Construction of an algorithm to analytically solve a problem on the free vibrations of a composite plate of variable thickness

Trapezon, Kirill; Trapezon, A. G.

doi:10.15587/1729-4061.2020.191123

Cited by 2 publications

(4 citation statements)

References 15 publications

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“…Additionally, the obtained results by inverse hyperbolic shear deformation theory (IHSDT) as well as ITSDT were more accurate and similar to the FEM than those of EPT, SPT as well as HPT, and the LSE also has been considered more obviously. While, Trapezon et al [302] investigated the FV of CP with variable thickness by developing a novel analytical algorithm.…”

Section: Analytical Solution Without Considering the Sdementioning

confidence: 99%

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Al Mahmoud,

Safaei,

Sahmani

et al. 2024

Arch Computat Methods Eng

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Recently, the mechanical performance of various mechanical, electrical, and civil structures, including static and dynamic analysis, has been widely studied. Due to the neuroma's advanced technology in various engineering fields and applications, developing small-size structures has become highly demanded for several structural geometries. One of the most important is the nano/micro-plate structure. However, the essential nature of highly lightweight material with extraordinary mechanical, electrical, physical, and material characterizations makes researchers more interested in developing composite/laminated-composite-plate structures. To comprehend the dynamical behavior, precisely the linear/nonlinear-free vibrational responses, and to represent the enhancement of several parameters such as nonlocal, geometry, boundary condition parameters, etc., on the free vibrational performance at nano/micro scale size, it is revealed that to employ all various parameters into various mathematical equations and to solve the defined governing equations by analytical, numerical, high order, and mixed solutions. Thus, the presented literature review is considered the first work focused on investigating the linear/nonlinear free vibrational behavior of plates on a small scale and the impact of various parameters on both dimensional/dimensionless natural/fundamental frequency and Eigen-value. The literature is classified based on solution type and with/without considering the size dependency effect. As a key finding, most research in the literature implemented analytical or numerical solutions. The drawback of classical plate theory can be overcome by utilizing and developing the elasticity theories. The nonlocality, weight fraction of porosity, or the reinforcements, and its distribution type of elastic foundation significantly influence the frequencies.

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Section: Analytical Solution Without Considering the Sdementioning

confidence: 99%

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Al Mahmoud,

Safaei,

Sahmani

et al. 2024

Arch Computat Methods Eng

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“…In [14], an algorithm was built for the analytical solution of the problem of self-oscillations of a composite two-stage annular plate with stages of variable (concave) and constant thickness. The authors obtained ratios that allow studying the distribution of deflections and determining the values of the amplitudes of bending vibrations of the annular plate.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…The authors obtained ratios that allow studying the distribution of deflections and determining the values of the amplitudes of bending vibrations of the annular plate. The forms of oscillations are built on the basis of the provisions of the symmetry and factorization methods devised and developed by the authors of [14]. In the cited work, the frequency equation for a two-stage annular plate of variable thickness, which is rigidly fixed on the inner contour and has a free outer contour, is constructed.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

See 1 more Smart Citation

Determining the frequency of transverse oscillations of an elastically fixed disk of a circular saw

Dziuba,

Chmyr,

Menshykova

et al. 2023

EEJET

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The object of the study is a circular saw blade. An annular plate of constant thickness with a free outer contour and a fixed inner contour was taken as the calculation scheme of the saw blade. The real conditions for fixing the internal circuit correspond to the elastic fixing of the saw blade with clamping flanges on the shaft of the machine. For the accepted calculation scheme of the circular saw, the dynamic model was a fourth-order nonlinear differential equation of the transverse oscillations of the annular plate with the corresponding boundary conditions. The rotation of the circular saw was taken into account in the dynamic model due to the radial force in the middle surface of the ring plate. This force arises as a result of the action of centrifugal forces during the rotation of the saw blade. The solution to the fourth-order nonlinear differential equation was constructed using the Bubnov-Galyorkin numerical method. The boundary conditions for constructing the solution were as follows: the outer contour of the saw disk was considered free; the inner contour of the saw disk – elastically fixed with a certain stiffness coefficient. The solution was implemented in the Maple 15 mathematical environment in the form of a developed program. According to the obtained frequency equation, the values of cyclic and natural frequencies of transverse oscillations of circular saw disks of different thicknesses with the same radius of the inner contour and three values of the radii of the outer contour were determined: 150 mm, 200 m, and 250 mm. The effect of the rigidity of the internal contour fixing and the angular speed of rotation of the saw blade on the natural frequencies of transverse oscillations was studied. The study was performed for saw disks in the case of oscillations with one, two, and three nodal diameters. It was established that the rigidity of the internal contour of the saw blade has the greatest influence on the natural frequency of transverse oscillations with one nodal diameter

show abstract

Construction of an algorithm to analytically solve a problem on the free vibrations of a composite plate of variable thickness

Cited by 2 publications

References 15 publications

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Determining the frequency of transverse oscillations of an elastically fixed disk of a circular saw

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