Exact Solution of Bending Free Vibration Problem of the FGM Beams with Effect of Axial Force

2010 ◽  
pp. 135-154
Author(s):  
Justín Murín ◽  
Mehdi Aminbaghai ◽  
Vladimír Kutiš
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Axial Force ◽  
Vibration Problem

On the Free Vibration of Mono-Coupled Periodic Distributed Parameter Systems

1993 ◽  
Author(s):  
Gerhard G. G. Lueschen ◽  
Lawrence A. Bergman
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Periodic Structure ◽  
Classical Result ◽  
Discrete Systems ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
New Approach

Abstract A new approach to the exact solution is given for the free vibration of a periodic structure comprised of a multiplicity of identical linear distributed parameter substructures, closely coupled through identical linear springs. The method used is an extension of a classical result for periodic discrete systems.

Contribution to the free vibration problem of a free-free beam with large end masses

2018 ◽  
Vol 98 (5) ◽  
pp. 840-847
Author(s):  
Slaviša Šalinić ◽  
Aleksandar Obradović ◽  
Momčilo Dunjić ◽  
Dragan Sekulić ◽  
Željko Lazarević
Keyword(s):  
Free Vibration ◽  
Vibration Problem ◽  
Free Beam

Free vibration of high-speed rotating Timoshenko shaft with various boundary conditions: effect of centrifugally induced axial force

2014 ◽  
Vol 84 (12) ◽  
pp. 1691-1700 ◽  
Author(s):  
Benyamin Gholami Bazehhour ◽  
Seyed Mahmoud Mousavi ◽  
Anoushiravan Farshidianfar
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Axial Force ◽  
High Speed ◽  
Various Boundary Conditions

Free vibration of bi-material cylindrical shells

2016 ◽  
Vol 230 (15) ◽  
pp. 2637-2649 ◽  
Author(s):  
Saeed Sarkheil ◽  
Mahmud S Foumani ◽  
Hossein M Navazi
Keyword(s):  
Exact Solution ◽  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
State Space ◽  
Thin Shell ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Space Technique ◽  
Thin Shell Theory

Based on the Sanders thin shell theory, this paper presents an exact solution for the vibration of circular cylindrical shell made of two different materials. The shell is sub-divided into two segments and the state-space technique is employed to derive the homogenous differential equations. Then continuity conditions are applied where the material of the cylindrical shell changes. Shells with various combinations of end boundary conditions are analyzed by the proposed method. Finally, solving different examples, the effect of geometric parameters as well as BCs on the vibration of the bi-material shell is studied.

Free Vibration of Damaged Frame Structures Considering the Effects of Axial Extension, Shear Deformation and Rotatory Inertia: Exact Solution

2017 ◽  
Vol 17 (10) ◽  
pp. 1750111
Author(s):  
Ugurcan Eroglu ◽  
Ekrem Tufekci
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Shear Deformation ◽  
Natural Frequencies ◽  
Plane Motion ◽  
Mode Shapes ◽  
Frame Structures ◽  
Crack Identification ◽  
Rotatory Inertia ◽  
Axial Extension

In this paper, a procedure based on the transfer matrix method for obtaining the exact solution to the equations of free vibration of damaged frame structures, considering the effects of axial extension, shear deformation, rotatory inertia, and all compliance components arising due to the presence of a crack, is presented. The crack is modeled by a rotational and/or translational spring based on the concept of linear elastic fracture mechanics. Only the in-plane motion of planar structures is considered. The formulation is validated through some examples existing in the literature. Additionally, the mode shapes and natural frequencies of a frame with pitched roof are provided. The variation of natural frequencies with respect to the crack location is presented. It is concluded that considering the axial compliance, and axial-bending coupling due to the presence of a crack results in different dynamic characteristics, which should be considered for problems where high precision is required, such as for the crack identification problems.

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