Researcher Database

Researcher Profile and Settings

Master

Affiliation (Master)

  • Faculty of Engineering Mechanical and Aerospace Engineering Mechanics and Materials

Affiliation (Master)

  • Faculty of Engineering Mechanical and Aerospace Engineering Mechanics and Materials

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Profile and Settings

Degree

  • Ph. D. in Engineering(2009/03 Hokkaido University)

Profile and Settings

  • Name (Japanese)

    HONDA
  • Name (Kana)

    Shinya
  • Name

    201201085824423198

Achievement

Research Interests

  • 最適設計   スマート構造   圧電素子   曲線状繊維   振動モード   繊維強化複合材料   打撃試験   周波数応答関数   振動試験   

Research Areas

  • Manufacturing technology (mechanical, electrical/electronic, chemical engineering) / Control and systems engineering
  • Manufacturing technology (mechanical, electrical/electronic, chemical engineering) / Design engineering
  • Informatics / Mechanics and mechatronics
  • Manufacturing technology (mechanical, electrical/electronic, chemical engineering) / Machine materials and mechanics

Research Experience

  • 2013/11 - Today 北海道大学 工学(系)研究科(研究院) 准教授
  • 2013/09 - 2014/06 ETH Zurich
  • 2009/04 - 2013/10 北海道大学 工学(系)研究科(研究院) 助教
  • 2007/04 - 2009/03 Hokkaido Univ.

Education

  • 2007/04 - 2009/03  Hokkaido University  Graduate School of Engineering

Published Papers

  • Kazuaki Katagiri, Choong Sik Park, Sonomi Kawakita, Masato Tamayama, Shinya Honda, Katsuhiko Sasaki
    AIAA SciTech Forum and Exposition, 2024 2024 
    Seeing a large bird that slowly and gracefully soars high in the sky, it is found that the flight is controlled by slightly twisting the entire wing. Although unmanned aerial vehicles (UAVs) for long-range flight require elongated wings with a high aspect ratio, it is assumed that the morphing wing that can twist the entire wing would be preferable to actuating ailerons. Previously, the authors have developed the twist morphing wing for the UAVs. The CFRP skeletal structure for the morphing was optimally designed, and manufactured by applying the electrodeposition resin impregnation method that was originally developed. Further, aerodynamic properties of the morphing wing were confirmed by wind tunnel test, and the first flight test was conducted. Currently, the development of the third prototype is planned to improve the morphing wing. The morphing wing is going to be more flexible, therefore, it is important to accurately measure the deformation. In this study, the deformation measurement system for the skeletal structure of the morphing wing was developed by using the stereo vision. As a result, the greatly morphed geometries could be measured under the bending and torsion loads. Additionally, tracking the measured points on the twist morphing wing, it was found that the displacement of the members that composes the skeletal structure could be estimated.
  • Tomohiro Tsuruya, Musashi Danseko, Katsuhiko Sasaki, Shinya Honda, Ryo Takeda
    IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM 2019- 1227 - 1232 2019/07/01 
    This study proposes a new processing method by using the count rate of the acoustic emission (AE) signal and machine learning. To analyze the AE count, machine learning, using a multilayered neural networks, is implemented for a deep drawing process. In a press processing, a quality inspection is often carried out for each lot in a later process. Once a failure occurs in the process, a large number of defective products may be produced due to the fast processing speed. In order to prevent this, it is important to immediately stop the processing just after the defect occurs. The AE signal data has been often used for monitoring the condition of process. However, it is easily affected by noise and lacks repeatability. Also it is difficult to handle the number of AE data due to its high frequencies of target signals. Therefore, the improvement of the data processing method and recognition rate is required and thus the machine learning approach is applied in this study.
  • Yoshihiko Kaito, Shinya Honda, Yoshihiro Narita
    JVC/Journal of Vibration and Control 24 (18) 4081 - 4095 1741-2986 2018/09/01 
    This paper deals with the vibration modeling of a glass panel, with emphasis on smartphone applications, and attempts to identify the elastic boundary condition to support the glass panel. This study is motivated to develop a more-efficient vibration function of the glass panel in smartphones. First, based on the classical plate theory, the vibration behavior is analyzed with consideration of the elastic translational and rotational springs distributed along the panel edge. The accuracy of applying the energy method (Ritz method) is verified by comparing the analytical results with the experimental results by a modal analysis technique, and it is shown that the plate theory used for crystalline materials (i.e. metals and plastics) is applicable also to the glass (non-crystalline) plates. Second, the elastic constants of such distributed springs are identified by a combination of the genetic algorithm and the present Ritz method, and the design approach is summarized for developing more effective use of the vibrating function on glass panels in the smartphones and other tablet terminals.
  • Analytical and experimental study for vibration of laminated VGCF/Al circular plates
    Naoaki Koya, Shinya Honda, Katsuhiko Sasaki, Yoshihiro Narita
    7th Asian-Australasian Conference on Composite Materials 2010, ACCM 2010 1 721 - 724 2010 
    An analysis method is presented for vibration of laminated composite circular plates composed of vapor growth carbon fiber (VGCF) and aluminum. Based on the classical laminated plate theory, the Ritz method is applied to the problem, and a frequency equation is derived by minimizing the total potential energy with respect to unknown coefficients of the displacement function. Various kinds of boundary conditions are incorporated by using boundary indexes. The natural frequencies calculated by the method show good agreement with the results from the finite element analysis and the experimental modal analysis.
  • Analysis, experiment and cost design for vibration of hybrid laminated plates
    Takashi Koshiba, Shinya Honda, Yoshihiro Narita
    7th Asian-Australasian Conference on Composite Materials 2010, ACCM 2010 2 827 - 830 2010 
    The vibration characteristics of hybrid laminated plates with various thicknesses of core materials under various boundary edge conditions are investigated. The hybrid plates composed of aluminum (Al) core and carbon fiber reinforced plastics (CFRP) outer-layers are used for mechanical structures due to low costs and attractive mechanical properties. Especially for the out-of-plane problem, outer layers have greater influences to bending stiffness than inner layers and CFRP/Al hybrid laminated plates have advantages. In this work, an optimization method is presented to maximize fundamental frequencies of CFRP/Al hybrid laminated plates by designing lay-up configurations of CFRP layers. As an optimizer, a layerwise optimization (LO) method which is based on a simple physical observation is employed. In the bending problem, the outer region of cross-section of plate is more sensitive to bending stiffnesses of plates and fiber orientation angles can be determined sequentially from the outermost to the innermost layer. The Ritz solution is used to derive frequency equations. The present work deals with CFRP/Al hybrid plates with relatively high thicknesses and the first-order shear deformation theory is applied to formulate vibration problems. Referring to the numerical results, test specimens are made by hand lay-up methods, and natural frequencies and modal shapes are measured by experimental modal analysis with impulse hammer. From comparison of both results, the validity of the present methods is successfully confirmed and optimization results for various thicknesses of core materials enable cost design of CFRP/Al hybrid laminated plates.
  • Vibration optimization of laminated parallelogram plates with experimental verification
    Toshinori Fujii, Shinya Honda, Yoshihiro Narita
    7th Asian-Australasian Conference on Composite Materials 2010, ACCM 2010 1 773 - 776 2010 
    In this study, the fiber orientation angles of laminated parallelogram plates are optimized to maximize fundamental frequencies. A layerwise optimization (LO) approach is employed as an optimizer. The LO approach is based on a simple physical fact, and it can reduce computational efforts and make the optimization insensitive to increase of number of layers. For calculations of natural frequencies, the Ritz method using the first-order shear deformation theory (FSDT) is applied. The Ritz method is not flexible with respect to plate shapes but it has advantages over the finite element method (FEM) in calculation time and parametric studies. An accuracy of the present analysis is confirmed by comparing the present results with those from FEM, and for validation of the optimization results, the present results are compared also with experimental results. Test specimens are made by a hand lay-up method to refer to the optimization results, and the frequency responses and modal shapes are measured by an experimental modal analysis with impulse tests. Both sets of results agree well in terms of frequencies and modal shapes, and it is thus revealed that the LO approach is applicable in efficient way to the parallelogram plates.
  • Optimization of fibrous composite plates for in-plane strength using curvilinear fibers
    Shinya Honda, Kosuke Owatari, Yoshihiro Narita
    7th Asian-Australasian Conference on Composite Materials 2010, ACCM 2010 1 769 - 772 2010 
    Locally anisotropic structures induced by curvilinear fibers are designed optimally to improve in-plane strength of fibrous composites. Objectives of the present optimizations are maximizing in-plane strength of the fibrous composite plates with circular holes. As the strength indexes, Tsai-Wu failure model is employed here. Curvilinear fiber shapes are described by the projections of contour lines for a cubic-polynomial surface. Various surfaces are described by varying coefficients of the polynomial and they are used as design variables in the present optimization. Originally developed finite element analysis (FEA) code is used to analyze stress distributions, and a simple genetic algorithm (SGA) method is employed as an optimizer. The numerical results show that the present plates with curvilinearly shaped fibers give lower failure indexes than conventional plates reinforced by parallel fibers.
  • Buckling analysis of composite rectangular plates reinforced by curvilinear fibers
    Yoshimasa Oonishi, Shinya Honda, Yoshihiro Narita, Katsuhiko Sasaki
    Progress of Composites 2008 in Asia and Australasia - Proceedings of the 6th Asian-Australasian Conference on Composite Materials, ACCM 2008 315 - 318 2008 
    A composite plate reinforced by curvilinear fibers presents non-homogenous properties in the region of the plate and has locally anisotropic property due to curvilinear fibers. If fiber shapes are designed optimally, the local anisotropy may be distributed in the appropriate region where it is needed. This suggests that the plate with curvilinear fibers has great design flexibility and strong possibility to sophisticate plate properties. Thus, the present study proposes a buckling analysis method of the plate with curvilinear fibers. Although in-plane stresses before buckling behavior indicate non-homogenous distribution caused by curvilinear fibers, the stress distribution is approximated as homogenous state in this study. The validity of this approximation is verified by a comparison between the present results and those by the finite element method. It is clarified in numerical comparisons that there exist a range of applicability where such approximation is available and the stress distribution is not significant.
  • Vibration analysis of laminated composite plates reinforced by arbitrarily shaped curvilinear fibers
    Shinya Honda, Yoshimasa Oonishi, Yoshihiro Narita, Katsuhiko Sasaki
    Progress of Composites 2008 in Asia and Australasia - Proceedings of the 6th Asian-Australasian Conference on Composite Materials, ACCM 2008 347 - 350 2008 
    The development of tow-placement technology has made it possible to control fiber tows individually and place fibers with curvilinear shapes along distinct paths in each layer of a laminated plate. The variation of fiber direction within the plane gives the locally anisotropic property, and this kind of plate property offers the potential of great design flexibility in comparison with conventional plates with homogenous properties. Hence, this paper proposes an analytical method for analyzing the natural frequencies and vibration modes of laminated plates with curvilinearly shaped reinforcing fibers. Spline functions are employed to represent arbitrarily shaped fibers, and Ritz solutions are used to derive frequency equations. The strain energy is obtained by numerical integration involving the fiber orientation angle, and is calculated by using the derivative of the spline function in minute intervals. The results show that the natural frequencies of the present plate agree well with the results from the finite element method and the vibration modes of the present plates reflect clear influences of the fiber shapes.
  • Vibration analysis of fibrous composite plates reinforced along arbitrary curvilinear fiber shapes
    Shinya Honda, Yoshimasa Oonishi, Yoshihiro Narita, Katsuhiko Sasaki
    15th International Congress on Sound and Vibration 2008, ICSV 2008 2 1514 - 1521 2008 
    The development on tow-placement technology made us possible to control fiber tows individually and place fiber paths in each layer of a laminated plate with curvilinear shapes. Due to the variation of fiber direction within the plane, the plate has variable-stiffnesses or locally anisotropic properties, and such plates create a lot of flexibility for designing and different features when they are compared with conventional plates with homogenous properties. The designing flexibility suggests the possibility to sophisticate the plate property better. Hence, an analytical method for natural frequencies and vibration modes of the laminated plate with curvilinearly shaped reinforcing fibers are proposed in this study. Spline functions are employed to represent arbitrarily shaped fibers and the Ritz solutions which allow the arbitrary sets of boundary conditions of rectangular plates are used to derive frequency equations. In numerical results, the natural frequencies of the present plate agree well with those of approximated finite element plate model, and the vibration modes of the present plates clarifies distinct influences of the fiber shapes.
  • 本田 真也
    日本機械学会論文集C編(NOTE) 第74巻第743号 1926 - 1927 2008 [Refereed]

MISC

  • 清水佑音, 本田真也, 佐々木克彦, 武田量, 片桐一彰  Dynamics & Design Conference (CD-ROM)  2023-  2023
  • 本田 真也  研究報告書 フジクラ財団 [編]  1  -12  2013
  • HONDA Shinya, NARITA Yoshihiro, KAJIWARA Itsuro, NAKAMURA Satoshi  最適化シンポジウム講演論文集  2010-  (9)  "302  -1"-"302-5"  2010/12/09  
    The present smart composite structures are composed of PZT actuators and graphlte-epoxy composites to improve the performance of vibration suppression. The control performance of PZT actuators strongly depends on their placements and vibration characteristics of laminated composites are varied by their lay-up configurations. Thus, a multidisciplinary optimization method employing actuator placements, lay-ups of laminated composite plates and control systems as design variables is proposed here. First, a database containing the frequencies and modal matrixes is made to avoid the FEA repeatedly. Then, the H_2 norm of control response is minimized with respect to the above design variables with referring the database by a simple genetic algorithm with assuming that the state feedback is available. Finally, the output feedback system is reconstructed with the dynamic compensator based on the linear matrix inequality (LMI) approach. The effectiveness of the present optimization technique is confirmed by the experimental and numerical results.
  • Kitagawa Yu, Maeda Hideki, Narita Yoshihiro, Honda Shinya  北海道支部講演会講演概要集  2010-  (49)  9  -10  2010/11/07
  • Maeda Hideki, Kitagawa Yu, Honda Shinya, Narita Yoshihiro  北海道支部講演会講演概要集  2010-  (49)  5  -6  2010/11/07
  • FUJII Toshinori, HONDA Shinya, NARITA Yoshihiro  北海道支部講演会講演概要集  2010-  (49)  3  -4  2010/11/07
  • KOYA Naoaki, HONDA Shinya, NARITA Yoshihiro  北海道支部講演会講演概要集  2010-  (49)  33  -34  2010/11/07
  • Lee Seung-Cheol, HONDA Shinya, NARITA Yoshihiro  北海道支部講演会講演概要集  2010-  (49)  37  -38  2010/11/07
  • WADA Masaaki, HONDA Shinya, NARITA Yoshihiro  北海道支部講演会講演概要集  2010-  (49)  15  -16  2010/11/07
  • Yugami Kumpei, Honda Shinya, Narita Yoshihiro  北海道支部講演会講演概要集  2010-  (49)  45  -46  2010/11/07
  • KOSHIBA Takashi, HONDA Shinya, NARITA Yoshihiro  北海道支部講演会講演概要集  2010-  (49)  17  -18  2010/11/07
  • MINAMI Takashi, HONDA Shinya, NARITA Yoshihiro  北海道支部講演会講演概要集  2010-  (49)  47  -48  2010/11/07
  • LEE Miyong, HONDA Shinya, NARITA Yoshihiro  設計工学・システム部門講演会講演論文集  2010-  (20)  "3203  -1"-"3203-2"  2010/10/27  
    It is different by an individual how to feel about objects, and it is a subjective characteristic by the Kansei of the individual. This study aimed to evaluate an impression of the three-dimensional objects using the Kansei evaluation, and to investigate an element of the 3D objects and the connection with the impression. As the results of experiment, the shapes which became the first impression correspond with the element of the 3D objects. Therefore we think that the elements and the impressions are related deeply. This study becomes the fundamental researches in the manufacturing such as mechanical engineering, Kansei engineering and the product design.
  • LEE Miyong, HONDA Shinya, NARITA Yoshihiro  The Computational Mechanics Conference  2010-  (23)  485  -486  2010/09/23
  • HONDA Shinya, NARITA Yoshihiro, KAJIWARA Itsuro  The Computational Mechanics Conference  2010-  (23)  580  -581  2010/09/23
  • Kato Takeru, HONDA Shinya, NARITA Yoshihiro  Dynamics & Design Conference  2010-  "134  -1"-"134-6"  2010/09/14  
    Shapes and lay-up configurations of composite laminated shallow shells are optimized simultaneously to maximize the fundamental frequency by a simple genetic algorithm method with the elitist tactics. The shell shape is defined by a cubic polynomial and various shapes of shells with inconstant curvature radii can be expressed by varying the value of coefficient for each term. The coefficients and the lay-up configuration of the laminated shell are directly employed as design variables, and constraints are imposed on the coefficients and curvature radii to keep shells shallow. The frequencies are calculated by using the Ritz method due to its flexibleness for shell shapes. Results of the present analysis technique agreed well with experimental and finite element analysis results in terms of frequencies and mode shapes, obtained optimum solutions resulted in higher fundamental frequencies than the shells with general shapes and lay-up configurations.
  • HONDA Shinya, YUGAMI Kumpei, NARITA Yoshihiro  Dynamics & Design Conference  2010-  "133  -1"-"133-5"  2010/09/14  
    The vibration characteristics of the composite plate model with curvilinear fibers are investigated in this study. The curvilinear fiber is realized by the plastic deformation of steel wires and the present composite model is composed of the curved steel wires and epoxy resin. The natural frequency and mode shape are obtained by the experimental modal analysis method where the plate is excited by the impulse hammer and acceleration response is measured. The experimental results showed that the present model has the specific skewed mode shape and it agrees well with the finite element analysis result in terms of the frequency and mode shape. Then the curvilinear fiber shape is optimized for the maximum fundamental frequency by using the genetic algorithm method. The numerical results showed that the optimum curvilinear fiber results in the higher fundamental frequency than the plate with typical curvilinear fibers.
  • Owatari Kosuke, Honda Shinya, Narita Yoshihiro  北海道支部講演会講演概要集  2009-  (48)  143  -144  2009/11/28
  • AOKI Ryoji, HONDA Shinya, NARITA Yoshihiro  北海道支部講演会講演概要集  2009-  (48)  1  -2  2009/11/28
  • KOYA Naoaki, HONDA Shinya, NARITA Yoshihiro  北海道支部講演会講演概要集  2009-  (48)  9  -10  2009/11/28
  • Maeda Hideki, Kitagawa Yu, Narita Yoshihiro, Honda Shinya  北海道支部講演会講演概要集  2009-  (48)  21  -22  2009/11/28
  • KOSHIBA Takashi, NARITA Yoshihiro, HONDA Shinya  北海道支部講演会講演概要集  2009-  (48)  3  -4  2009/11/28
  • Kitagawa Yu, Maeda Hideki, Narita Yoshihiro, Honda Shinya  北海道支部講演会講演概要集  2009-  (48)  19  -20  2009/11/28
  • Kato Takeru, Narita Daisuke, Honda Shinya, Narita Yoshihiro  北海道支部講演会講演概要集  2009-  (48)  13  -14  2009/11/28
  • FUJII Toshinori, HONDA Shinya, NARITA Yoshihiro  北海道支部講演会講演概要集  2009-  (48)  11  -12  2009/11/28
  • FUJII Toshinori, HONDA Shinya, NARITA Yoshihiro  Dynamics & Design Conference  2009-  "231  -1"-"231-6"  2009/08/03  
    The carbon fiber reinforced plastics (CFRP) is classified as high performance composite materials that are superior to conventional materials in the specific strength and stiffness ratios. They are applied to light-weight structures in aircraft and space industries. In such fields, wings are often approximated as a parallelogram plate, but the past studies were carried out by using the classical plate theory. This analysis is however based on the shear deformation plate theory (FSDT). A Ritz method is used to calculate natural frequencies of symmetrically laminated parallelogram plates, and the layerwise optimization method is used to optimize the best lay-up designs. It is shown that the LO method is applicable to the parallelogram plates successfully.
  • KOSHIBA Takashi, HONDA Shinya, NARITA Yoshihiro  Dynamics & Design Conference  2009-  "254  -1"-"254-6"  2009/08/03  
    A method of analysis is presented for determining the free vibration frequencies of hybrid laminated plates, and the layerwisr optimization method is used to determine the optimum fiber orientation angles for the maximum fundamental frequency under general edge conditions. The hybrid plates made of aluminum core and CFRP skins are made for reducing the material costs. Based on the first-order shear deformation theory (FSDT) applicable to thick plates, the Ritz solution is used to derive a frequency equation, and these results give good agreement with those from finite element method. An extensive set of numerical results is given in tabular and graphical form, illustrating the maximum fundamental frequency with the optimum lay-ups of the laminated hybrid plates. Comparison of the results gives tendencies caused by boundary conditions and laminated composition.
  • HONDA Shinya, OONISHI Yoshimasa, NARITA Yoshihiro  M&M材料力学カンファレンス  2009-  357  -358  2009/07/24
  • HONDA Shinya, NARITA Yoshihiro, SASAKI Katsuhiko  最適化シンポジウム講演論文集  2008-  (8)  185  -190  2008/11/26  
    A new design method is proposed here to maximize the fundamental frequency of laminated composite plates reinforced by curvilinear fibers. Spline functions represent arbitrarily shaped fibers and Ritz solutions generate frequency equations. The optimum curvilinear shapes are searched for the maximum fundamental frequencies using genetic algorithms, and the increments of data points which define the spline shape are used as design variables under the limited range of undulation. Comparison of the present analysis method gives good agreement with the finite element method in terms of natural frequencies and vibration modes, and the optimized results show that the present plate with optimally shaped curvilinear fibers gives higher or equal fundamental frequencies than those of the conventional plate with optimally oriented parallel fibers.
  • 上甲 康之, 趙 希禄, 本田 真也, 成田 吉弘  Dynamics & Design Conference  2008-  "169  -1"-"169-6"  2008/09/02  
    It is desirable to optimize the fiber orientation angles to maximize the fundamental frequencies of the fiber reinforced plastic plates. The optimization is studied here by using the experimental design for nonlinear problems, and it turned out that significantly less number of calculations is necessary as compared to other methods, such as a layerwise optimization approach (LOA). The numerical examples show that assumption of appropriate level values is efficient to obtain the optimum frequency in the vibration problem.
  • HONDA Shinya, NARITA Yoshihiro, SASAKI Katsuhiko  北海道支部講演会講演概要集  2007-  (46)  105  -106  2007/09/29
  • HONDA Shinya, NARITA Yoshihiro  Dynamics & Design Conference  "203  -1"-"203-6"  2007  
    A new design method of functional fiber reinforced plastics (FRP) materials which imitates the micro structure of bone or shell in the natural world is proposed in this work. The material has local anisotropy induced by optimally distributed short fibers. The present design method combines a genetic algorithm method (GA) with layerwise optimization concept. The first frequency of thin plates is chosen as an objective function to be maximized in the optimization and it is turned out that the present plates always give higher natural frequencies compared to conventional plates which are reinforced by parallel fibers. Moreover, it is also revealed that optimally distributed short fibers tend to be allocated with certain tendency.
  • HONDA Shinya, NARITA Yoshihiro  最適化シンポジウム講演論文集  2006-  (7)  275  -280  2006/12/08  
    A lamination parameter approach, recently proposed by the authors, is extended in this work to solve a minimum weight design problem for optimizing buckling behavior of laminated composite plates. The present approach basically consists of two parts: the first part is to optimize the lamination parameters by a gradient method, and the second part is to obtain the optimum lay-up (i.e., the fiber orientation angles) by minimizing the errors between the optimum parameters and the parameters for all possible discrete lay-up designs. In the extension of approach, the minimum number of layers with equal thickness is determined so that the plate has higher buckling loads than the specified values. Numerical examples demonstrate that the proposed approach is quite effective in determining the optimum lay-ups for the minimum weight design.
  • HONDA Shinya, NARITA Yoshihiro, SASAKI Katsuhiko  北海道支部講演会講演概要集  2006-  (45)  105  -106  2006/09/25
  • NARITA Yoshihiro, HONDA Shinya  Dynamics & Design Conference  2005-  "726  -1"-"726-6"  2005/08/22  
    The fiber reinforced plastics (FRP) have been utilized in applications of automobile and aircraft structures, since they have advantages of high specific strength and stiffness ratios. The FRP composites are typically fabricated by stacking orthotropic layers, each composed of reinforcing parallel fibers and matrix material. In this work, the optimum lamination parameters are determined by the mathematical programming, and the corresponding fiber orientation angles are derived by minimizing the error of the optimized parameters and possible sets of discrete fiber orientation angles. Numerical examples show various applications of optimization in vibration behaviors of laminated plates, including the maximum fundamental frequencies with corresponding optimum lay-ups (fiber orientation angles) and the maximum difference of the fundamental and second natural frequencies.

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