Thermoelastic Vibration and Damping for Circular Timoshenko Beams

1975 ◽  
Vol 42 (2) ◽  
pp. 405-410 ◽  
Author(s):  
R.-C. Shieh
Keyword(s):  
Boundary Conditions ◽  
Circular Cross Section ◽  
Timoshenko Beams ◽  
Thermoelastic Damping ◽  
Governing Equations ◽  
Damping Coefficients ◽  
Thermal Boundary Conditions ◽  
Transverse Vibrations ◽  
Thermoelastic Vibration ◽  
Linear Thermoelasticity

Within the framework of the theories of coupled linear thermoelasticity and Timoshenko beams, the vibration and thermoelastic damping (with emphasis on the transverse ones) of circular cross-section beams are studied. The governing equations are derived for the case of general mechanical boundary conditions and special thermal boundary conditions that follow the Newton surface heat transfer law. A variational principle governing the eigenfunctions associated with an eigenvalue is formulated. An exact solution, together with the thermoelastic damping coefficient, is obtained for the case of transverse vibrations of a simply supported beam with lateral surfaces thermally insulated and end surfaces kept at constant temperature. Numerical results, together with the discussion for the first two eigenvalues and the thermoelastic damping coefficients, are also presented.

Eigensolutions for Coupled Thermoelastic Vibrations of Timoshenko Beams

1979 ◽  
Vol 46 (1) ◽  
pp. 169-174 ◽  
Author(s):  
R. C. Shieh
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Solution Procedure ◽  
Surface Heat ◽  
Timoshenko Beams ◽  
Thermal Boundary Conditions ◽  
Linear Thermoelasticity ◽  
Special Case

A general solution procedure, together with two special case solutions, for the free-vibration boundary-value problem of a circular or rectangular cross-section Timoshenko beam under general mechanical boundary conditions and the thermal boundary conditions that follow the Newton surface heat transfer law is presented within the context of coupled linear thermoelasticity.

Dynamic Instability of a Cantilever Column Subjected to a Follower Force Including Thermomechanical Coupling Effect

1971 ◽  
Vol 38 (4) ◽  
pp. 839-846 ◽  
Author(s):  
R. C. Shieh
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Critical Loads ◽  
Dynamic Instability ◽  
Coupling Effect ◽  
Follower Force ◽  
Thermomechanical Coupling ◽  
Damping Coefficients ◽  
Critical Dynamic ◽  
Linear Thermoelasticity

Within the context of the linear thermoelasticity theory, including thermomechanical coupling effect, the dynamic instability of equilibrium of an elastic cantilever column subjected to a follower-type force at its free end is studied. The surfaces of the column are either kept at constant temperature (isothermal) or thermally insulated (adiabatic). The boundary-value problem is first formulated, and then it is solved in general and in particular for the depth-length ratio much less than unity. Numerical results for the critical loads are given for various values of the thermal parameters. It is shown that, for a tangential follower force, the critical dynamic (oscillatory) instability load may be reduced through the coupling effect to approximately one half of that of the corresponding uncoupled isothermal problem (which was solved by Beck [14] in 1952). Analytical results are also obtained for the damping coefficients for both adiabatic and isothermal boundary conditions. From a comparison with available experiment for aluminum, it appears that material damping, at least for this material, is almost entirely due to thermomechanical coupling.

Thermoelastic Damping of the Axisymmetric Vibration of Laminated Trilayered Circular Plate Resonators

2013 ◽  
Vol 313-314 ◽  
pp. 600-603 ◽  
Author(s):  
Yu Xin Sun ◽  
Yan Jiang ◽  
Jia Ling Yang
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Plate Theory ◽  
Axisymmetric Vibration ◽  
Laminated Plate ◽  
Thermoelastic Damping ◽  
Governing Equations ◽  
Out Of Plane ◽  
Laminated Circular Plate ◽  
Thermoelastic Problems

In this paper, thermoelastic damping of the axisymmetric vibration of laminated circular plate resonators will be discussed. Based on the classical laminated plate theory assumptions, the governing equations of coupled thermoelastic problems are established for axisymmetric out-of-plane vibration of trilayered circular plate with fully clamped boundary conditions. The analytical expression for thermoelastic damping is obtained and the accuracy is verified through comparison with FEM results.

Vibration Analysis of Postbuckled Timoshenko Beams Using a Numerical Solution Methodology

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
M. Faghih Shojaei ◽  
R. Ansari ◽  
V. Mohammadi ◽  
H. Rouhi
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Natural Frequency ◽  
Axial Load ◽  
Continuation Method ◽  
Free Vibrations ◽  
Timoshenko Beams ◽  
Governing Equations ◽  
Technical Interest ◽  
Solution Methodology

In this article, a numerical solution methodology is presented to study the postbuckling configurations and free vibrations of Timoshenko beams undergoing postbuckling. The effect of geometrical imperfection is taken into account, and the analysis is carried out for different types of boundary conditions. Based on Hamilton's principle, the governing equations and corresponding boundary conditions are derived. After introducing a set of differential matrix operators that is used to discretize the governing equations and boundary conditions, the pseudo-arc length continuation method is applied to solve the postbuckling problem. Then, the problem of free vibration around the buckled configurations is solved as an eigenvalue problem using the solution obtained from the nonlinear problem in the previous step. This study shows that, when the axial load in the postbuckling domain increases, the vibration mode shape of buckled beam corresponding to the fundamental frequency may change. Another finding that can be of great technical interest is that, for all types of boundary conditions and in both prebuckling and postbuckling domains, the natural frequency of imperfect beam is higher than that of ideal beam. Also, it is observed that, by increasing the axial load, the natural frequency of both ideal and imperfect beams decreases in the prebuckling domain, while it increases in the postbuckling domain. The reduction of natural frequency in the transition area from the prebuckling domain to the postbuckling domain is due to the severe instability of the structure under the axial load.

scholarly journals Analysis of Functionally Graded Timoshenko Beams by Using Peridynamics

2020 ◽  
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Boundary Conditions ◽  
Lagrange Equation ◽  
Functionally Graded ◽  
Timoshenko Beams ◽  
Governing Equations ◽  
Element Analysis ◽  
Free Boundary Conditions ◽  
Support Roller ◽  
Roller Support ◽  
Good Agreement

Abstract In this study, a new peridynamic formulation is presented for functionally graded Timoshenko beams. The governing equations of the peridynamic formulation are obtained by utilising Euler-Lagrange equation and Taylor’s expansion. The proposed formulation is validated by considering a Timoshenko beam subjected to different boundary conditions including pinned support-roller support, clamped-roller support and clamped-free boundary conditions. Results from peridynamics are compared against finite element analysis results. A very good agreement is obtained for transverse displacements, rotations and axial displacements along the beam.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

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