# Effect of the Fiber Lamination Angle of a Carbon-Fiber, Laminated Composite Plate Roof on the Car Interior Noise

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## Abstract

The paper presents the change of the interior noise according to the lamination angles of the carbon fiber in the carbon-fiber reinforced plastic (CFRP) laminated composite plate. In the previous paper, the charateristics of the sound radiated from a CFRP plate was studied in the free field condition. In this paper, vibro-acoustic interaction for the CFRP plate with various lamination angles was studed considering the application of the CFRP plate to car roof. In order to study the vibro-acoustic interaction, a certain enclosure with flexible wall was required and then the closed rectangular box was prepared. The one flexible wall of the rectangular box consisted of CFRP plate. Three CFRP plates with fiber lamination angles of [-15/15/15/-15]s, [-30/30/30/-30]s, and [-75/75/75/-75]s were fabricated and used as one flexible wall of the closed box. These plates were excited by an impact force, and the interior sound pressure within the closed box was calculated both theoretically and experimentally. Then, the identified vibro-acoustic characteristics were used to apply the CFRP plate to the roof of a car, thereby shifting the resonance frequency of the interior noise.

## Key words

CFRP (Carbon-Fiber-Reinforced Plastic) Interior noise Lamination angle Vibro-acoustic Car interior noise NVH (Noise Vbrtion Harshness)## Nomenclature

**f(t)**force, N

- x
position of measuring the sound pressure in the cavity, m

**y**position of excited by force on the flexible wall, m

**p**sound pressure, Pa

*u*vibration velocity, m/s

- ψ
_{n}(**x**) uncoupled cavity mode shape function

**ψ**vectors of ψ

_{n}(**x**)*a*_{n}(ω)complex amplitude of the sound pressure modes, Pa

**a**vectors of

*a*_{n}(ω)- ϕ
_{m}(**y**) uncoupled vibration mode shape function

**Φ**vectors of ϕ

_{m}(**y**)*b*_{m}(ω)complex amplitude of the vibration velocity modes, m/s

**b**vectors of

*b*_{m}(ω)*V*volume of the cavity, m

^{3}- ρ
_{0} density in air, kg/m

^{3}*c*_{0}speed of sound in air, m/s

*S*_{f}surface area of the CFRP plate, m

^{2}*u*(**y**, ω)normal velocity of a CFRP plate with a surface area of S

_{f}, m/s*A*_{n}(ω)cavity mode resonance term, rad·s

*T*_{a}time constant of the first mode, s

- ω
_{n} natural frequency of the nth cavity mode, rad/s

- ζ
_{n} damping ratio of the nth cavity mode

*C*_{n,m}geometric coupling coefficient between the uncoupled vibration and cavity mode shape functions, m

^{2}**q**_{s}modal source strength vector, m

^{3}/s**C**vibro-acoustic mode shape coupling matrix, m

^{2}**Z**_{a}uncoupled cavity-mode modal impedance matrix, kg/m

^{4}**A**(

*N*×*N*) diagonal matrix in which each (*n*,*n*) diagonal term consists of*A*_{n}, rad·s- ρ
_{s} density of the plate material, kg/m

^{3}*h*thickness of the plate, m

*f*(**y**,ω)force distribution function, N/m

^{2}*p*(**y**,ω)cavity sound pressure distribution, Pa

*B*m(ω)vibration mode resonance term, rad·s

- ω
_{m} natural frequency of the

*m*th mode, rad/s- ζ
_{m} amping ratio of the

*m*th mode**g**generalized modal force caused by the external force distribution

*f*(**y**,ω), N**g**_{a}modal force vector acting on the acoustic system, N

**Y**_{s}uncoupled vibration modal mobility matrix, s/kg

**B**(

*M*×*M*) diagonal matrix in which each (*m*,*m*) diagonal term consists of*B*_{m}, rad/s**I**identity matrix

*L*_{x}Dimension of the rectangular box in the x-direction, m

*L*_{y}Dimension of the rectangular box in the y-direction, m

*L*_{z}Dimension of the rectangular box in the z-direction, m

**k**_{b}vibration wave number, m

^{−1}

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