Free vibration analysis of singly curved shells using the isogeometric finite strip method

Borković, Aleksandar; Radenković, G.; Majstorović, D.; Milovanović, Snježana Z.; Milašinović, Dragan D.; Cvijić, Radomir

doi:10.1016/j.tws.2020.107125

Cited by 17 publications

(9 citation statements)

References 38 publications

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“…The article [14] presents a new theory of hyperbolic shear deformation that can be applied to the analysis of free vibrations of laminated, functionally classified, isotropic, and sandwich composite plates. The authors of the article [15] propose a new way of dimensional discretization of two-dimensional regions to calculate the natural frequencies of curved shells.…”

Section: Introductionmentioning

confidence: 99%

Approximate calculation of natural frequencies of oscillations of the diamond-shaped plates of the discrete-continuous inter-resonance vibrating table

Lanets

Maistruk

Derevenko

et al. 2023

IOP Conf. Ser.: Mater. Sci. Eng.

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Conventional single- and two-mass vibrating machines do not have a sufficient level of energy efficiency. There are vibration machines based on inter-resonance oscillating systems, which make possible the significant reduction in the use of electricity. To implement highly effective inter-resonance operation modes of vibrating machines, the oscillating masses of such a system must precisely calculate values of inertial-rigid parameters, as well as their frequency of oscillations. Since the synthesis of continuous sections into classical discrete models of multi-mass mechanical oscillating systems has recently become widespread, the most optimal option is to use a continuous member as a reactive mass of a vibrating machine. The continuous member combines inertial and stiffness parameters and makes it extremely easy to perform the reactive mass. In particular, rectangular plates are used as continuous members. The rectangular shape of the plate is not the only option for making a continuous member. This paper proposes the construction of a discrete-continuous inter-resonance vibration machine with electromagnets, where a diamond-shaped plate is used as a continuous member. The authors carried out the computation of the first natural frequency of the diamond-shaped plate using the Rayleigh-Ritz method with the equation of the hyperboloid. The determined eigenfrequency was confirmed in the Ansys software.

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Section: Introductionmentioning

confidence: 99%

Approximate calculation of natural frequencies of oscillations of the diamond-shaped plates of the discrete-continuous inter-resonance vibrating table

Lanets

Maistruk

Derevenko

et al. 2023

IOP Conf. Ser.: Mater. Sci. Eng.

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“…A similar approach was used by Fakkaew et al [34]. Lastly, the latest contributions focus on the finite element method (FEM) using the block Lanczos iteration method [35], the reverberation-ray matrix approach [36], Galerkin projections of the partial differential equations governing the shell equations of motion [37], the symplectic approach [38,39], and the isogeometric analysis [40] to extend the theory of natural vibrations to various thin-walled structures, also in composite materials [41].…”

Section: Introductionmentioning

confidence: 99%

A Dynamic Matrix for the Study of Free Vibrations of Thin Circular Cylindrical Shells under Different Boundary Conditions

Cammalleri,

Castellano

2023

Designs

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Although free vibrations of thin-walled cylinders have been extensively addressed in the relevant literature, finding a good balance between accuracy and simplicity of the procedures used for natural frequency assessment is still an open issue. This paper proposes a novel approach with a high potential for practical application for rapid esteem of natural frequencies of thin-walled cylinders under different boundary conditions. Starting from Donnell–Mushtari’s shell theory, the differential problem is simplified by using the principle of virtual work and introducing the flexural waveforms of a beam as constrained as the cylinder. Hence, the formulation is reduced to the eigenvalue problem of an equivalent 3 × 3 dynamic matrix, which depends on the cylinder geometry, material, and boundary conditions. Several comparisons with experimental, numerical, and analytical approaches are presented to prove model reliability and practical interest. An excellent balance between fast usability and accuracy is achieved. The user-friendliness of the model makes it suitable to be implemented during the design stage without requiring any deep knowledge of the topic.

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“…Studies and employment of FSM have been extensive in recent decades. However, some research works are recently carried out to use this approach for various problems; for example, see References 58–63. More detailed information on FSM can be found in the books by Cheung 57 and Cheung and Tham 64 …”

Section: Introductionmentioning

confidence: 99%

Finite strip method based on Carrera unified formulation for the free vibration analysis of variable stiffness composite laminates

Shojaee

Hamzehei‐Javaran

2022

Numerical Meth Engineering

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This work presents a refinement of the finite strip method (FSM) based on the Carrera unified formulation (CUF) and is applied to free vibration analysis of variable stiffness composite laminated (VSCL) plates. VSCL plates considered here are composed of layers with curvilinear fibers in which their orientation angle changes linearly with respect to one of the in‐plane coordinates. The FSM permits the plate to be divided into some finite strips connected along the so‐called nodal lines. The conventional finite strip method involves an approximation of the solution of a plate problem by using continuously harmonic series in the longitudinal direction along the nodal lines and simple polynomial shape functions (the usual beam shape functions) in the transverse direction of the plate. However, refined finite strip model that presented in this paper allows one to express the unknown variables as a set of thickness functions that only depend on the thickness coordinate and the corresponding variable that depends on the in‐plane coordinates which involve continuously harmonic series and polynomial shape functions. Thanks to this new finite strip model, the shape functions used in the transverse direction can be chosen as 1D bar shape functions, and also, all three components of the displacement field are considered in each nodal line. Moreover, based on this approach, three‐dimensional displacement field is approximated in a compact form as a generic N‐order expansion. Therefore, explicit expressions of fundamental nuclei of finite strip matrices are obtained in a compact form and presented here. The results obtained by the present formulation for VSCL plates are compared with those obtained from published data. The results show that this kind of strip is efficient and useful. Further, several numerical examples are presented, and the effect of the order of expansion, the number of strips, curvilinear fiber angle, and various boundary conditions are examined.

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Free vibration analysis of singly curved shells using the isogeometric finite strip method

Cited by 17 publications

References 38 publications

Approximate calculation of natural frequencies of oscillations of the diamond-shaped plates of the discrete-continuous inter-resonance vibrating table

Approximate calculation of natural frequencies of oscillations of the diamond-shaped plates of the discrete-continuous inter-resonance vibrating table

A Dynamic Matrix for the Study of Free Vibrations of Thin Circular Cylindrical Shells under Different Boundary Conditions

Finite strip method based on Carrera unified formulation for the free vibration analysis of variable stiffness composite laminates

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