Effects of a Concentrated Mass on Chaotic Vibrations of a Clamped Circular Plate With Initial Deformation

2011 ◽  
Author(s):  
Kenji Okada ◽  
Ken-ichi Nagai ◽  
Shinichi Maruyama ◽  
Takao Yamaguchi
Keyword(s):  
Circular Plate ◽  
Fourier Spectrum ◽  
Principal Component ◽  
Frequency Region ◽  
Initial Deformation ◽  
Periodic Excitation ◽  
Contribution Ratio ◽  
Concentrated Mass ◽  
Chaotic Vibrations ◽  
Maximum Lyapunov Exponents

Experimental results are presented on effects of a concentrated mass on chaotic vibrations of a clamped circular plate. The plate has initial deformation due to initial deflection and initial in-plane compressive constraint at the boundary. The concentrated mass is attached on the center of the plate. Under periodic excitation, non-periodic responses with dynamic snap-through are generated on the plates. The responses are inspected by the Fourier spectrum, the Poincare´ projection, the maximum Lyapunov exponents and the principal component analysis. The non-periodic responses are found to be chaotic responses. The lowest mode of vibration shows the largest contribution ratio. When the concentrated mass is attached on the plate, the region of the response is shifted to the lower frequency. Furthermore, the width of the frequency region is decreased. The contribution ratio of the lowest mode slightly increases.

258 Experiments on Chaotic Vibrations of a Clamped Circular Plate with Initial Deformation

2009 ◽  
Vol 2009 (0) ◽  
pp. _258-1_-_258-6_
Author(s):  
Kenji OKADA ◽  
Shinichi MARUYAMA ◽  
Ken-ichi Nagai ◽  
Takao YAMAGUCHI
Keyword(s):  
Circular Plate ◽  
Initial Deformation ◽  
Chaotic Vibrations

141 Effects of a Concentrated Mass on Chaotic Vibrations of a Clamped Circular Plate

2010 ◽  
Vol 2010 (0) ◽  
pp. _141-1_-_141-6_
Author(s):  
Kenji OKADA ◽  
Shinichi MARUYAMA ◽  
Ken-ichi Nagai ◽  
Takao YAMAGUCHI
Keyword(s):  
Circular Plate ◽  
Concentrated Mass ◽  
Chaotic Vibrations

133 Experiments on Chaotic Vibrations of a Circular Plate with Initial Deformation

2008 ◽  
Vol 2008 (0) ◽  
pp. _133-1_-_133-6_
Author(s):  
Shinichi MARUYAMA ◽  
Ken-ichi NAGAI ◽  
Yusuke HAYASHI ◽  
Takao YAMAGUCHI
Keyword(s):  
Circular Plate ◽  
Initial Deformation ◽  
Chaotic Vibrations

An Integral Equation Method for Free Vibration of Circular Plate with Concentrated Mass at Arbitrary Positions

2011 ◽  
Vol 255-260 ◽  
pp. 1830-1835 ◽  
Author(s):  
Gang Cheng ◽  
Quan Cheng ◽  
Wei Dong Wang
Keyword(s):  
Integral Equation ◽  
Eigenvalue Problem ◽  
Free Vibration ◽  
Green’S Function ◽  
Circular Plate ◽  
Green's Function ◽  
Integral Equation Method ◽  
Free Vibrations ◽  
Equation Method ◽  
Concentrated Mass

The paper concerns on the free vibrations of circular plate with arbitrary number of the mounted masses at arbitrary positions by using the integral equation method. A set of complete systems of orthogonal functions, which is constructed by Bessel functions of the first kind, is used to construct the Green's function of circular plates firstly. Then the eigenvalue problem of free vibration of circular plate carrying oscillators and elastic supports at arbitrary positions is transformed into the problem of integral equation by using the superposition theorem and the physical meaning of the Green’s function. And then the eigenvalue problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order. Numerical examples are presented.

Vibrating circular plate carrying a concentrated mass: Comparison of results

1990 ◽  
Vol 138 (2) ◽  
pp. 335-336 ◽  
Author(s):  
M.J. Maurizi ◽  
P.A.A. Laura ◽  
D.V. Bambill ◽  
C. Rossit
Keyword(s):  
Circular Plate ◽  
Concentrated Mass ◽  
Comparison Of Results ◽  
Mass Comparison

110 Effects of a Concentrated Mass on Chaotic Vibrations of an Annular Plate

2008 ◽  
Vol 2008 (0) ◽  
pp. _110-1_-_110-6_
Author(s):  
Ken-ichi NAGAI ◽  
Kenji OKADA ◽  
Shinichi MARUYAMA ◽  
Takao YAMAGUCHI
Keyword(s):  
Annular Plate ◽  
Concentrated Mass ◽  
Chaotic Vibrations

Chaotic Vibrations on a Coupled Vibrating System of a Post-Buckled Cantilevered Beam and an Axial Vibrating Body Connected With a Stretched String

2009 ◽  
Author(s):  
Shinichi Maruyama ◽  
Ken-ichi Nagai ◽  
Kota Muto ◽  
Takao Yamaguchi
Keyword(s):  
Principal Component Analysis ◽  
Vibration Mode ◽  
Harmonic Balance Method ◽  
Principal Component ◽  
Component Analysis ◽  
Axial Displacement ◽  
Chaotic Vibrations ◽  
Vibrating System ◽  
Chaotic Response ◽  
Cantilevered Beam

Analytical results are presented on chaotic vibrations on a coupled vibrating system of a post-buckled cantilevered beam and an axial vibrating body connected with a stretched string. The string is stretched between the top end of the cantilevered beam and the axial vibrating body which consists of a mass and a spring. As an initial axial displacement is applied to the spring, the beam is buckled by the tensile force of the string. The main scope of this paper is to investigate the effects of the axial inertia of the vibrating body on the chaotic vibrations of the system. The dynamical model involves nonlinear geometrical coupling between the deformation and the axial force of the beam at the boundary. Furthermore, the problem includes the static buckling and the nonlinear vibration. By using the mode shape function, which was proposed by the senior author, as a coordinate function of the governing equations, nonlinear ordinary differential equations in multiple-degree-of-freedom system are derived by the modified Galerkin procedure. Periodic responses of the beam are calculated with the harmonic balance method, while chaotic responses are integrated numerically. Chaotic time responses are inspected with the Fourier spectra, the Poincare´ projections, the maximum Lyapunov exponents and the principal component analysis. Chaotic responses are generated from the sub-harmonic resonance responses of 1/2 and 1/3 orders. The results of the principal component analysis shows that the lowest mode of vibration contributes to the chaotic response dominantly, while the second mode of vibration also contribute to the chaos with small amount of amplitude. Inspection of the kinetic energy of each vibration mode shows that the vibration mode with large axial displacement is also dominant in the chaotic response.

Sign in / Sign up

Export Citation Format

Share Document