TY - JOUR

T1 - Natural Damped Vibrations of Anisotropic Box Beams of Polymer Composite Materials. 2. Numerical Experiments

AU - Ryabov, V.M.

AU - Yartsev, B.A.

N1 - Ryabov, V.M., Yartsev, B.A. Natural damped vibrations of anisotropic box beams of polymer composite materials. 2. Numerical experiments. Vestnik St.Petersb. Univ.Math. 49, 260–268 (2016). https://doi.org/10.3103/S1063454116030110

PY - 2016

Y1 - 2016

N2 - The influence of the orientation of reinforcing fibers on the natural frequencies and mechanical loss coefficient of coupled vibrations of unsupported symmetric and asymmetric box beams, as evaluated in numerical experiments, is discussed. The calculations were performed under the assumption that the real parts of the complex moduli and mechanical loss coefficient are frequency-independent. Vibration modes were identified by their surface shapes. The boundaries of the regions of mutual transformation of interacting vibration modes were determined by the joint analysis of the dependences of the coupled and partial eigenfrequencies and the mechanical loss coefficients on the orientation angle of reinforcing fibers. It is established that vibrations of a symmetric box beam give rise to two primary interactions: bending–torsional and longitudinal–shear ones, which are united into a unique longitudinal–bending–torsional–shear interaction by the secondary interaction caused by transverse shear strains. Vibrations of an asymmetric box beam give rise to longitudinal–torsional and bending–bending (in two mutually orthogonal planes) interactions. It is shown that in a number of cases variation in the orientation angle of reinforcing fibers is accompanied with a mutual transformation of coupled vibration modes. If the differential equations for natural vibrations involve odd-order derivatives with respect to the spatial variable (a symmetric beam and the bending–bending interaction of an asymmetric beam), then, with variation in the orientation angle of reinforcing fibers, the mutual transformation of coupled vibration modes proceeds. If the differential equations for natural vibrations involve only even-order derivatives (the longitudinal–torsional interaction of an asymmetric beam), no mutual transformation of coupled vibration modes occurs.

AB - The influence of the orientation of reinforcing fibers on the natural frequencies and mechanical loss coefficient of coupled vibrations of unsupported symmetric and asymmetric box beams, as evaluated in numerical experiments, is discussed. The calculations were performed under the assumption that the real parts of the complex moduli and mechanical loss coefficient are frequency-independent. Vibration modes were identified by their surface shapes. The boundaries of the regions of mutual transformation of interacting vibration modes were determined by the joint analysis of the dependences of the coupled and partial eigenfrequencies and the mechanical loss coefficients on the orientation angle of reinforcing fibers. It is established that vibrations of a symmetric box beam give rise to two primary interactions: bending–torsional and longitudinal–shear ones, which are united into a unique longitudinal–bending–torsional–shear interaction by the secondary interaction caused by transverse shear strains. Vibrations of an asymmetric box beam give rise to longitudinal–torsional and bending–bending (in two mutually orthogonal planes) interactions. It is shown that in a number of cases variation in the orientation angle of reinforcing fibers is accompanied with a mutual transformation of coupled vibration modes. If the differential equations for natural vibrations involve odd-order derivatives with respect to the spatial variable (a symmetric beam and the bending–bending interaction of an asymmetric beam), then, with variation in the orientation angle of reinforcing fibers, the mutual transformation of coupled vibration modes proceeds. If the differential equations for natural vibrations involve only even-order derivatives (the longitudinal–torsional interaction of an asymmetric beam), no mutual transformation of coupled vibration modes occurs.

KW - Composite materials

KW - natural vibrations

KW - coupled vibrations

UR - https://link.springer.com/article/10.3103/S1063454116030110

M3 - Article

VL - 49

SP - 260

EP - 268

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -