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Structural Design for Curved Panels by Laminated Composite Materials (Identification of Lamination Parameters Using Modal Testing Method ) Tetsuya NARISAWA, Shohei IWATA Abstract - Using a modal

1 Structural Design for Curved Panels by Laminated Composite Materials (Identification of Lamination Parameters Using Modal Testing Method ) Tetsuya NARISAWA, Shohei IWATA Abstract - Using a modal testing method, the identification study for the laminated composite curved panels are examined for the purpose of weight saving structural design. The vibration modes are largely changed as the aspect ratio, curvature and stacking sequences of laminated curved panels. For example, natural frequencies and modal patterns of automobile door panels are examined using modal testing and Ritz s vibration analysis. As the result, identified stacking sequence of angle-ply three layered laminated composite panels was [-/-3/-4] for simply supported condition. This report presents a new tailored design method using FRP materials instead of steel materials to achieve desired strength and stiffness. Key Word: Modal Testing, Ritz s Method, Composite Materials, Structural Design Latch Ry b Door Knob h Test Piece (Door Panel) a Hinge Press Line Fig.1 Experimental unit PC (Modal Analysis Soft) Impulse Hammer Acceleration Pickup Charge Amp & FFT Analyzer Fig. Door panel (Type-A)

Type-A Fig.3 Test object Type-B Table1 Natural frequency [Hz] f 1 f f 3 Y X Type-A Type-B Fig.

line peak node door knob & press line Y 3rd X :peak node door knob & press line [Unit:mm]

Mode shape for fundamental three modes σx Q11 Q1 Q ε 16 x σ = Q Q ε y 6 y τ xy symm.

2 Type-A Fig.3 Test object Type-B Table1 Natural frequency [Hz] f 1 f f 3 Y X Type-A Type-B Fig.4 Frequency responses peak node oor knob & press line [Unit:mm] :peak node door knob & press line peak node door knob & press line Y 3rd X :peak node door knob & press line [Unit:mm] peak node door knob & press line peak node door knob & press line Type-A Type-B Fig. Mode shape for fundamental three modes σx Q11 Q1 Q ε 16 x σ = Q Q ε y 6 y τ xy symm. Q γ 66 xy Q ij Middle surface Fiber orientation Fig.6 Analytical model for laminated curved composite panels Laminae

3 (,, ) w xyt u = u ( xyt,, ) z, x 1 w( xyt,, ) v= v ( x, yt, ) z, w= w,, Ry x ( xyt) () ε κ u u w εx = = z = ε, x + zκy x x x u v w w εy = = z + = ε, y + zκy y x y Ry γ = + = = γ + κ y x y x x y u v u v w xy + z xy z xy U V W u ( x, y) = a φ ( x, y) i= j= n n v ( x, y) = b φ ( x, y) n n w ( x, y) = c φ ( x, y) ij ij ij ij i= j= n n ij ij i= j=,, (4) i j a ij b ij c ij n φ ij Tmax Umax L L=Tmax-Umax () L L L,, =,, a b c (6) ij ij ij K λm = ; λ = ω (7) K M ω (3) Table Convergence study for various boundary conditions B.C. f 1 f f 3 f 4 f FFFF SFFF CFFF SFSF CFSF CFCF a/h 1.66 (1.67).917 (.933).6 (.643).467 (.463) 1.6 (.97) 1.91 (1.34).91 (.69). (.767) (1.463) (1.881).43 (.69) 3.4 (3.17) 3.77 (3.84) 3.9 (3.47) 3.18 (3.19) (3.98).648 (.88).6 (.774).19 (.9) 4.6 (.) 4. (4.8) (4.794) (7.8) 6.78 (6.8).19 (.16).89 (6.1).668 (.71) (6.9) 9.37 (9.36) 8.9 (9.1) Table 3 Convergence study for various stack sequences 1 a /Ry [ /9/9/] [ /9] [9/] inf..1.. inf (1.39) (14.7) 18.9 (18.19) 3.17 (9.6) 11.9 (1.39) (1.4) 1.17 (1.6) (13.9) 8.7 (8.71) 1.86 (1.97) 1.8 (1.9) 8.4 (8.1) 8. (8.69) 8.66 (8.78) 8.97 (9.6) 1.79 (1.78) 8.6 (8.77) 1.86 (1.97) 1.83 (1.93) 7.8 (8.63) 8.6 (8.69) 8.64 (8.81) 8.9 (9.1) 1.67 (1.9) Ω=ω ρe 1 h ρ E 1

4 3rd Ω Ω 3rd Ω Ω 3 3 a/b=. a/b=. (,1) (,) (1,) (,) 1 (,1) 1 1 (,1) 1 (,1) a/b=1. a/b= (1,1) (1,) a/b=. a/b=. 1 a/b=1. 1 a/b= Fig.7 Natural frequency for single layered flat panels 3 (1,) 1 (,1) (,1) 1 (,1) (,1) (,1) a/b= a/b= th Ω Ω 4th Ω 3 (1,1) a/b=. (1,) a/b=. a/b=1. 1 (,1) a/b=1. Ω 3 a/b=. (,3) (,) (,1) (,) 1 1 (,1) (,1) a/b= Fig.8 Natural frequency for three layered flat panels ([/-/],)

5 (1,) (,1) (1,) (1,1) a/b a/b a/b rd b/ry b/ry b/ry (,1) (1,1) (1,) Fig.9 Mode patterns of single layered curved panels (b/h=1,=) ρ( kg/ m 3 ) Table4 Parameter of door panel of Type-A a(m) b(m) t(m) Ry(m) * 1.8 [ 1 / / 3 ]

6 Ω:3.9 [//9] 9.4 [/3/9] 9.7 [/4/9] 9.4 [/6/9] 9.4 [/9/9] (148Hz) (788Hz) 3rd (131Hz) Experimental result by modal test Ω:3.13 [/9/] 3.1 [/9/3] 3.3 [/9/4].99 [/9/6] 3.9 [/9/9] Fig.1 Mode shape and Ω of square panels (a/b=1) (114Hz) (33Hz) 3rd(4Hz) Analytical result by Rit s method ([-/-3/-4]) Fig.13 Compare for experimental result and analytical solution Ω:1.89 [//9] Ω:4.4 [//9] Ω:97.3 [//-9] Ω:8.73 [/9/] 1.93 [/3/9] [/3/9] [/-3/9] 6.8 [/9/3] 1.9 [/4/9] 4.4 [/4/9] 1.8 [/-4/9].99 [/9/-4] 1.87 [/6/9] 4.8 [/6/9] 8.7 [/-6/9].89 [/9/-6] Fig.1 Mode shape and Ω of curved panels (a/b=1.6, b/ry=.64) 1.76 [/9/9] 6.6 [/9/9] Fig.11 Mode shape and Ω of rectangular panels () 9.44 [/9/9] 78.3 [/9/9] 1 3 (7), , (7), 7-1. M.S.Qatau, Vibration of Laminated Shells and Plates, Elsevier Academic Press, (4). (7),

‰IŠv05„´“ever4.pmd

‰IŠv05„´“ever4.pmd Application of High Stiffness and Light Weight FRP Structural Materials Tetsuya NARISAWA, Shigeru AOKI, Norihiko UWABO Abstract - Fiber reinforced plastics (FRP) are one of the high-strength, high-stiffness,