COMPLEX EIGENFREQUENCIES AND DAMPING PROPERTIES OF AN ELONGATED PLATE WITH AN INTEGRAL DAMPING COATING
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COMPLEX EIGENFREQUENCIES AND DAMPING PROPERTIES OF AN ELONGATED PLATE WITH AN INTEGRAL DAMPING COATING V. N. Paimushina,b,∗ , V. A. Firsova , and V. M. Shishkinc
UDC 532.517: 539.3
Abstract: This paper considers the classical methods of surface damping of bending vibrations of thin-walled structures and a promising integral version of a damping coating consisting of two layers of a material with pronounced viscoelastic properties separated by a thin reinforcing layer of a high modulus material. A finite element with 14 degrees of freedom for modeling an elongated plate with the specified damping coating has been developed with consideration of the transverse compression of damping layers under high-frequency vibrations of the plate. The generalized problem of complex eigenvalues in the lower part of the spectrum of complex modes and frequencies of free vibrations of a damped plate is solved by the subspace iteration method taking into account the frequency dependence of the dynamic elastic moduli of the material. The damping properties of the plate are determined from the imaginary parts of the complex eigenfrequencies and the relative energy dissipation at resonance. Keywords: plate, damping coating, logarithmic decrement of vibrations, finite element, complex frequency. DOI: 10.1134/S0021894420040148 INTRODUCTION Traditional structural materials (metals and their alloys) with high elastic and strength parameters, as a rule, have weak damping properties [1, 2]. Therefore, to reduce the vibration activity and dynamic stress of thin-walled structural elements, it is common to use various coatings of viscoelastic materials, which were first considered in [3– 6]. The importance of the problem and the attention of researchers to it are noted in a paper [7] dealing with the influence exerted on damping by various physical factors: temperature, vibration frequency, layer thickness, loading level, etc. The results of these studies were used as the basis in the American standard test method for measuring vibration-damping properties of materials [8]. According to [7], there are two classical methods of surface damping, depending on the nature of dominant deformations in the damping layer: (1) free layer damping (FLD); (2) constrained layer damping (CLD). In the first method, a damping layer of a viscoelastic material is rigidly attached to a damped thin-walled structure, whose bending under transverse vibrations gives rise to cyclic tension–compression deformations and their corresponding damping forces in the damping layer. However, this damping method is inefficient [7] since the
a
Tupolev Kazan National Research Technical University, Kazan, 420111 Russia; ∗ [email protected]; vafirsov [email protected]. b Kazan Federal University, Kazan, 420008 Russia. c Vyatka State University, Kirov, 610000 Russia; [email protected]. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 61, No. 4, pp. 114–127, July–August, 2020. Original article submitted February 26, 2020; revision submitted February 26, 2020; accepted for publicatio
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