Abstract:
An optical pickup device includes a lens for projecting a light onto a recording medium, a lens holder elastically supported by a frame and holding said lens, an actuator mounted in and driving said lens holder, and a weight part balanced with a weight of said actuator.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention generally relates to optical pickup devices, and more particularly to an optical pickup device having a lens for projecting a light onto a recording medium and optically reading information stored in the recording medium by controlling the orientation of the lens. 
   2. Description of the Related Art 
   In a disk unit loaded with a disk recording medium (hereinafter referred to as a disk), such as a CD-ROM apparatus, for instance, information stored in the disk is read by projecting a laser beam onto the disk. An optical pickup device incorporated into this type of disk unit has an objective lens for projecting the laser beam emitted from a laser diode onto the disk, and controls the orientation of the objective lens so that the laser beam projected through the objective lens is focused on a recording surface of the disk. 
   That is, in the optical pickup device, focus control and tracking control are performed so that the objective lens follows the surface fluctuation of the disk or the motion of a track due to eccentricity. Such control of the objective lens is performed by an actuator utilizing electromagnetic force. Generally, the actuator is composed of a combination of a coil and a magnet. 
   A lens holder holding the objective lens is reduced in size and weight so that focus control and tracking control can be performed easily. Further, the lens holder is supported by a support structure where four wire-like elastic supporters are provided in parallel so that a sensitive control operation of the objective lens is performed by a driving force from the actuator. 
   However, the conventional optical pickup device has its movable part such as the lens holder moved easily in order to increase the accuracy of the above-mentioned focus and tracking controls. Therefore, variations in component size, for instance, cause a deviation between the center of gravity of the movable part and the driving point position of the actuator, thus generating a turning moment in the movable part. This turning moment causes unnecessary vibrations to be generated in the movable part, thus destabilizing focus and tracking controls. 
   Further, insufficient stiffness of the movable part due to a thinner lens holder increases the magnitude of higher-order-harmonic resonance so that a servo system starts oscillating. 
   Moreover, if variations in component size or assembly errors are caused, the center of gravity of the movable part or the position of a driving point on which the driving force from the actuator is exerted is deviated. Therefore, unnecessary vibrations may be caused by a turning moment generated in the movable part. 
   In the optical pickup device, a natural frequency may be considered to be a factor of the generation of unnecessary vibrations. Since the natural frequency is determined by a component shape and/or material, it is required to increase or decrease the level of the natural frequency by changing such a factor (factors). 
   Further, it is also possible to eliminate the deviation of the center of gravity of the movable part or the driving point of the actuator by increasing the processing or assembly accuracy of components. However, increasing the processing or assembly accuracy of components causes a problem of an increase in the costs of mass production. 
   Furthermore, in order to manage the position of the center of gravity with high accuracy, it is required to be informed quantitatively of an error between calculated and actual positions of the center of gravity by repeating trial production and evaluation. Therefore, in the case of managing the position of the center of gravity, there has been a problem that a product development period becomes longer due to repetition of the trial production and evaluation. 
   In addition, in order to lower the level of the natural frequency of the movable part, it is required to increase the stiffness of an individual component. However, it has been difficult to increase component stiffness by increasing component thickness due to restriction of component interference. It is possible as a method of solving such a problem to increase stiffness by forming the lens holder with a metal strip being inserted therein by insert molding. However, this causes a problem of an increase in production costs. 
   SUMMARY OF THE INVENTION 
   It is a general object of the present invention to provide an optical pickup device in which the above-described disadvantages are eliminated. 
   A more specific object of the present invention is to provide an optical pickup device that can reduce the magnitude of higher-order-harmonic resonance of a lens holder with a relatively simple structure. 
   The above objects of the present invention are achieved by an optical pickup device including a lens for projecting a light onto a recording medium, a lens holder elastically supported by a frame and holding the lens, an actuator mounted in and driving the lens holder, and a weight part balanced with a weight of the actuator. 
   According to the above-described optical pickup device, since the weight part balanced with the weight of the actuator is provided, the generation of a moment causing unnecessary vibrations can be controlled so that the magnitude of higher-order-harmonic resonance of the lens holder can be decreased by relatively easy work. Therefore, even if variations in component size or assembly errors are caused, the deviation of the position of center of gravity can be corrected by the weight part, and the magnitude of higher-order-harmonic resonance can be damped. 
   The above objects of the present invention are also achieved by an optical pickup device including a lens for projecting a light onto a recording medium, a lens holder elastically supported by a frame and holding the lens, a weight part fixed to the lens holder, and an adhesive agent fixing the weight to the lens holder, the adhesive agent having viscoelasticity such that the weight part serves as a dynamic vibration absorber. 
   According to the above-described optical pickup device, since the weight part is fixed to the lens holder by the adhesive agent having viscoelasticity such that the weight part serves as a dynamic vibration absorber, the generation of a moment causing unnecessary vibrations can be controlled so that the magnitude of higher-order-harmonic resonance of the lens holder can be lowered by relatively easy work. Therefore, even if variations in component size or assembly errors are caused, the deviation of the position of center of gravity can be corrected by the weight part, and the magnitude of higher-order-harmonic resonance can be damped by the dynamic vibration absorber effect produced by the viscoelasticity of the adhesive agent. 
   The above objects of the present invention are also achieved by an optical pickup device including a lens for projecting a light onto a recording medium, a lens holder elastically supported by a frame and holding the lens, an actuator mounted in and driving the lens holder, a weight part balanced with a weight of the actuator, and an adhesive agent fixing the weight to the lens holder, the adhesive agent having viscoelasticity such that the weight part serves as a dynamic vibration absorber. 
   According to the above-described optical pickup device, the same effects as those described above can be produced. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Other objects, features and advantages of the present invention will become more apparent from the following detailed description when read in conjunction with the accompanying drawings, in which: 
       FIG. 1  is a perspective view of an embodiment of an optical pickup device of the present invention; 
       FIG. 2  is a plan view of the embodiment of the optical pickup device of the present invention; 
       FIG. 3  is a longitudinal sectional view of the embodiment of the optical pickup device of the present invention; 
       FIG. 4  is a diagram showing a physical model of a dynamic vibration absorber where a weight is attached to a tip of a lens holder; 
       FIG. 5  is a graph showing conventional frequency characteristics of a focus direction; 
       FIG. 6  is a graph showing frequency characteristics of a focus direction according to the present invention; 
       FIGS. 7A and 7B  are diagrams for illustrating a theoretical background of using a weight balancer as a dynamic balancer; and 
       FIG. 8  is a diagram showing calculation results of equations for verifying a dynamic vibration absorber effect of the present invention. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   A description will now be given, with reference to the accompanying drawings, of an embodiment of the present invention. 
     FIGS. 1 through 3  are a perspective view, a plan view, and a longitudinal sectional view of an embodiment of an optical pickup device of the present invention, respectively. In  FIGS. 1 through 3 , directions indicated by arrows X 1  and X 2  are collectively referred to as a first lateral direction of an optical pickup device  10 , directions indicated by arrows Y 1  and Y 2  are collectively referred to as a second lateral or tracking direction of the optical pickup device  10 , and directions indicated by arrows Z 1  and Z 2  are collectively referred to as a vertical or focus direction of the optical pickup device  10 . 
   As shown in  FIGS. 1 through 3 , the optical pickup device  10  includes an objective lens  12 , a lens holder  14  supporting the objective lens  12 , a yoke base (frame)  15  supporting the lens holder  14 , a focus coil  16  and tracking coils  18  attached to the lens holder  14 , a pair of magnets  30  and  32 , a yoke  22  formed integrally with the yoke base  15  and supporting the magnets  30  and  32 , a suspension holder (a support part)  24  fixed to the yoke base  15 , and four wire-like elastic supporters (cantilever springs)  26   a  through  26   d  provided between the suspension holder  24  and the lens holder  14 . 
   The focus coil  16  is an actuator for actuating the objective lens in the vertical direction, and the tracking coils  18  are an actuator for actuating the objective lens  12  in the second lateral direction. The yoke  22  bent into a U-letter shape and having a pair of arm parts  22   a  and  22   b  extending in the vertical direction is fixed to a bottom plate  15   c  provided between a pair of arm parts  15   a  and  15   b  of the yoke base  15  which arm parts extend in the second lateral direction. The magnet  30  is attached to the arm part  22   a  of the yoke  22  so as to penetrate the focus coil  16 , and the magnet  32  is attached to the other arm part  22   b  so as to oppose the tracking coils  18 . 
   The suspension holder  24 , together with a base plate  34 , is fixed to a fixing part  15   d  of the yoke base  15  by tightening up a screw  36 . The elastic supporters  26   a  through  26   d  are arranged so as to extend in the second lateral direction with their base ends (proximal ends) penetrating the base plate  34  to be fixed and their tip parts (free ends or distal ends) penetrating respective connection parts  38   a  through  38   d  projecting from both sides of the lens holder  14  to be fixed. A silicon-based adhesive agent  40  in a gel form for elastically fixing the periphery of each of the elastic supporters  26   a  through  26   d  adheres to an end surface of the suspension holder  24 . The adhesive agent  40 , which is gelled by ultraviolet irradiation, provides the elastic supporters  26   a  through  26   d  with viscosity damping with respect to movements of the lens holder  14  in the focus and tracking directions. 
   Further, end parts of the focus coil  16  and the tracking coils  18  are connected to coil relay substrates  42  and  44  penetrated by the tip parts of the elastic members  26   a  through  26   d  so that electric currents are supplied via the elastic members  26   a  through  26   d  to the focus coil  16  and the tracking coils  18 . A movable part  46  subjected to focus control and tracking control is composed of the objective lens  12 , the lens holder  14 , the focus coil  16 , the tracking coils  18 , and the coil relay substrates  42  and  44 . 
   A laser beam emitted from a laser diode  28  is reflected from a reflecting mirror  60  to reach the objective lens  12 , which focuses the laser beam on a disk  62  opposing the objective lens  12  thereabove. The magnets  30  and  32  are attached to the U-letter-shaped arm parts  22   a  and  22   b  of the yoke  22 , respectively, so as to oppose each other. The magnets  30  and  32  also oppose the focus coil  16  and the tracking coils  18  provided to the lens holder  14 . Further, the lens holder  14  is supported movably by the four elastic supporters  26   a  through  26   d  extending in the second lateral direction. 
   The objective lens  12  supported on the lens holder  14  is controlled to a position where electromagnetic forces generated in the focus coil  16  and the tracking coils  18  provided in a magnetic field produced by the magnets  30  and  32  are balanced with gravity exerted on the movable part  46 . 
   The lens holder  14  includes a lens holding part (a free end part or distal end part)  14   a  for holding the objective lens  12 , a coil holding part (a base end part or proximal end part)  14   b  extending toward the suspension holder  24  from the lens holding part  14   a  for holding the focus coil  16  and the tracking coils  18 , and a concave part  14   d  formed in a tip  14   c , which is formed on the lens holding part  14   a  on the side opposite to the side of the focus coil  16  and the tracking coils  18 . The concave part  14   d  is formed into a rectangular shape extending in the first lateral direction in the tip  14   c.    
   A weight (weight part)  48  formed of a rigid body and having a weight necessary to damp the vibration of the lens holder  14  is bonded and fixed to the concave part  14   d  by an adhesive agent  50  as a weight balancer. The weight  48  is formed of a metal material having a specific gravity higher than that of the lens holder  14 , such as a brass material, and is formed into a rectangular shape to be fitted and fixed in the concave part  14   d . Therefore, in bonding the weight  48 , a bonding position thereof can be easily determined only by fitting the weight  48  inside the concave part  14   d  after applying the adhesive agent  50  thereon, thus increasing working efficiency. 
   Further, the weight  48  minimizes a turning moment generated in the movable part  46  (or changes the natural frequency of the lens holder  14 ) and controls the generation of vibration by adjusting the position of the center of gravity of the movable part  46 . Moreover, since the weight  48  is formed of a material having a higher stiffness than the lens holder  14 , the weight  48  serves to increase the stiffness of the lens holder  14  formed of a resin material. 
     FIG. 4  is a diagram showing a physical model of a dynamic vibration absorber where the weight  48  is attached to the tip  14   c  of the lens holder  14 . 
   As shown in  FIG. 4 , by bonding the weight  48  to the concave part  14   d  formed in the tip  14   c  of the lens holder  14 , the adhesive agent  50  generates viscoelasticity so that the weight  48  serves as a dynamic vibration absorber that damps vibration with respect to the vibration mode of the movable part  46 . The dynamic vibration absorber has a mass m of the weight  48 , a spring constant k of the adhesive agent  50 , and a viscosity damping coefficient c of the adhesive agent  50 . 
   In the case of using a UV-hardening-type silicon-based TB3168 (damping gel) as the adhesive agent  50 , the constants of the physical model of  FIG. 4 , for instance, are as follows:
         m=3 mg, k=3680 Pa, c=3385 Pa·s, M=300 mg, K=490 Pa, and C=0.14 Pa·s.       

   Therefore, the weight  48  is allowed to have the function of a dynamic vibration absorber to damp the vibration of the movable part  46  by being bonded to the tip  14   c  of the lens holder  14 . Further, the rectangular weight  48  is bonded to the tip  14   c  of the lens holder  14  so as to increase the stiffness thereof, thereby reducing amplitude at the time of occurrence of vibrations. 
     FIG. 5  is a graph showing conventional frequency characteristics of the focus direction. 
   In  FIG. 5 , a curve I shows a relationship between a “frequency” and a “displacement amount per unit voltage” and a curve II shows a relationship between the “frequency” and a “phase” at the time of inputting a driving current with a sine wave to the focus coil of a conventional optical pickup device. 
   The curve I shows that higher-order-harmonic resonance occurs in the neighborhood of 20 KHz in the conventional optical pickup device. Further, the curve II shows that an unnecessary vibration A is generated in the neighborhood of 1 KHz due to the deviation of center of gravity in the conventional optical pickup device. 
   On the other hand, in the optical pickup device  10  of the present invention, since the weight  48  is bonded to the concave part  14   d  formed in the tip  14   c  of the lens holder  14 , the weight  48  adjusts the deviation of the center of gravity and serves as a dynamic vibration absorber to damp vibration, as previously described. 
     FIG. 6  is a graph showing frequency characteristics of the focus direction according to the present invention. 
   In  FIG. 6 , a curve III shows a relationship between a “frequency” and a “displacement amount per unit voltage” and a curve IV shows a relationship between the “frequency” and a “phase” at the time of inputting a driving current with a sine wave to the focus coil  16  of the optical pickup device  10 . 
   The curve III shows that the magnitude of higher-order-harmonic resonance is improved in the optical pickup device  10 . The curve IV shows that the unnecessary vibration A due to the deviation of the center of gravity is scarcely generated in the optical pickup device  10 . 
   Therefore, by bonding the weight  48  to the tip  14   c  of the lens holder  14 , the higher-order-harmonic resonance in the neighborhood of 20 KHz is improved by approximately 5 dB. Further, a phase shift in the neighborhood of 1 KHz is improved by approximately 20 degrees. 
   In the above-describe embodiment, the rectangular weight  48  is bonded to the tip  14   c  of the lens holder  14 . However, a weight shape is not limitedly rectangular, and a weight of another shape may be used. Further, as for a weight material, a material other than a metal, such as a resin material having high stiffness and high specific gravity, may naturally be used. 
   Here, a description will be given of the theoretical background of using a weight balancer as a dynamic balancer in order to verify the dynamic vibration absorber effect produced by the present invention. 
   The effect of using a weight balancer as a dynamic balancer can be obtained by finding and comparing forced vibration solutions x 1  and x 2  of a one-degree-of-freedom system shown in  FIG. 7A  and a two-degree-of-freedom system shown in  FIG. 7B . 
   For simplicity purposes, complex notation is used in what follows. A complex variable is distinguishably expressed as {overscore (z)}, and the fact that a stationary solution {overscore (x)} j  converges to {overscore (x)} j =Ā j e iωt  if a forced external force {overscore (F)} satisfies {overscore (F)}=fe iωt  is used. 
   From a differential relationship, the following expressions are self-evident. 
   
     
       
         
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                       ⁢ 
                       
                         
                           A 
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   (A) Forced Vibration Solution of the One-degree-of-freedom System 
   An equation of motion is: 
   
     
       
         
           
             
               
                 m 
                 1 
               
               ⁢ 
               
                 
                   
                     x 
                     _ 
                   
                   ¨ 
                 
                 1 
               
             
             + 
             
               
                 c 
                 1 
               
               ⁢ 
               
                 
                   
                     x 
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                 1 
               
             
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                 k 
                 1 
               
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                 1 
               
             
           
           = 
           
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               t 
             
           
         
       
     
   
   Since {overscore (x)} 1 =Ā 1 e iωt ,
 
(−ω 2   m   1   +iωc   1   +k   1 ) Ā   1   =f 
 
   
     
       
         
           
             
               
                 
                   ∴ 
                   
                     
                       
                         A 
                         _ 
                       
                       1 
                     
                     f 
                   
                 
                 = 
                 
                   1 
                   
                     
                       ( 
                       
                         
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                           1 
                         
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                             2 
                           
                           ⁢ 
                           
                             m 
                             1 
                           
                         
                       
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                     + 
                     
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                       ⁡ 
                       
                         ( 
                         
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                             c 
                             1 
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 1 
                 ) 
               
             
           
         
       
     
   
   (B) Forced Vibration Solution of the Two-degree-of-freedom System 
   Equations of motion are: 
   
     
       
         
           { 
           
             
               
                 
                   
                       
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                             m 
                             1 
                           
                           ⁢ 
                           
                             
                               
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                             1 
                           
                         
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   These equations are also expressed as: 
   
     
       
         
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                             m 
                             1 
                           
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   With the substitution of {overscore (x)} 1 =Ā 1 e iωt  and {overscore (x)} 2 =Ā 2 e iωt , the equations are:
 
{−ω 2   m   1   +iω ( c   1   +c   2 )+( k   1   +k   2 )} Ā   1   +{−iωc   2   −k   2   }Ā   2   =f 
 
{− iωc   2   −k   2   }Ā   1+{−ω   2   m   2   +iωc   2   +k   2   }Ā   2 =0
 
   These equations are expressed in matrices as: 
   
     
       
         
           
             
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                         ( 
                         
                           
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                         A 
                         _ 
                       
                       1 
                     
                   
                 
                 
                   
                     
                       
                         A 
                         _ 
                       
                       2 
                     
                   
                 
               
               ] 
             
           
           = 
           
             [ 
             
               
                 
                   f 
                 
               
               
                 
                   0 
                 
               
             
             ] 
           
         
       
     
   
   If the above-described equation is expressed as 
                 T   _     ⁡     [             A   _     1                 A   _     2           ]       =     [         f           0         ]       ,         
the determinant {overscore (D)} of {overscore (T)} ({overscore (D)}=det({overscore (T)})) can be given by:
 
   
     
       
         
           
             
               
                 
                   D 
                   _ 
                 
                 = 
                   
                 ⁢ 
                 
                   
                     
                       { 
                       
                         
                           ( 
                           
                             
                               k 
                               1 
                             
                             + 
                             
                               k 
                               2 
                             
                             - 
                             
                               
                                 ω 
                                 2 
                               
                               ⁢ 
                               
                                 m 
                                 1 
                               
                             
                           
                           ) 
                         
                         + 
                         
                           ⅈ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 c 
                                 1 
                               
                               + 
                               
                                 c 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                       } 
                     
                     · 
                     
                       { 
                       
                         
                           ( 
                           
                             
                               k 
                               2 
                             
                             - 
                             
                               
                                 ω 
                                 2 
                               
                               ⁢ 
                               
                                 m 
                                 2 
                               
                             
                           
                           ) 
                         
                         + 
                         
                           ⅈ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             c 
                             2 
                           
                         
                       
                       } 
                     
                   
                   - 
                 
               
             
           
           
             
               
                   
                 ⁢ 
                 
                   
                     ( 
                     
                       
                         k 
                         2 
                       
                       - 
                       
                         ⅈ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           c 
                           2 
                         
                       
                     
                     ) 
                   
                   2 
                 
               
             
           
           
             
               
                 = 
                   
                 ⁢ 
                 
                   
                     { 
                     
                       
                         
                           ( 
                           
                             
                               k 
                               1 
                             
                             + 
                             
                               k 
                               2 
                             
                             - 
                             
                               
                                 ω 
                                 2 
                               
                               ⁢ 
                               
                                 m 
                                 1 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               k 
                               2 
                             
                             - 
                             
                               
                                 ω 
                                 2 
                               
                               ⁢ 
                               
                                 m 
                                 2 
                               
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           ω 
                           2 
                         
                         ⁢ 
                         
                           
                             c 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 c 
                                 1 
                               
                               + 
                               
                                 c 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                       - 
                       
                         k 
                         2 
                         2 
                       
                       + 
                       
                         
                           ω 
                           2 
                         
                         ⁢ 
                         
                           c 
                           2 
                         
                       
                     
                     } 
                   
                   + 
                 
               
             
           
           
             
               
                   
                 ⁢ 
                 
                   ⅈ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   ω 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           ( 
                           
                             
                               k 
                               1 
                             
                             + 
                             
                               k 
                               2 
                             
                             - 
                             
                               
                                 ω 
                                 2 
                               
                               ⁢ 
                               
                                 m 
                                 1 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           c 
                           2 
                         
                       
                       + 
                       
                         
                           ( 
                           
                             
                               k 
                               2 
                             
                             - 
                             
                               
                                 ω 
                                 2 
                               
                               ⁢ 
                               
                                 m 
                                 2 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               c 
                               1 
                             
                             + 
                             
                               c 
                               2 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         2 
                         ⁢ 
                         
                           k 
                           2 
                         
                         ⁢ 
                         
                           c 
                           
                             2 
                             } 
                           
                         
                       
                     
                   
                 
               
             
           
           
             
               
                 = 
                   
                 ⁢ 
                 
                   
                     { 
                     
                       
                         
                           k 
                           1 
                         
                         ⁢ 
                         
                           k 
                           2 
                         
                       
                       + 
                       
                         
                           ω 
                           4 
                         
                         ⁢ 
                         
                           m 
                           1 
                         
                         ⁢ 
                         
                           m 
                           2 
                         
                       
                       - 
                       
                         
                           ω 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 m 
                                 1 
                               
                               ⁢ 
                               
                                 k 
                                 2 
                               
                             
                             + 
                             
                               
                                 m 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     k 
                                     1 
                                   
                                   + 
                                   
                                     k 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 c 
                                 1 
                               
                               ⁢ 
                               
                                 c 
                                 2 
                               
                             
                           
                           ) 
                         
                       
                     
                     } 
                   
                   + 
                 
               
             
           
           
             
               
                   
                 ⁢ 
                 
                   ⅈ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   ω 
                   ⁢ 
                   
                     { 
                     
                       
                         
                           ( 
                           
                             
                               k 
                               2 
                             
                             - 
                             
                               
                                 ω 
                                 2 
                               
                               ⁢ 
                               
                                 m 
                                 2 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           c 
                           1 
                         
                       
                       + 
                       
                         
                           ( 
                           
                             
                               k 
                               1 
                             
                             - 
                             
                               
                                 ω 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     m 
                                     1 
                                   
                                   + 
                                   
                                     m 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           c 
                           2 
                         
                       
                     
                     } 
                   
                 
               
             
           
         
       
     
   
   The inverse matrix {overscore (T)} −1  of {overscore (T)} can be expressed by using the above-described {overscore (D)} as follows: 
   
     
       
         
           
             
               T 
               _ 
             
             
               - 
               1 
             
           
           = 
           
             
               1 
               
                 D 
                 _ 
               
             
             ⁡ 
             
               [ 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             k 
                             2 
                           
                           - 
                           
                             
                               ω 
                               2 
                             
                             ⁢ 
                             
                               m 
                               2 
                             
                           
                         
                         ) 
                       
                       + 
                       
                         ⅈω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           c 
                           2 
                         
                       
                     
                   
                   
                     
                       
                         k 
                         2 
                       
                       + 
                       
                         ⅈ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           c 
                           2 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         k 
                         2 
                       
                       + 
                       
                         ⅈ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           c 
                           2 
                         
                       
                     
                   
                   
                     
                       
                         ( 
                         
                           
                             k 
                             1 
                           
                           + 
                           
                             k 
                             2 
                           
                           - 
                           
                             
                               ω 
                               2 
                             
                             ⁢ 
                             
                               m 
                               1 
                             
                           
                         
                         ) 
                       
                       - 
                       
                         ⅈ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               c 
                               1 
                             
                             + 
                             
                               c 
                               2 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ] 
             
           
         
       
     
     
       
         
           Hence 
           , 
           
             
               [ 
               
                 
                   
                     
                       
                         A 
                         _ 
                       
                       1 
                     
                   
                 
                 
                   
                     
                       
                         A 
                         _ 
                       
                       2 
                     
                   
                 
               
               ] 
             
             = 
             
               
                 
                   
                     T 
                     _ 
                   
                   
                     - 
                     1 
                   
                 
                 ⁡ 
                 
                   [ 
                   
                     
                       
                         f 
                       
                     
                     
                       
                         0 
                       
                     
                   
                   ] 
                 
               
               = 
               
                 
                   f 
                   
                     D 
                     _ 
                   
                 
                 ⁡ 
                 
                   [ 
                   
                     
                       
                         
                           
                             ( 
                             
                               
                                 k 
                                 2 
                               
                               - 
                               
                                 
                                   ω 
                                   2 
                                 
                                 ⁢ 
                                 
                                   m 
                                   2 
                                 
                               
                             
                             ) 
                           
                           + 
                           
                             ⅈ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               c 
                               2 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             k 
                             2 
                           
                           + 
                           
                             ⅈ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               c 
                               2 
                             
                           
                         
                       
                     
                   
                   ] 
                 
               
             
           
         
       
     
   
   It is only {overscore (x)} 1  that is required for comparison with the one-degree-of-freedom system, and 
   
     
       
         
           
             
               
                 
                   
                     
                       A 
                       _ 
                     
                     1 
                   
                   f 
                 
                 = 
                 
                   
                     
                       ( 
                       
                         
                           k 
                           2 
                         
                         - 
                         
                           
                             ω 
                             2 
                           
                           ⁢ 
                           
                             m 
                             2 
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ⅈ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       ω 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         c 
                         2 
                       
                     
                   
                   
                     D 
                     _ 
                   
                 
               
             
             
               
                 ( 
                 2 
                 ) 
               
             
           
         
       
     
   
   A difference between the equations (1) and (2) can be judged to be the dynamic vibration absorber effect (dynamic damper effect). 
   The calculation results of the equations (1) and (2) are indicated by Xs and black circles in  FIG. 8 , respectively. 
   Suppose that a weight balancer of 3 mg is fixed by the damping gel TB3168 (tanδ=0.92, G*=500 Pa) in a PUW208 model, the dynamic damper (dynamic vibration absorber) of this model has a natural frequency of approximately 5.6 kHz and a damping effect of approximately 15 dB. 
   The present invention is not limited to the specifically disclosed embodiment, but variations and modifications may be made without departing from the scope of the present invention. 
   The present application is based on Japanese priority application No. 2001-028720 filed on Feb. 5, 2001, the entire contents of which are hereby incorporated by reference.