Two new approximate methods for analyzing free vibration of structural components

Bert, Charles W.; Jang, S. K.; Striz, Alfred G.

doi:10.2514/3.9941

Cited by 282 publications

(121 citation statements)

References 23 publications

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“…In formulating C x lk and D x lk , w ,x = 0 at nodes 1 and N has been built-in by using MMWC-3 [16,32]. The MMWC-3 is very simple and only B x jk is computed slightly different from Equation (14), namely,…”

Section: Stress Analysis By the Hdqmmentioning

confidence: 99%

Harmonic Differential Quadrature Analysis of Soft-Core Sandwich Panels under Locally Distributed Loads

Wang

Yuan

2016

Applied Sciences

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Sandwich structures are widely used in practice and thus various engineering theories adopting simplifying assumptions are available. However, most engineering theories of beams, plates and shells cannot recover all stresses accurately through their constitutive equations. Therefore, the soft-core is directly modeled by two-dimensional (2D) elasticity theory without any pre-assumption on the displacement field. The top and bottom faces act like the elastic supports on the top and bottom edges of the core. The differential equations of the 2D core are then solved by the harmonic differential quadrature method (HDQM). To circumvent the difficulties in dealing with the locally distributed load by point discrete methods such as the HDQM, a general and rigorous way is proposed to treat the locally distributed load. Detailed formulations are provided. The static behavior of sandwich panels under different locally distributed loads is investigated. For verification, results are compared with data obtained by ABAQUS with very fine meshes. A high degree of accuracy on both displacement and stress has been observed.

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Section: Stress Analysis By the Hdqmmentioning

confidence: 99%

Harmonic Differential Quadrature Analysis of Soft-Core Sandwich Panels under Locally Distributed Loads

Wang

Yuan

2016

Applied Sciences

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“…The details of the polynomial-based and Fourier series expansionbased DQ methods can be found in the book of [24]. The DQ method has been extensively applied in engineering for the rapid and accurate solution of various linear and non-linear differential equations [22,23,24,25,26,27,28,29,30]. In general, the polynomial-based and Fourier series expansion-based DQ methods can achieve very accurate results by using a considerable small number of grid points.…”

Section: Introductionmentioning

confidence: 99%

A numerical study of RBFs-DQ method for multi-asset option pricing problems

Ranjbar

Khodayari

2018

B Soc Paran Mat

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In this paper, we propose a numerical scheme to solve multi-dimensional Black-Scholes equation using the global radial basis functions-based differential quadrature (RBFs-DQ) method. Before applying the method, it is needed to remove mixed derivatives from the Black-Scholes equation by making an appropriate change of variables. Then, any spatial derivativeis are approximated by a linear weighted sum of all the function values in the whole physical domain. In the RBFs-DQ method the weighting coefficients are computed by RBFs. The method is very easy to implement and the non-singularity is ensured. The proposed method combines the advantages of the conventional DQ method and the RBFs. It also preserves mesh-free feature of RBFs.

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“…Bert et al (1988) applied the DQM to investigate static and dynamic response of structures for the first time, and afterwards it was improved by Bert and Malik (1996). Also, Bert et al (1989) used DQM for composite plates for the first time and analyzed nonlinear bending of orthotropic rectangular plates.…”

Section: Introductionmentioning

confidence: 99%

Aerothermoelastic Analysis of Functionally Graded Plates Using Generalized Differential Quadrature Method

Shahverdi

Khalafi

Noori

2016

Lat. Am. j. solids struct.

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In the present paper, the aerothermoelastic behavior of Functionally Graded (FG) plates under supersonic airflow is investigated using Generalized Differential Quadrature Method (GDQM). The structural model is considered based on the classical plate theory and the von Karman strain-displacement relations are utilized to involve the nonlinear behavior of the plate. To consider the supersonic aerodynamic loads on the plate, the first order piston theory is applied. The material properties of the FG panel are assumed to be temperature independent and alter in the thickness direction according to a power law distribution. The temperature distribution on the surface of the plate is assumed to be constant and in the thickness direction is obtained by one-dimensional steady conductive heat transfer equation. The discretized governing equations via GDQM are solved by the fourth order Runge-Kutta method. Comparison of the obtained results with those available in literature confirms the accuracy and ability of the GDQM to perform the aerothermoelastic analysis of FG plates. Also, the effect of some important parameters such as Mach number, inplane thermal load, plate aspect ratio and volume fraction index on the plate aerothermoelastic behavior is examined.

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Two new approximate methods for analyzing free vibration of structural components

Cited by 282 publications

References 23 publications

Harmonic Differential Quadrature Analysis of Soft-Core Sandwich Panels under Locally Distributed Loads

Harmonic Differential Quadrature Analysis of Soft-Core Sandwich Panels under Locally Distributed Loads

A numerical study of RBFs-DQ method for multi-asset option pricing problems

Aerothermoelastic Analysis of Functionally Graded Plates Using Generalized Differential Quadrature Method

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