Exact closed-form solutions for the natural frequencies and stability of elastically connected multiple beam system using Timoshenko and high-order shear deformation theory

2013 ◽  
Vol 332 (3) ◽  
pp. 563-576 ◽  
Author(s):  
Vladimir Stojanović ◽  
Predrag Kozić ◽  
Goran Janevski
Keyword(s):  
Closed Form ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
High Order ◽  
Closed Form Solutions ◽  
Multiple Beam ◽  
Beam System

scholarly journals Thermal Buckling and Free Vibration Analysis of Functionally Graded Plate Resting on an Elastic Foundation According to High Order Shear Deformation Theory Based on New Shape Function

2020 ◽  
Vol 10 (12) ◽  
pp. 4190
Author(s):  
Aleksandar Radaković ◽  
Dragan Čukanović ◽  
Gordana Bogdanović ◽  
Milan Blagojević ◽  
Blaža Stojanović ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shape Function ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
High Order ◽  
Functionally Graded Plate

Functionally graded square and rectangular plates of different thicknesses placed on the elastic foundation modeled according to the Winkler-Pasternak theory have been studied. The thermal and mechanical characteristics, apart from Poisson’s ratio, are considered to continuously differ through the thickness of the studied material as stated in a power-law distribution. A mathematical model of functionally graded plate which include interaction with elastic foundation is defined. The equilibrium and stability equations are derived using high order shear deformation theory that comprises various kinds of shape function and the von Karman nonlinearity. A new analytically integrable shape function has been introduced. Hamilton’s principle has been applied with the purpose of acquiring the equations of motion. An analytical method for identifying both natural frequencies and critical buckling temperature for cases of linear and nonlinear temperature change through the plate thickness has been established. In order to verify the derived theoretical results on numerical examples, an original program code has been implemented within software MATLAB. Critical buckling temperature and natural frequencies findings are shown below. Previous scientific research and papers confirms that presented both the theoretical formulation and the numerical results are accurate. The comparison has been made between newly established findings based on introduced shape function and the old findings that include 13 different shape functions available in previously published articles. The final part of the research provides analysis and conclusions related to the impact of the power-law index, foundation stiffness, and temperature gradient on critical buckling temperature and natural frequencies of the functionally graded plates.

scholarly journals Analytical solution for statif bending analyses of functionally grades plates with porosities

2020 ◽  
Vol 15 (55) ◽  
Author(s):  
Slimane Merdaci ◽  
Adda Hadj Mostefa ◽  
Youcef Beldjelili ◽  
Mohamed Merazi ◽  
Sabrina Boutaleb ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Shear Strain ◽  
Closed Form ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
High Order ◽  
Gradient Index ◽  
Simply Supported ◽  
Strain Function

The paper examines a static bending of porous functional plates (FGP) and rectangular plate solutions, based on an underlying high-order shear deformation theory. The proposed high-order shear deformation theory, as opposed to other theories, includes four unknowns. For this reason, a new shear strain function is considered. The technique of Navier is used in closed-form FGP solutions. Results of deflections and stresses are presented for simply supported border conditions. Current figures are contrasted with the non-poreous plate deflecting solutions and the literature's stresses. Effects of different parameters, including thickness, gradient index and porosity of FGM plates, are discussed.

A New Shear Deformation Theory for Free Vibration of Functionally Graded Beams

2013 ◽  
Vol 455 ◽  
pp. 198-201 ◽  
Author(s):  
Song Xiang
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Present Theory ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A n-order shear deformation theory is used to study the free vibration of functionally graded beams. Present theory satisfies the zero transverse shear stress boundary conditions on the top and the bottom surface of the beam. The natural frequencies computed by present theory are compared with previous published results which demonstrate the accuracy of present theory.

A Trigonometric Shear Deformation Theory for Free Vibration Analysis of Functionally Graded Plates

2014 ◽  
Vol 680 ◽  
pp. 284-287
Author(s):  
Jiang Wu ◽  
Song Xiang
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Functionally Graded Plate ◽  
Simply Supported

A trigonometric shear deformation theory is presented to analyze the free vibration of functionally graded plate. The Navier-type analytical method is used to solve the governing differential equations. The natural frequencies of simply supported functionally graded plates are calculated and compared with the available results.

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