Forced and free vibrations of composite beams solved by an energetic boundary functions collocation method

2020 ◽  
Vol 177 ◽  
pp. 152-168 ◽  
Author(s):  
Chein-Shan Liu ◽  
Botong Li
Keyword(s):  
Collocation Method ◽  
Composite Beams ◽  
Free Vibrations ◽  
Boundary Functions

Dynamic Analysis of Steel-Concrete Composite Frames with Partial Interaction

2012 ◽  
Vol 594-597 ◽  
pp. 904-907 ◽  
Author(s):  
Jun Xia ◽  
Z. Shen ◽  
Bin Chen
Keyword(s):  
Boundary Condition ◽  
Free Vibration ◽  
Dynamic Analysis ◽  
Free Vibration Analysis ◽  
Slip Boundary Condition ◽  
Composite Beams ◽  
Free Vibrations ◽  
Frame Structures ◽  
Shear Connection ◽  
Slip Boundary

The finite element formulations of steel-concrete composite (SCC) beams considering interlayer slip with end shear restraint were established. Free vibrations of SCC beams and frame structures under different slip boundary conditions were examined. The influences of the shear connection stiffness and the slip boundary condition on dynamic characteristics were analyzed. It is shown that the low order 8-DOF element may exhibit slip locking phenomenon in free vibration analysis for very stiff connection. The free vibration frequencies of composite beams and frame structures increase with the shear connection stiffness increasing. Besides, it is found that the natural vibration properties of SCC frame structures are significantly affected by the slip boundary condition, and it should be suitably imposed on all composite beams in dynamic analysis.

Postbuckling and Free Vibrations of Composite Beams

2007 ◽  
Author(s):  
Samir A. Emam ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequency ◽  
Axial Load ◽  
Closed Form Solution ◽  
Composite Beams ◽  
Free Vibrations ◽  
Form Solution ◽  
Mode Shapes ◽  
Axial Stiffness ◽  
Fundamental Natural Frequency ◽  
Transverse Vibrations

An exact solution for the postbuckling configurations of composite beams is presented. The equations governing the axial and transverse vibrations of a composite laminated beam accounting for the midplane stretching are presented. The inplane inertia and damping are neglected, and hence the two equations are reduced to a single equation governing the transverse vibrations. This equation is a nonlinear fourth-order partial-integral differential equation. We find that the governing equation for the postbuckling of a symmetric or antisymmetric composite beam has the same form as that of a metallic beam. A closed-form solution for the postbuckling configurations due to a given axial load beyond the critical buckling load is obtained. We followed Nayfeh, Anderson, and Kreider and exactly solved the linear vibration problem around the first buckled configuration to obtain the fundamental natural frequencies and their corresponding mode shapes using different fiber orientations. Characteristic curves showing variations of the maximum static deflection and the fundamental natural frequency of postbuckling vibrations with the applied axial load for a variety of fiber orientations are presented. We find out that the line-up orientation of the laminate strongly affects the static buckled configuration and the fundamental natural frequency. The ratio of the axial stiffness to the bending stiffness is a crucial parameter in the analysis. This parameter can be used to help design and optimize the composite beams behavior in the postbuckling domain.

Vibration of Steel–Concrete Composite Beams Using the Timoshenko Beam Model

2005 ◽  
Vol 11 (6) ◽  
pp. 829-848 ◽  
Author(s):  
Stefan Berczyński ◽  
Tomasz Wróblewski
Keyword(s):  
Dynamic Behavior ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Composite Beams ◽  
Free Vibrations ◽  
Timoshenko Beam Theory ◽  
Analytical Models ◽  
Beam Model ◽  
Euler Beam ◽  
Flexural Vibrations

In this paper we present a solution of the problem of free vibrations of steel–concrete composite beams. Three analytical models describing the dynamic behavior of this type of constructions have been formulated: two of these are based on Euler beam theory, and one on Timoshenko beam theory. All three models have been used to analyze the steel–concrete composite beam researched by others. We also give a comparison of the results obtained from the models with the results determined experimentally. The model based on Timoshenko beam theory describes in the best way the dynamic behavior of this type of construction. The results obtained on the basis of the Timoshenko beam theory model achieve the highest conformity with the experimental results, both for higher and lower modes of flexural vibrations of the beam. Because the frequencies of higher modes of flexural vibrations prove to be highly sensitive to damage occurring in the constructions, this model may be used to detect any damage taking place in such constructions.

Exact solutions for coupled free vibrations of tapered shear-flexible thin-walled composite beams

2008 ◽  
Vol 316 (1-5) ◽  
pp. 298-316 ◽  
Author(s):  
Marcelo T. Piovan ◽  
Carlos P. Filipich ◽  
Víctor H. Cortínez
Keyword(s):  
Exact Solutions ◽  
Composite Beams ◽  
Free Vibrations ◽  
Thin Walled

Vibration Analysis of Composite Beams with Sinusoidal Periodically Varying Interfaces

2017 ◽  
Vol 73 (1) ◽  
pp. 57-67 ◽  
Author(s):  
Botong Li ◽  
Chein-Shan Liu ◽  
Liangliang Zhu
Keyword(s):  
Laminated Composite ◽  
Rayleigh Quotient ◽  
Composite Beams ◽  
Vibration Modes ◽  
The Finite Element Method ◽  
Laminated Beam ◽  
Boundary Functions ◽  
Expansion Coefficients ◽  
Sinusoidal Functions ◽  
Laminated Composite Beams

AbstractAs an increasing variety of composite materials with complex interfaces are emerging, we develop a theory to investigate composite beams and shed some light on new physical insights into composite beams with sinusoidal periodically varying interfaces. For the natural vibration of composite beams with continuous or periodically varying interfaces, the governing equation has been derived according to the generalised Hamiltonian principle. For composite beams having different boundary conditions, we transform the governing equations into integral equations and solve them by using the sinusoidal functions as test functions as well as the basis of the vibration modes. Due to the orthogonality of the sinusoidal functions, expansion coefficients in closed form can be found. Therefore, the proposed iterative schemes, with the help of the Rayleigh quotient and boundary functions, can quickly find the eigenvalues and free vibration modes. The obtained natural frequencies agree well with those obtained using the finite element method. In addition, the proposed method can be extended easily to laminated composite beams in more general cases or complex components and geometries in vibration engineering. The effects of different material properties of the upper and lower components and varying interface geometry function on the frequency of the composite beams are examined. According to our investigation, the natural frequency of a laminated beam with a continuous or periodically varying interface can be changed by altering the density or elastic modulus. We also show the responses of the frequencies of the components to the varying periodic interface.

Postbuckling and free vibrations of composite beams

2009 ◽  
Vol 88 (4) ◽  
pp. 636-642 ◽  
Author(s):  
Samir A. Emam ◽  
Ali H. Nayfeh
Keyword(s):  
Composite Beams ◽  
Free Vibrations
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