二層円筒殻の粘弾性制動について
1968 年 24 巻 6 号 p. 325-334
詳細
1968 年 24 巻 6 号 p. 325-334
Cylindrical shell structures are used in various constructions such as water drain systems, air conditioning ducts, chemical plants and the fuselages of airplanes. Solid-borne vibrations associated with these structures have to be controlled not only from the point of view of noise radiation but also from that of fatigue. Fatigue is greatly related to the maxmum stresses caused, as well as to the frequency of occurrence. One method of eliminating large vibrational amplitudes is to coat one side of shell surface with a damping material. The pupose of the present paper is to evaluate and estimate the damping capabilities of two-layer cylindrical shells (see Fig. 1). From the practical point of view, the uncoupled five principal modes (see Fig. 2) are disscussed with respect to natural frequency and damping (logarithmic decrement). As was discussed by Oberst, the logarithmic decrements of the extensional and the bending vibrations of two-layer beams are as follows respectively: (δ/π)_<ex. >≈g_<ε2>r_εr_h, (I) (δ/π)_<bend. >≈3g_<ε2>r_εr_h(a+2r_h+4/3r_h^2 (II) provided r_εr_h<<1 and g_<ε2>r_εr_h, where g_<ε1> and g_<ε2> are the loss factors of the two layers respectively, r_<ε> is the ratio of Young's modulus and r_h is the ratio of thickness. The damping is known to be at least three times greater for the bending mode than for the extensional mode. Dampings for various modes of cylindrical shells are sometimes more complicated, because the extensional and the bending vibrations with respect to the shell layers are essentially coupled with each other. The results for different modes are as follows: 1) Torsional mode The logarithmic decrement (L. D. ) is given by the equation of the same form as eq. (I), where g_<ε2> and r_<ε> are replaced by g_<G2> and r_G, i, e. the loss factor of shear modulus and the ratio of shear modulus respectively. 2) Radial mode The breathing motion is coupled with the bending of the shell layers. For a long wavelength, L. D. is given by eq. (I). According as the wavelength becomes shorter, the damping effect increases up to the value given by eq. (II). 3) Longitudinal mode L. D. is given by eq. (I). For a very short wavelength, however, since the motion is dominantly associated with the bending of the shell layers, L. D. comes close to the value given by eq. (II). 4)Non-axially symmetric mode This is a bending motion around the axis, so that L. D. is given by eq. (II). 5) Flexural mode This as a whole is a bending motion along the axis, but an extensional motion is dominantly associated with the shell layers themselves. For a long wavelength, L. D. is given by eq. (I).
