefficients, compared with the approach of the Fourier series.
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| 3.
論文 |
論文
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永井, 健一 ; 長屋, 幸助 ; 武田, 定彦 ; 荒井, 徳幸
概要:
application/pdf<br />Journal Article<br />The free bending vibrations of beams with a concentrated mass subjected to axial forces caused by axial acceleration are analyzed by the Galerkin method, introducing the mode shape functions which
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are the sum of the products of the finite power series and the trigonometrical function. This analytical method makes it easy to construct the equations of motion in each boundary condition only by exchanging the coefficients of the finite power series. Numerical calculations are carried out under four sets of boundary conditions combined with simply supported and clamped edges. The natural frequencies and the corresponding modes of vibration are determined under both various locations of the concentrated mass and axial forces. it is found that the transverse inertia force and the axial force, due to the concentrated mass, have significant effects on the change of the natural frequencies for beams. Furthermore the distinction of boundary conditions gives predominant influence to the variation of natural frequencies.
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