Exact solution of free vibration of a uniform tensioned beam combined with both lateral and rotational linear sub-systems

2015 ◽  
Vol 341 ◽  
pp. 206-221 ◽  
Author(s):  
Y. Chen ◽  
D.M. McFarland ◽  
B.F. Spencer ◽  
L.A. Bergman
Keyword(s):  
Exact Solution ◽  
Free Vibration

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.

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.

scholarly journals A dynamic coefficient matrix method for the free vibration of thin rectangular isotropic plates

2021 ◽  
Author(s):  
Supun Jayasinghe ◽  
Seyed M. Hashemi
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Free Vibration Analysis ◽  
Flexural Vibration ◽  
Coefficient Matrix ◽  
Dynamic Coefficient ◽  
Rectangular Plates ◽  
Various Boundary Conditions ◽  
Unique Method ◽  
Benchmark Solutions

The free flexural vibration of thin rectangular plates is revisited. A new, quasi-exact solution to the governing differential equation is formed by following a unique method of decomposing the governing equation into two beam-like expressions. Using the proposed quasi-exact solution, a Dynamic Coefficient Matrix (DCM) method is formed and used to investigate the free lateral vibration of a rectangular thin plate, subjected to various boundary conditions. Exploiting a special code written on MATLAB, the flexural natural frequencies of the plate are found by sweeping the frequency domain in search of specific frequencies that yield a zero determinant. Results are validated extensively both by the limited exact results available in the open literature and by numerical studies using ANSYS and in-house conventional FEM programs using both 12- and 16-DOF plate elements. The accuracy of all methods for lateral free vibration analysis is assessed and critically examined through benchmark solutions. It is envisioned that the proposed quasi-exact solution and the DCM method will allow engineers to more conveniently investigate the vibration behaviour of two-dimensional structural components during the preliminary design stages, before a detailed design begins.

scholarly journals Effects of local thinning defects and stepped thickness for free vibration of cylindrical shells using a symplectic exact solution approach

2021 ◽  
Vol 178 ◽  
pp. 658-671
Author(s):  
J.F. Jia ◽  
A.D. Lai ◽  
J.L. Qu ◽  
J.Y. Zhao ◽  
J.B. Sun ◽  
...  
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Solution Approach
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