The Influence of Geometric and Material Design Variables on the Free Vibration of Thin-Walled Composite Material Beams

1989 ◽  
Vol 111 (3) ◽  
pp. 290-297 ◽  
Author(s):  
L. C. Bank ◽  
C. H. Kao
Keyword(s):  
Shear Deformation ◽  
Beam Theory ◽  
Material Design ◽  
Mode Shapes ◽  
Cross Sectional ◽  
Advanced Composite Materials ◽  
Design Variables ◽  
Maximum Stiffness ◽  
Thin Walled ◽  
Materials Used

The natural frequencies and mode shapes of thin-walled beams constructed of walls, or panels, of advanced composite materials depend upon both the geometry of the cross-section and the mechanical properties of the materials used in the panels. A shear deformation beam theory having the form of a Timoshenko beam theory is used to investigate the influence of these design variables. It is found that the maximum stiffness of a particular beam configuration is obtained when the contributions from the bending and shearing modes of deformation are optimized. Results show the influence of shear deformation even in the fundamental mode of vibration. Simply-supported, cantilever and free-free beams of various cross-sectional shapes and materials are analyzed.

scholarly journals Natural Frequency Characteristics of the Beam with Different Cross Sections Considering the Shear Deformation Induced Rotary Inertia

2020 ◽  
Vol 10 (15) ◽  
pp. 5245
Author(s):  
Chunfeng Wan ◽  
Huachen Jiang ◽  
Liyu Xie ◽  
Caiqian Yang ◽  
Youliang Ding ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Cross Sections ◽  
Timoshenko Beam ◽  
High Frequency ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Timoshenko Beam Theory ◽  
Rotary Inertia ◽  
Cross Sectional

Based on the classical Timoshenko beam theory, the rotary inertia caused by shear deformation is further considered and then the equation of motion of the Timoshenko beam theory is modified. The dynamic characteristics of this new model, named the modified Timoshenko beam, have been discussed, and the distortion of natural frequencies of Timoshenko beam is improved, especially at high-frequency bands. The effects of different cross-sectional types on natural frequencies of the modified Timoshenko beam are studied, and corresponding simulations have been conducted. The results demonstrate that the modified Timoshenko beam can successfully be applied to all beams of three given cross sections, i.e., rectangular, rectangular hollow, and circular cross sections, subjected to different boundary conditions. The consequence verifies the validity and necessity of the modification.

Optimum Design of Vibration Absorbers for Structurally Damped Timoshenko Beams

1998 ◽  
Vol 120 (4) ◽  
pp. 833-841 ◽  
Author(s):  
E. Esmailzadeh ◽  
N. Jalili
Keyword(s):  
Dynamic Response ◽  
Shear Deformation ◽  
Beam Theory ◽  
Optimization Procedure ◽  
Vibration Absorbers ◽  
Rotatory Inertia ◽  
Cross Sectional ◽  
Beam Dynamic ◽  
Practical Applications ◽  
Optimal Dynamic

A procedure in designing optimal Dynamic Vibration Absorbers (DVA) for a structurally damped beam system subjected to an arbitrary distributed harmonic force excitation, is presented. The Timoshenko beam theory is used to assess the effects of rotatory inertia and shear deformation. The method provides flexibility of choosing the number of absorbers depending upon the number of significant modes which are to be suppressed. Uniform cross-sectional area is considered for the beam and each absorber is modeled as a spring-mass-damper system. For each absorber with a selected mass, the optimum stiffness and damping coefficients are determined in order to minimize the beam dynamic response at the resonant frequencies for which they are operated. For this purpose, absorbers each tuned to a different resonance, are used to suppress any arbitrarily number of resonances of the beam. The interaction between absorbers is also accounted for in the analysis. The optimum tuning and damping ratios of the absorbers, each tuned to the mode of concern, are determined numerically by sloving a min-max problem. The Direct Updated Method is used in optimization procedure and the results show that the optimum values of the absorber parameters depend upon various factors, namely: the position of the applied force, the location where the absorbers are attached, the position at which the beam response should be minimized, and also the beam characteristics such as boundary conditions, rotatory inertia, shear deformation, structural damping, and cross sectional geometry. Through the given examples, the feasibility of using proposed study is demonstrated to minimize the beam dynamic response over a broad frequency range. The resulting curves giving the non-dimensional absorber parameters can he used for practical applications, and some interesting conclusions can be drown from the study of them.

GBT-BASED BUCKLING ANALYSIS OF THIN- WALLED STEEL FRAMES WITH ARBITRARY LOADING AND SUPPORT CONDITIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 363-385 ◽  
Author(s):  
CILMAR BASAGLIA ◽  
DINAR CAMOTIM ◽  
NUNO SILVESTRE
Keyword(s):  
Finite Element ◽  
Beam Theory ◽  
Mode Shapes ◽  
Shear Stresses ◽  
Transverse Beam ◽  
Space Frames ◽  
Buckling Behavior ◽  
Global Buckling ◽  
Thin Walled ◽  
Support Conditions

This paper is concerned with the development and application of a Generalized Beam Theory (GBT) formulation to analyse the local and global buckling behavior of thin-walled steel plane and space frames with arbitrary loadings and various support conditions. This formulation takes into account the geometrical effects stemming from the presence of longitudinal normal stress gradients and also the ensuing pre-buckling shear stresses. Following a description of the main concepts and procedures involved in determining the finite element and frame linear and geometric stiffness matrices (incorporating the influence of joints, applied loading and support conditions), one presents and discusses some numerical results concerning the local and global buckling behavior of (i) simple "L-shaped" frames and (ii) space frames formed by two symmetrical portal frames joined through a transverse beam. For validation purposes, the GBT-based results are compared with those obtained by rigorous shell finite element analyses using ANSYS. An excellent correlation, for both the critical buckling loads and mode shapes, is found in all cases.

Nonorthogonal solution for thin-walled members – a finite element formulation

2006 ◽  
Vol 33 (4) ◽  
pp. 421-439 ◽  
Author(s):  
R Emre Erkmen ◽  
Magdi Mohareb
Keyword(s):  
Finite Element ◽  
Computational Cost ◽  
Beam Theory ◽  
Torsional Stiffness ◽  
Element Formulation ◽  
Field Equations ◽  
Cross Sectional ◽  
Special Cases ◽  
Thin Walled ◽  
Shell Finite Element

Conventional solutions for the equations of equilibrium based on the well-known Vlasov thin-walled beam theory uncouple the equations by adopting orthogonal coordinate systems. Although this technique considerably simplifies the resulting field equations, it introduces several modelling complications and limitations. As a result, in the analysis of problems where eccentric supports or abrupt cross-sectional changes exist (in elements with rectangular holes, coped flanges, or longitudinal stiffened members, etc.), the Vlasov theory has been avoided in favour of a shell finite element that offer modelling flexibility at higher computational cost. In this paper, a general solution of the Vlasov thin-walled beam theory based on a nonorthogonal coordinate system is developed. The field equations are then exactly solved and the resulting displacement field expressions are used to formulate a finite element. Two additional finite elements are subsequently derived to cover the special cases where (a) the St.Venant torsional stiffness is negligible and (b) the warping torsional stiffness is negligible. Key words: open sections, warping effect, finite element,thin-walled beams, asymmetric sections.

An Experimental Study on the Performance of Fixed-End Supported PFRP Channel Beams under Flexure

2013 ◽  
Vol 702 ◽  
pp. 31-36 ◽  
Author(s):  
Jaksada Thumrongvut ◽  
Sittichai Seangatith
Keyword(s):  
Shear Deformation ◽  
Beam Theory ◽  
Beam Equation ◽  
Vertical Deflection ◽  
Cross Sectional ◽  
Modes Of Failure ◽  
Theory Equation ◽  
Flexural Torsional Buckling ◽  
Fixed End ◽  
Structural Behaviors

The experimental investigation on the fixed-end supported PFRP channel beams subjected to three-point loading is presented. The objectives of this study are to evaluate the effects of the span on the structural behaviors, the critical buckling loads and the modes of failure of the PFRP beams, and to compare the obtained deflections with those obtained from the Timoshenko’s shear deformation beam theory equation in order to check the adequacy of the equation. The beam specimens have the cross-sectional dimensions of 152 43 10 mm with span-to-depth ratio ranging from 16 to 33. A total of twenty-two specimens were performed. Based on the experimental results, it was found that the loads versus mid-span vertical deflection relationships of the beam specimens are linear up to the failure, but the load versus mid-span lateral deflection relationships are geometrically nonlinear. The general modes of failure are the flexural-torsional buckling. Finally, the Timoshenko’s shear deformation beam equation can satisfactorily predict the vertical deflection of the beams within acceptable engineering error.

Dynamic Response of Thin-Walled Composite Material Timoshenko Beams

1990 ◽  
Vol 112 (2) ◽  
pp. 149-154 ◽  
Author(s):  
L. C. Bank ◽  
C.-H. Kao
Keyword(s):  
Natural Frequencies ◽  
Fiber Composite ◽  
Beam Theory ◽  
Composite Beams ◽  
Mode Shapes ◽  
Structural Members ◽  
Timoshenko Beams ◽  
Conventional Steel ◽  
Thin Walled ◽  
Offshore Industry

Thin-walled structural members are used extensively in the offshore industry in applications ranging from marine risers to platforms and frames. Advanced fiber composite structural members may offer advantages over their conventional steel counterparts in certain situations. Use of composite members will require modifications to existing structural analysis codes. This paper presents a beam theory for thin-walled composite beams that can be incorporated into existing codes. Timoshenko beam theory is utilized to account for shear deformation effects, which cannot be neglected in composite beams, and for the variability in material properties in different walls of the beam cross section. The theory is applied to the analysis of the free vibration problem and shows the dependence of the natural frequencies and mode shapes on the in-plane properties of the laminates that form the walls of the beam. Forced periodic and forced arbitrary problems are also discussed and the deflected shapes and maximum deflections are shown as functions of wall layups.

Buckling Analysis of Thin-Walled Steel Structural Systems Using Generalized Beam Theory (GBT)

2015 ◽  
Vol 15 (01) ◽  
pp. 1540004 ◽  
Author(s):  
Cilmar Basaglia ◽  
Dinar Camotim
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Beam Theory ◽  
Mode Shapes ◽  
Structural Systems ◽  
Hollow Section ◽  
Buckling Behavior ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

This paper deals with the application of beam finite element models based on generalized beam theory (GBT) to analyze the buckling behavior of four thin-walled steel structural systems, namely (i) beams belonging to storage rack systems, (ii) pitched-roof industrial frames, (iii) portal frames built from cold-formed rectangular hollow section (RHS) profiles and (iv) roof-supporting trusses, exhibiting different support conditions and subjected to various loadings. In particular, taking advantage of the GBT unique and structurally clarifying modal features, it is possible to assess how different geometries and/or bracing arrangements affect (improve) the local, distortional and/or global buckling behavior of the above structural systems. The accuracy of the GBT-based buckling results is assessed through the comparison with values yielded by rigorous shell finite element analyzes carried out in the code ANSYS. In spite of the disparity between the numbers of degrees of freedom involved, which are orders of magnitude apart, there is a virtual coincidence between the critical loads and mode shapes provided by the GBT (beam) and ANSYS (shell) finite element analyzes.

The effects of shear deformation on the free vibration of elastic beams with general boundary conditions

2009 ◽  
Vol 224 (1) ◽  
pp. 71-84 ◽  
Author(s):  
J Li ◽  
H Hua
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Dynamic Stiffness ◽  
Beam Theory ◽  
Mode Shapes ◽  
Governing Equations ◽  
One Dimensional ◽  
Elastic Beams ◽  
Shear Deformable

Free vibration characteristics of shear deformable elastic beams subjected to different sets of boundary conditions are investigated. The analysis is based on a unified one-dimensional shear deformation beam theory. The governing equations of the elastic beams are obtained by means of Hamilton's principle. Four different boundary conditions are considered. The natural frequencies and mode shapes are obtained by applying the dynamic stiffness method, where the elements of the exact dynamic stiffness matrix are derived by using the analytical solutions of the governing equations of the beam in free vibration. The numerical results for the particular beams with different slenderness ratios are presented and compared with those available in the literature.

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