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論文
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永井, 健一 ; 大佐々, 吉宏 ; 長屋, 幸助 ; 武田, 定彦 ; 谷藤, 克也
概要:
application/pdf<br />Journal Article<br />An analytical method is presented for the bending vibration of a circular dise carrying concentrated masses, introducing a new mode of shape function to the Galerkin method. Deflection of
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the plate is expressed by a product of the mode shape function along radial direction and the circumferential periodic function. The mode shape function is assumed to be the sum of the product of the trigonometrical function and the finite power series. The coefficients of the power series are found to be satisfied by the boundary condition of the plate. Applying the Galerkin method, the number of sets of differential equation with second-order time functions are reduced. It is found that this method gives good accuracy to the natural frequencies within the small number of terms for unknown time functions
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論文
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永井, 健一 ; 渥美, 全弘 ; 杉山, 晋一 ; 長屋, 幸助 ; 谷藤, 克也 ; 武田, 定彦
概要:
application/pdf<br />Journal Article<br />This paper presents analytical results of non-linear vibrations of a traveling beam levitated by magnetic forces. The problem is modeled as the Euler-Bernoulli beam with a variable cross section
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supported by non-linear springs. The beam and the springs move on an undulated line. Introducing a new mode shape function which is expressed as the product of the trigonometric function and the power series truncated to the fourth order and utilizing the galerkin procedure, basic equations are reduced to the coupled non-linear equations. The steady state solutions of the beam was obtained using the harmonic balance method. It is found that the non-linear responses show the type of soft-spring, the unsymmetric support of the spring or the unsymetric cross section to the mid-point of the beam show large amplitude vibrations of a rotating motion and that of a translating motion in relatively large frequency range.
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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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