• Structural Engineering and Mechanics
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• v.55 no.4
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• pp.719-742
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• 2015

This paper dealt the free vibration analysis of thick truncated conical composite sandwich shells with transversely flexible cores and simply supported boundary conditions based on a new improved and enhanced higher order sandwich shell theory. Geometries were used in the present work for the consideration of different radii curvatures of the face sheets and the core was unique. The coupled governing partial differential equations were derived by the Hamilton's principle. The in-plane circumferential and axial stresses of the core were considered in the new enhanced model. The first order shear deformation theory was used for the inner and outer composite face sheets and for the core, a polynomial description of the displacement fields was assumed based on the second Frostig's model. The effects of types of boundary conditions, conical angles, length to radius ratio, core to shell thickness ratio and core radius to shell thickness ratio on the free vibration analysis of truncated conical composite sandwich shells were also studied. Numerical results are presented and compared with the latest results found in literature. Also, the results were validated with those derived by ABAQUS FE code.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.340-343
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• 2007

The differential equations governing free, in-plane vibrations of non-circular arches with the translational (radial and tangential directions) and rotational springs at the ends, including the effects of rotatory inertia, shear deformation and axial deformation, are solved numerically using the corresponding boundary conditions. The lowest four natural frequencies for the parabolic geometry are calculated over a range of non-dimensional system parameters: the arch rise to span length ratio, the slenderness ratio, and the translational and rotational spring parameters.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.1181-1184
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• 2007

The differential equations governing free, in-plane vibrations of linearly elastic circular arches with rotationally flexible supports, including the effects of rotatory inertia, shear deformation and axial deformation, are solved numerically using the corresponding boundary conditions. The lowest four natural frequencies and the corresponding mode shapes are obtained over a range of non-dimensional system parameters: the subtended angle, the slenderness ratio, and the rotational spring stiffness.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.846-851
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• 2003

The differential equations governing free, in-plane vibrations of non-circular arches with non-uniform cross-section, including the effects of rotatory inertia, shear deformation and axial deformation, are derived and solved numerically to obtain frequencies. The lowest four natural frequencies are calculated for the prime parabolic arches with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. Three general taper types for rectangular section are considered. A wide range of arch rise to span length ratios, slenderness ratios, and section ratios are considered. The agreement with results determined by means of a finite element method is good from an engineering viewpoint.

• Structural Engineering and Mechanics
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• v.25 no.4
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• pp.405-421
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• 2007

A four-node hybrid stress element for analysing orthotropic folded plate structures is presented. The formulation is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. The proposed element has six degree of freedom per node and permits an easy connection to other type of elements. An equilibrated stress field in each element and inter element compatible boundary displacement field are assumed independently. Static and free vibration analyses of folded plates are carried out on numerical examples to show that the validity and efficiency of the present element.

• Structural Engineering and Mechanics
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• v.42 no.2
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• pp.131-152
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• 2012

In-plane free vibrations of circular beams with stepped cross-sections are investigated by using the exact analytical solution. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The stepped arch is divided into a number of arches with constant cross-sections. The exact solution of the governing equations is obtained by the initial value method. Several examples of arches with different step ratios, different locations of the steps, boundary conditions, opening angles and slenderness ratios for the first few modes are presented to illustrate the validity and accuracy of the method. The effects of the geometric parameters on the natural frequencies are investigated in details. Several examples in the literature are solved and the results are given in tables. The agreement of the results is good for all examples considered. The mode transition phenomenon is also observed for the stepped arches. Some examples are solved also numerically by using the commercial finite element program ANSYS.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.1 s.244
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• pp.18-25
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• 2006

The purpose of this research work is to demonstrate a successful application of hybrid-mixed formulation and nodeless degrees of freedom in developing a very accurate in-plane curved beam element for free vibration analysis. To resolve the numerical difficulties due to the spurious constraints, the present element, based on the Hellinger-Reissner variational principle and considering the effect of shear deformation, employed consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees. The stress parameters were eliminated by the stationary condition, and the nodeless degrees were condensed by Guyan Reduction. Several numerical examples indicated that the property of the mass matrix as well as that of the stiffness matrix have a great effect on the numerical performance. The element with consistent mass matrix produced best results on convergence and accuracy in the numerical analysis of Eigenvalue problems. Also, the higher-order mixed curved beam element showed a superior numerical behavior for the free vibration analyses.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.105-110
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• 2007

The differential equations governing free, in-plane vibrations of circular curved beams with elastic springs at beth ends, including the effects of axial deformation, rotatory inertia and shear defamation. are solved numerically using the corresponding boundary conditions. The lowest three natural frequencies are calculated over a wide range of non-dimensional system parameters, the radial, tangential and rotational spring parameters, the subtended angle, the slenderness ratio and the shear parameter.

• Steel and Composite Structures
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• v.36 no.3
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• pp.293-305
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• 2020

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.

• Steel and Composite Structures
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• v.12 no.4
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• pp.275-289
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• 2012

In this paper the influence of stiffener location, rise/span ratio and fibre orientation on vibration behavior of corner supported hypar shells is studied by using a four-node hybrid stress finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. Benchmark problems are solved to validate the approach and free vibration response of stiffened orthotropic hypar shells is studied both with respect to fundamental frequency and mode shapes by varying the location of stiffeners, rise/span ratio and fiber orientation.