We have developed a new kind of repetitive control to reduce position error caused by both synchronous and asynchronous disturbances to disc rotation in optical disc drives. Conventional repetitive control greatly decreases position error synchronized with the disc rotation, but increases asynchronous position error. To decrease the asynchronous position error, a new method that averages control input signal every disc rotation has been incorporated into the conventional method. Experimental tests show that, at 9200-rpm disc rotation, the new control method significantly decreases the synchronous position error but does not increase the asynchronous position error. In other words, the new method achieves total position error 48% less than that of the conventional method (i.e., without using repetitive control).

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A numerical approach for analyzing the forced vibration problem of an unsymmetrically laminated FRP (fiber reinforced plastic) composite plate has already been proposed by us. The purpose of this study was to apply the numerical approach to a clamped antisymmetrically laminated rectangular plate and to compare numerical results with experimental ones. First, we attempted to estimate numerically the steady-state response of a rectangular plate, and discussed the convergence of the results. Next, the accelerances of the clamped antisymmetrically laminated square and rectangular plates made of CFRP were obtained experimentally. These experimental accelerances were compared with and found to agree well with the numerical results computed using the measured structural damping factors of the lamina.

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A numerical approach is proposed for analyzing forced vibration problems of a symmetrically laminated FRP (fiber reinforced plastic) composite plate. The numerical results for the forced vibration problem of a clamped symmetrically laminated plate are compared with experimental ones. First, we attempted to estimate numerically the steady-state response of a square plate, and the convergence of the results is discussed. The effect of structural damping factors on the steady-state response of the plate is numerically investigated. Second, by applying an experimental modal analysis technique to the beams produced from a lamina, the structural damping factors of the lamina are measured. Using the measured structural damping factors, the accelerance of the clamped symmetrically laminated rectangular plate is computed. Finally, the accelerance of the plate is obtained experimentally. Good agreement was observed from a comparison of experimental and numerical accelerances.

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In this paper the vibration characteristics of rectangular, symmetric composite sandwich plates and the layup optimization of their laminated FRP composite faces are examined. The honeycomb core is modeled as a thick plate whose transverse shear deformation is taken into consideration based on a higher-order shear deformation theory, and the top and bottom FRP faces are modeled as a very thin sheet. A two-dimensional finite element method is developed using an eight-node isoparametric element. First, the fundamental frequency of the composite sandwich plate is discussed in the subspace of four in-plane lamination parameters of the FRP face. Next, the layup optimization of the FRP face for maximizing the fundamental frequency of the composite sandwich plate is performed by a nonlinear mathematical programming method, and the optimum laminate configuration of the FRP face is determined.

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The damping properties of the Flexural vibration for a composite rectangular sandwich plate with a viscoelastic core and composite laminated faces are presented. The damping analysis is carried out using the Ritz method. The elastic moduli of the plate are treated as complex quantities, and the shear modulus and loss factor of the viscoelastic core depend on the excited frequency. The present complex eigenvalue problem is solved by means of an iterative procedure, and the damped natural frequencies and modal loss factors are determined. The present solutions are validated by comparison with published data. The effects of the frequency dependence on the core material, core thickness, the fiber angle and stacking sequence of the composite laminated faces upon the damping properties are studied.

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An analysis is presented for the free vibration of a CFRP cantilever annular sector plate. Kinetic and strain energies are obtained in Cartesian coordinates and are then transformed into polar ones for the convenience of the following analysis. The Ritz method is used to derive the frequency equation, and power series are employed as admissible functions. Natural frequencies and mode shapes of symmetrically laminated plates are calculated numerically and are compared with those obtained by the finite-element method and experiments.

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The steady-state response to a sinusoidally varying point force is determined for an internally damped cantilever quadrilateral plate by the Ritz method. A quadrilateral plate is conveniently transformed into a square plate with unit length by a transformation of variables. The transverse displacement of the transformed plate is approximately expressed in a series of the beam eigenfunction, and the driving-point impedance is derived analytically. By the application of the present method, the response curves of the cantilever skew plates driven at an arbitrary point are calculated numerically, together with the natural frequencies and the mode shapes. The effects of the aspect ratio, skew angle, damping factor and the location of the driving point on vibrations of the cantilever skew plates are clarified quantitatively.

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Natural frequencies and the corresponding mode shapes of circular cylindrical shells were experimentally investigated by time-averaged holographic interferometry. The shells used in the experiment had two kinds of boundary conditions, one of which was clamped at one end and free at the other, and the other of which was clamped at both ends. The natural frequencies which were measured ranged from 1137 to 7758 Hz, and the fifty-nine mode shapes were obtained. Some rough tendencies could be identified, although an exact conclusion could not be drawn due to insufficient numbers of experimental samples.

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The real time technique of time averaged holographic interferometry has been applied to determine the natural frequencies and the corresponding mode shapes for the transverse vibrations of clamped circular plates with a straight eccentric narrow slit. Eccentricity and length of the slit have been selected as parameters, while width of the slit has been kept to be constant. The first six natural modes are discussed. Most of the natural frequencies show a decreasing tendency as the slit length increases, and the tendency becomes larger when the slit coincides with, or is parallel to one of nodal diameters. The change of the natural frequencies with the slit eccentricity varies with each mode, and especially that of the higher modes than the third mode cannot be found any regularity.

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This paper deals with axisymmetric vibrations of sandwich spherical shells having cross-ply laminated faces. Vibration analysis is carried out using the Ritz method. The expressions for the total strain and kinetic energies of the shells include the effect of transverse shear deformation of laminated faces and a core. Displacement functions satisfying boundary conditions are expressed as power series. The natural frequencies and corresponding mode shapes of the shells are computed. The accuracy and validity of the present results are confirmed by convergence study and comparison with published data. The results of parametric study are discussed for sandwich spherical shells having different orthotropy ratios, thickness ratios and opening angles.

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A steady-state response is presented for a damped cantilever annular sector plate with curved radial edges by the Ritz method. The plate is transformed into a regular sector plate with a unit outer radius by a transformation of variables. The transverse displacement of the transformed plate is approximately expressed in terms of the power functions, and the driving-point impedance is derived analytically. By the application of the present method, the response curves of the cantilever annular sector plate with curved radial edges, driven at an arbitrary point, are calculated numerically. The effects of the shifting angle, damping factor and the location of the driving point on the steady-state responses are clarified quantitatively for the cantilever annular sector plate with curved radial edges.

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Steady state response to a sinusoidally varying transverse deflection is determined for an internally damped cantilever quadrilateral plate by means of the Ritz method. A quadrilateral plate of general shape is transformed into a square plate with unit length by a transformation of variables. The transverse displacement of the transformed square plate is approximately expressed in a series of the beam eigenfunction. Substituting the expressions for the kinetic energy and strain energy of the plate into Lagrange's equation, the equation of motion is developed. The dynamic response of the plate is determined by solving the equation of motion of the plate. Numerical work is done for the skew cantilever plate driven by a sinusoidally varying transverse deflection, and the steady state response of the plate is studied.

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The analysis of composite rectangular sandwich plates composed of an orthotropic core and composite laminated faces is presented for bending and free vibration. A method of solution based upon the Ritz method is used. A displacement field which includes transverse shear deformation of the face layer is applied to the honeycomb sandwich plate. The effect of transverse shear deformation on the center deflection and natural frequencies is studied, and the applicability of the displacement field is discussed. Also, the effects of fiber angle on the face layer, core thickness and transverse shear modulus of the core on natural frequencies of the honeycomb sandwich plate are discussed.

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The steady state response problem is solved for cantilevered rectangular plates made of symmetrically laminated FRP (fiber reinforced plastic) composites. The bending rigidities are obtained by using the thin-plate laminate theory, and the governing equation of motion for generally orthotropic plates is solved by the Ritz approach. In numerical study, driving point impedance is calculated for three types of FRP materials, and the effects of various parameters (material, number of layers, fiber orientation) upon the responses are discussed.

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This paper presents an analytical method for determining the steady-state response of laminated composite rectangular plates. The bending rigidities are obtained by use of the orthotropic thin plate theory. The Ritz approach is used to yield a governing equation of motion, and steady-state response solution is derived for a simply supported laminated plate. In numerical example, driving point impedance is calculated for three types of FRP (Fiber Reinforced Plastic) materials, and the effects of varying the orientation angle of lamina and configuration of a laminate are discussed.

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This paper presents an analytical method of solving the free vibration problem of cantilever plates made of laminated composite materials. The analytical approach is based on the well-known Ritz method, with displacement functions in complete power series, and is applied to laminated plates of various shapes with straight-line boundaries. A computer program code was developed to accommodate a wide range of material constants for FRP (fiber reinforced plastic) and a variety of plate planforms. Numerical examples include cantilever plates of triangular, L-shaped and parallelogram planforms.

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