A unified formulation for free in-plane vibrations of arbitrarily-shaped straight-sided quadrilateral and triangular thin plates

Liu, Tao; Hu, Guo-qing; Wang, Ailun; Wang, Qingshan

doi:10.1016/j.apacoust.2019.06.014

Cited by 28 publications

(4 citation statements)

References 46 publications

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“…Liu et al 15 carried out free in-plane vibration analyses of plates in curvilinear domains by the differential quadrature hierarchical finite element method. Liu et al 16 investigated free in-plane vibration of arbitrarily shaped straight-sided quadrilateral and triangular plates based on the improved Fourier series method together with the coordinate transformation.…”

Section: Introductionmentioning

confidence: 99%

Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions

et al. 2023

Sci Rep

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This work reports new analytic free in-plane vibration solutions for orthotropic non-Lévy-type rectangular plates, i.e., those without two opposite edges simply supported, by the symplectic superposition method (SSM), which has never been applied to in-plane elasticity problems in any existing works. Such analytic solutions are not accessible through conventional analytic methods as seeking analytic solutions that meet both the governing partial differential equations and various non-Lévy-type boundary conditions is an acknowledged challenge in mechanical analysis of plates. The clamped and free plates are considered as two most representative cases of non-Lévy-type plates. The SSM is implemented in the Hamiltonian system-based symplectic space, where the separation of variables and the symplectic eigen expansion prove to be well-grounded. These two mathematical treatments are adopted to first gain the analytic solutions of two elementary problems. The final analytic free in-plane vibration solutions are obtained by superposition of the two elementary problems. Comprehensive new natural frequencies and vibration modes are studied and validated by reference solutions from the finite element method or other approaches. The rigorous solution procedure, fast convergence, and highly accurate results render the present framework capable of serving as benchmarks for future comparison and applicable to analytic investigation of more plate problems.

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Section: Introductionmentioning

confidence: 99%

Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions

et al. 2023

Sci Rep

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“…Two dimensional temperature effect on the vibration is computed in [5] for the first time for a clamped triangular plate with two dimensional thickness by using the Rayleigh Ritz method. A unified formulation was proposed in [6] for the free in-plane vibration of arbitrarily shaped straight-sided quadrilateral and triangular plates with arbitrary boundary conditions by improved Fourier series method (IFSM). Fourier series method is used in [7] for free vibration of arbitrary shaped laminated triangular thin plates.…”

Section: Introductionmentioning

confidence: 99%

Vibrational frequency of triangular plate having circular thickness

Lather,

Kumar,

Yadav

et al. 2023

Vib. proced.

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In the current research, modes of frequency of isotropic tapered triangular plate having 1-D (one dimensional) circular thickness and 1-D (one dimensional) linear temperature profile for clamped boundary conditions are discussed. Authors implemented Rayleigh Ritz technique to solve the frequency equation of isotropic triangular plate and computed the first four modes with a distinct combination of plate parameters. Authors have performed the convergence study of modes of frequency of the isotropic triangular plate. Also, conducted comparative analysis of modes of frequency of the current study with available published papers and the results presented in tabular form. The aim of the present study is to show the impact of a one dimensional circular thickness and one dimensional linear temperature on modes of frequency of vibration of an isotropic tapered triangular plate.

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“…e theories on which studies for the analysis of static and dynamic characteristics of composite plates and shells are based can be classified into two types: two-dimensional theory and three-dimensional theory [11][12][13][14]. Two-dimensional theories include classical plate theory (CPT) [15][16][17], FSDT [18,19], and high order shear deformation theory (HSDT) [20][21][22][23]. Two-dimensional theories are based on the Kirchhoff hypothesis that normal to the middle surface remains normal to it during deformations and such assumptions are characterized by the middle surface displacements [24].…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Bulkhead-Stiffened Functionally Graded Open Shell Using a Meshless Method

Kwak¹,

Kim²,

Pang³

et al. 2022

Shock and Vibration

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This paper focuses on the free vibration analysis of bulkhead-stiffened functionally graded open shell (FGOS) by means of the first-order shear deformation theory (FSDT) and the meshless strong form method. The bulkhead-stiffened FGOS is decomposed into several segments without bulkhead, and the equations of motion and boundary conditions for each segment are discretized by meshless strong form method, and the displacement components are approximated using meshfree Legendre–RIPM shape function using the combined basis of multi-quadrics (MQ) radial function and Legendre polynomials. The continuous conditions of displacement are applied at the interfaces between segments. The boundary and continuous conditions are enforced by using the artificial spring technique. The accuracy and reliability of the current method are validated by comparing the present results with those of the kinds of literature and the finite element program ABAQUS. The effects of some geometrical parameters and boundary conditions on the natural frequencies of bulkhead-stiffened FGOS are investigated through numerical examples, which may serve as benchmark data.

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A unified formulation for free in-plane vibrations of arbitrarily-shaped straight-sided quadrilateral and triangular thin plates

Cited by 28 publications

References 46 publications

Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions

Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions

Vibrational frequency of triangular plate having circular thickness

Free Vibration Analysis of Bulkhead-Stiffened Functionally Graded Open Shell Using a Meshless Method

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