Beam Cross Section Research Articles

Obstacle-tolerant terahertz wireless link using self-healing Bessel beams

Wireless communications using highly directive terahertz (THz) waves exhibit lower immunity to obstructions than microwaves, limiting their applications. This study demonstrates an obstacle-tolerant THz wireless link established by a self-healing Bessel beam at 300 GHz. The Bessel beam is generated by sending a Gaussian beam through a dielectric axicon lens. Furthermore, experiments were conducted to investigate the short-range transmission (98 mm) reception characteristics with and without the dielectric cubic obstacle (7.5 λ in size) and the metallic obstacle (22 λ in length and 8 λ in width) in the Gaussian beam and self-healing Bessel beam cross sections. The maximum attenuation of the received power due to obstruction was 8.8 and 2.2 dB for the Gaussian and Bessel beams, respectively, when the dielectric obstacle is placed in the middle of the transmission path (49 mm from a transmission lens). This study further investigated the bit error rate (BER) characteristics (1 Gbps, on–off keying) with the dielectric obstacle crossing the beam cross section. When the obstacle crosses the Gaussian beam, the BER degrades as the obstacle approaches the optical axis, breaking the wireless link. In contrast, when the obstacle crosses the Bessel beam cross section, the BER is maintained at <3.8 × 10−3 (the forward error correction limit), and the wireless link is maintained. A self-healing beam, such as the Bessel beam, makes the THz wireless link more tolerant than the Gaussian beam to obstacle and expand applications for THz wireless communications.

FINITE ELEMENT MODELLING AND ANALYSIS OF FREE VIBRATIONS OF AXIALLY FUNCTIONALY GRADED BEAMS WITH NON-UNIFORM CROSS-SECTIONS

The finite element package Abaqus is used for modeling and analysis of free vibrations of axially functional graded beams with non-uniform cross-sections. Considerable attention has been paid to this aspect of the geometry, as it has a significant effect on the behavior of the beam as a structural component. User-defined material model subroutines (UMAT) were developed in a unified way for one- and three-dimensional models of the specified beams to provide numerical implementation of functional material gradients within each finite element. UMAT procedures were programmed in FORTRAN in the MS Visual Studio environment and compiled with the main program package using the Intel Fortran Compiler. In the procedures, material heterogeneity was assigned to each material integration point of appropriate standard one- and three-dimensional finite elements, eliminating the need to design graded finite elements via user-defined element subroutine. Frequencies and mode shapes of free vibrations of one- and three-dimensional axially functional graded beams with non-uniform cross-sections were found using the Lanczos method in Abaqus. An analysis of the accuracy and effectiveness of the proposed modeling approach was carried out, comparing the obtained results with data known in the literature. The presented modeling technique based on user-defined material subroutines provides valuable opportunities for scientists and engineers engaged in the dynamic analysis of structural components made of functionally gradient materials and having variable geometry along the axial direction. Keywords: axially functionally graded beams; non-uniform cross-section beams; free vibrations; graded finite element; Abaqus user defined subroutines

Inclined crack identification in bidirectional FG beams on an elastic foundation using the h-version of the finite element method

This article examines the impact of inclined transverse cracking on the natural frequency of Euler-Bernoulli-model imperfect FG beams on an elastic foundation, taking into account the pinned-pinned and clamped-clamped boundary conditions. The equations are diffused using the classic finite element method (h-version). Material properties are considered to vary in both directions of the beam; width and thickness, using the power-law formula. The approximate porosity model is adopted with a uniform distribution. Cracked element stiffness is determined by reducing the cross-section of a bi-directional FG beam. The numerical results are compared with those of previous convergence studies for dimensionless fundamental frequencies. Case studies were carried out to evaluate the effect of the porosity values, the crack depth, the crack location, slope angle, and the Winkler-elastic foundation parameters on the first three natural frequencies of a beam with different support conditions and material gradient. In addition, the results demonstrated that the two-way distribution function plays an important role in the convergence of frequencies.

Spin angular momentum at the sharp focus of a cylindrical vector vortex beam

Sharp focusing of a light field with double (phase and polarization) singularity is studied. Using the Richards-Wolf method, an exact analytical expression for the longitudinal projection of the spin angular momentum (SAM) vector at the focus is obtained. The expression derived suggests that 4 (n –1) subwavelength regions are formed at the focus, where n is the cylindrical vector beam order, with their centers located on a certain circle centered on the optical axis. Notably, the SAM projections are found to have the opposite sign in the neighboring regions. This means that in the neighboring focal regions, the light has alternating left or right elliptical polarization (manifestation of a spin Hall effect). At the center of the focal spot near the optical axis, the field is right-handed elliptically polarized at m > 0, or left-handed elliptically polarized at m < 0, where m is the vortex charge. The total longitudinal spin, i.e., the longitudinal SAM component averaged over the beam-cross section, is zero and preserved upon focusing. Due to the beam containing an optical vortex with charge m, the transverse energy flow rotates on a spiral path near the focal plane, rotating on a circle in the focal plane. The rotation direction near the optical axis is counterclockwise for m > 0, and clockwise for m < 0.

Flexural capacity and local buckling half-wavelength of high strength steel tubular beams under moment gradients: An experimental study

An experimental investigation into the effect of moment gradients on the flexural behaviour of hot-rolled high strength steel square hollow section (SHS) beams is presented in this paper. In total, 20 beam specimens in steel grades S690 and S770, and with cross-sections spanning from Class 2 to Class 4 based on the Eurocode 3 slenderness limits, were tested under three- and four-point bending. In the three-point bending tests, the beam spans were varied to achieve a range of moment gradients; the influence of different stiffening arrangements at the loading point was also considered. Local geometric imperfections were measured by means of 3D laser-scanning prior to testing and digital image correlation (DIC) was adopted to monitor the displacement and strain fields at critical regions and to assess the local buckling half-wavelengths of the test specimens for which a consistent measurement approach was proposed. The measured local buckling half-wavelengths were compared against the elastic local buckling half-wavelengths calculated using the finite strip method. It was observed that while the measured local buckling half-wavelengths remained approximately constant up to first yield, a significant reduction in half-wavelength was observed with increasing moment due to the non-uniform spread of plasticity. The comparisons also revealed that the local buckling half-wavelengths reduced with both the presence of moment gradients and intermediate stiffeners, with a new parameter proposed to quantify the local moment gradient. It was shown from the tests that the specimens subjected to moment gradients, despite the presence of shear, exhibited higher ultimate moment capacities (up to 10.5% for stiffened specimens and 3.4% for unstiffened specimens) than those subjected to uniform moments. This is attributed to the delay in the local buckling of the critical cross-section of beams under moment gradients due to the restraint provided by the less heavily stressed adjacent cross-sections.

Stiffening of I-section MRF beams against degradation due to local buckling

Moment resisting frame (MRF) beams under cyclic loading are vulnerable to local flange and web buckling. The Seismic Provisions for Structural Steel Buildings (AISC341) prescribe width-to-thickness ratio limits, which are contingent on target rotations during predefined cyclic loadings. Some rolled I-sections available in the market cannot be employed in special MRFs since they fall short of satisfying the AISC341 flange slenderness limit. Moreover, local buckling leads to a decrease in both strength and stiffness in cyclically loaded MRF beams, ultimately increasing the risk of frame side-sway collapse. This paper introduces a stiffening method aimed at improving the behavior of I-section MRF beams. The proposed method involves placing a pair of stiffeners at the plastic hinge regions. A two-phase numerical study was conducted to assess the effectiveness of this approach. In the first phase, nine unstiffened beam cross-sections with varying flange and web slenderness were considered. The slenderness limits specified by AISC341 were evaluated based on cyclic analyses of these beams. In the second phase, a parametric study was conducted on the same cross-sections, with the flange width and the placement of the pair of stiffeners considered as variables. The results revealed a substantial improvement in behavior with the addition of a pair of stiffeners. Cross-sections that failed to meet the flange slenderness limit could be used in MRFs when stiffened. The optimal location for the stiffeners was found to be significantly influenced by the flange width. Design recommendations for the ideal stiffener placement are presented in this paper.

Investigating the role of incident ion flux in solar wind space weathering of carbon-rich asteroidal regolith via H+ and He+ irradiation of the Murchison meteorite

We present results from a set of low and high flux 1 keV/amu H+ and He+ irradiation experiments performed on slabs of the Murchison CM2 carbonaceous chondrite. The low flux conditions for H+ and He+ irradiation were ~1–1.5 orders of magnitude lower than the high flux conditions, and each experiment was irradiated to a total fluence between ~3 × 1016 to ~6 × 1016 ions/cm2. Irradiation-induced changes in the surface chemistry and optical properties of the Murchison samples were evaluated using in situ X-ray photoelectron spectroscopy (XPS) and visible and near-infrared spectroscopy (VNIR). We characterized the microstructure and composition of ion damaged rims in focused ion beam (FIB) cross-sections extracted from olivine and matrix material in each irradiated Murchison slab using transmission electron microscopy (TEM). XPS results suggest that both low flux and high flux H+ and He+ irradiation cause minor sputtering of surface carbon as well as a reduction in the valence state of iron, from Fe3+ to Fe2+. Slope bluing is observed in VNIR spectra of the irradiated samples which may reflect carbonization and dehydrogenation of organic species and contrasts with reddening trends associated with npFe0 formation. Although we do not observe a strong flux-dependence on the crystallinity of ion-damaged olivine, TEM analyses reveal a variety of microstructures in all olivine FIB-sections, suggesting that crystallographic orientation may affect amorphization efficiency. Analyses of matrix FIB-sections indicate that phyllosilicate alteration is mainly driven by He+ irradiation, where the higher incident flux leads to greater amorphization and the formation of more distinct ion-damaged layers, similar to smooth layers in returned Ryugu particles. TEM results also provide some evidence that higher ion flux leads to greater vesiculation, with He+ irradiation being more efficient at vesiculation than H+ irradiation, and promotes the segregation of Mg and Si into laterally extensive lenses and layers in olivine samples. We discuss the implications of these findings for constraining the role that ion flux plays in the development of space weathering characteristics in silicate phases present in carbonaceous asteroidal regoliths. These results will be important for understanding the complexity of this process and how it operates on carbon-rich airless bodies like asteroids Bennu and Ryugu.

Formulation of a similarity law for static and low-velocity collision experiments for beam in gravitational field

Scaled testing offers a financially viable and pragmatic methodology for ascertaining the performance attributes of full-scale civil engineering structures. While the necessity for a similarity law to guide scaled experiments is well-understood, few studies has been directed toward formulating a similarity law that comprehensively addresses both geometrical and mechanical equivalences in experiments where material properties and gravitational factors remain constant between the scaled and full-scale tests. Our prior work has introduced a similarity law tailored for scaled experiments conducted within gravitational fields, utilising materials that bear a resemblance to those used in full-scale structures; however, the scope of applicability was restricted to elastic responses. This study introduces a method for approximating the elasto-plastic displacement in full-scale beams based on data gathered from scaled tests, utilising an integrated approach that combines the principles of similarity and equal-energy laws as formulated by Veletsos et al. Validation of this innovative method was achieved through static three-point bending tests using circular cross-sectional steel beams, with tests conducted at six varying similarity ratios, ranging from 0.26 to 1.00. The empirical results demonstrated that the estimated displacement for the full-scale structure exhibited an error margin of approximately 10 %. When an impact analysis involving a steel ball was carried out on a steel cantilever beam, the residual displacement estimates were found to be significantly imprecise when plastic deformations occurred at multiple locations within the structure. In conclusion, this research contributes to foundational advancements in the field of structural modelling through the introduction of a new methodological approach.

Variable cross-sectional effect on bi-directional blades–tower–soil–structure dynamic interaction on offshore wind turbine subject to wind–wave loads

BackgroundThis study introduces a numerical model designed to simulate interactions occurring between a wind turbine's tower and the surrounding soil, as well as between the nacelle, blades, and the surrounding environment. This simulation accounts for both fore–aft and side-to-side movements. To describe these interactions, the model leverages the Euler–Lagrange equations. It calculates wave loads utilizing the Morison equation, with wave data generated based on the JONSWAP spectrum. Furthermore, aerodynamic loads are determined using the blade element moment theory, and the wind spectrum is generated using the Von Karman turbulence model. The tower is represented as a variable cross-sectional beam, employing a two-noded Euler beam element with two degrees of freedom: transverse displacement and rotation, and utilizing Hermite polynomial shape functions.ResultsIn a comparative analysis against experimental data, this modified model demonstrates significant enhancements in accurately reproducing the dynamic behavior of wind turbines with variable cross-sectional towers, outperforming models that approximate the tower with a constant cross section. Our findings reveal that the modified model achieves a remarkable improvement of 15% in replicating the tower's dynamic response when compared to the constant cross-sectional models. As a case study, a 5 MW monopile wind turbine with a flexible foundation, specifically the one provided by the National Renewable Energy Laboratory (NREL), is employed to simulate its dynamic response.ConclusionsThis research presents a robust numerical model for simulating wind turbine behavior in various environmental conditions. The incorporation of variable cross-sectional tower representation significantly improves the model's accuracy, making it a valuable tool for assessing wind turbine dynamics. The study's findings highlight the importance of considering tower flexibility in wind turbine simulations to enhance their real-world applicability.

Computational implementation of alternative method for determining the loss of prestressing by deformation of the anchorage in post-tensioning

Due to its advantages, Prestressed Concrete has been used as a structural element in many buildings worldwide. In order to overcome large spans, limiting the formation of cracks, its application can be visualized, for example, in bridges, viaducts, and building slabs. These structures are executed by stretching steel cables with a subsequent release, introducing compressive stresses in the concrete. However, during this process, stress losses occur in the active reinforcement, requiring forecast by the designers. Quantifying these losses in certain cases is a long and iterative process. The present work aimed to present the computational implementation of an alternative method for determining the loss due to deformation of the anchorage in post-traction. In order to prove its effectiveness, this method was contrasted with two conventional methodologies established in the literature. To this end, two models of beams of the same cross-section were simulated, however, with different spans and cable paths. Both proposed simulations aimed to cover all possible situations for the development of prestressing stress along with the tensioned cables. The alternative method showed minor differences in all measurements compared to the conventional methods, proving its effectiveness. Furthermore, the computational tool, entitled vProt, proved to be reliable in the two proposed simulations, allowing its use in the elaboration and verification of structural projects.

Bending and torsion induced stresses in cylindrically orthotropic and inhomogeneous timber beams

The structural design of timber beams subject to bending often relies on the application of the simple Euler–Bernoulli beam theory. However, the simplistic formulas for stress calculations overlook the inherent characteristics of the wood material and the true distribution of the annual rings within the cross-sectional area. This paper introduces a method for determining all six stress components for a cantilever-type beam that is subjected to concentrated end loads. The method considers an inhomogeneous cross-section and employs cylindrically orthotropic material properties. Notably, this approach does not necessitate prior knowledge of elastic and shear centres. It is founded on the formulation of a displacement field incorporating unknown in-plane distortion and warping functions. These are then solved through a straightforward finite element procedure. The efficacy of the method is validated by a series of numerical examples that align with analytical results. Furthermore, a benchmark example for cylindrically orthotropic cross-sections is proposed. As a practical demonstration, an analysis is performed on a real sawn timber cross-section with material parameters representative of Norway spruce. The findings reveal significant disparities in the maximum stresses when compared to conventional engineering approaches. In this specific instance, the maximum longitudinal normal stress resulting from bending is approximately 20 % higher than the outcomes of typical engineering methods. This emphasizes the critical role played by the actual distribution of annual rings across the specific beam cross-section.

Fully analytical solution framework for general thin-walled composite beams with mixed variational approach

A variationally consistent analytical beam model that describes the theory in a Timoshenko-Vlasov level is developed based on Reissner’s mixed variational theorem. Starting from a shell theory, all the field-governing equations (equilibrium and continuity) and the boundary conditions of the shell wall are derived in closed form, and the mixed method enables finding the explicit forms of the reactive stresses and sectional warpings which are evaluated progressively depending on the level of beam model to be analyzed. The stress recovery part is incorporated in the post-stage of the analysis to compute the layer-wise distribution of stresses over the beam cross-section. The present analysis is validated against numerous benchmark examples available in the literature, including beams with multi-layered strip section, thin-walled anisotropic box sections with elastic couplings, and two-cell airfoil section. The comparison study demonstrates excellent correlations with the results from detailed three-dimensional finite element analysis and other up-to-date beam approaches. Also presented are symbolically expressed stiffness coefficients and the sectional warping modes of coupled composite beams to demonstrate the strength of the proposed beam model.

Investigation of the mechanical properties of lightweight concrete using expanded polystyrene reinforced with glass fibers

The use of lightweight concrete has gained popularity in the industrial construction sector owing to its ability to reduce dead weight and enable smaller cross-sections of beams. Adding expanded polystyrene to replace a portion of fine aggregate is a widely accepted solution to decrease the weight of concrete. However, lightweight expanded polystyrene concrete (EPSC) has poor mechanical properties and brittleness, limiting its application to non-bearing structures and thermal isolation. Glass fiber reinforcement is a promising solution to improve the mechanical properties of lightweight expanded polystyrene concrete. This study investigates the effect of glass fiber content on the mechanical properties of lightweight expanded polystyrene concrete. To investigate the impact of glass fiber on the mechanical properties of concrete, various volume percentages of glass fiber were incorporated into the mixture. The compressive and tensile strengths of the concrete were measured and compared for each percentage of glass fiber added. The results showed that the addition of glass fiber significantly reduced workability without causing a significant impact on volume density and compressive strength The study concludes that glass fiber reinforcement is a promising solution to improve the flexural strength of lightweight expanded polystyrene concrete and make it suitable for load-bearing applications in construction.

An efficient approach for free vibration analysis of functionally graded sandwich beams of variable cross-section

In this research paper, a powerful numerical method is implemented to examine the free vibration analysis of functionally graded (FG) sandwich beams of variable cross-section. The core of the beam is considered to be made from homogenous isotropic material and the faces of the sandwich beam are considered to be made of FG materials. The effect of the shear strain is considered in the formulations based on the first-order shear deformation theory (FSDT). The governing canonical equations for the dynamic response of FG sandwich beams are derived with the aid of the canonically conjugate momentums for the first time. To solve these equations numerically the Complementary Functions Method (CFM) is implemented. The free vibration behavior of the symmetric and asymmetric FG sandwich beams is investigated for different boundary conditions. The presented efficient numerical method is validated with the available literature. Moreover, detailed parametric studies are conducted to demonstrate the influence of layers, geometric constants, material volume fraction indexes, and beam slenderness on the natural frequencies of FG sandwich beams.

An analytical method for beam hardening correction in thermal-neutron radiography

The effect of polychromatic nature of thermal neutrons on neutron radiography was studied through experiments and simulations on borated and non-borated stainless steel with homogeneous composition. The results were compared to theoretical neutron-transmission results obtained for a monochromatic neutron beam.The evolution of total cross sections, neutron-transmission and gray level in neutron radiography image indicate the important effect of beam hardening.For that, an analytical procedure has been established for thermal cross section determination and beam hardening correction of the experimental and simulated data. The corrected data values agree well with those calculated theoretically indicating the effectiveness of the developed correction method.

Load-Bearing Capacity of Reinforced Concrete and Fiber Concrete Cross-Beam Systems

The results of experimental studies and computer modeling of reinforced concrete and fiber concrete cross-beam systems are presented. The authors have made a special stand, the design of which allows to carry out researches of bearing capacity and deformability of such systems under the concentrated and distributed static loads. Samples made of reinforced concrete and steel fiber concrete and consisting of four mutually perpendicular beams of rectangular cross-section were tested. The specimens were reinforced in the lower zone with longitudinal reinforcement of 8 mm in diameter, two rods in each beam. Steel-fiber concrete specimens have an additional dispersed reinforcement of steel fiber with bent ends in an amount of 1% by volume of concrete. A procedure of finite-element modeling and calculation of cross-beam systems in the licensed program ANSYS 17.1 was developed, and a comparison of the results obtained experimentally and on the basis of computer modeling was performed. The tests showed that dispersed reinforcement of the cross-beam system with steel fiber leads to an increase in its bearing capacity by 1.23 times. During modeling and finite-element analysis in the ANSYS 17.1 program, the increase in bearing capacity was 1.18 times. At the same time, the load-carrying capacity of the reinforced concrete cross-beam system obtained by the finite-element method was 13% lower than in the experiment, and that of the fiber-reinforced concrete system was 15% lower. At the same time, the discrepancy in the approaches considering torsion and not taking it into account is about 5% for all the samples studied in the work.

Generalized strain-based finite element for non-linear stability analysis of beams with thin-walled open cross-section

Based on the generalized strain theory a shear-deformable finite element is developed for nonlinear stability analysis of thin-walled open-section beams in multibody systems. In this formulation a finite number of deformations, characterized as generalized strains, is defined which are related to dual stress resultants in a co-rotational frame. The stiffness formulation is based on a second-order approximation of the local elastic displacement field. Timoshenko’s beam theory and Vlasov’s modified thin-walled beam theory are used to include the shear strain effects due to non-uniform bending and restrained warping torsion and their mutual coupling effects. Axial shortening associated with the Wagner Hypothesis is taken into account such that the nonlinear behaviour of the beam is predicted accurately, especially under large torsion. Coupling between bending and torsional deformation due to non-coincident centroid and shear centre is modelled using a second-order cross-section transformation matrix. Cubic Hermitian polynomials are used as shape functions for the lateral displacements and twist rotation to derive the elastic and geometric stiffness matrices. Geometric nonlinearities associated with axial elongation and bending curvatures are described by additional torsion, bending and warping-related quadratic deformation terms yielding a set of modified deformations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. The accuracy and the computational efficiency of the new beam element is demonstrated in several static and dynamic examples.

Approximate determination of shear stresses for a 2D beam made of a non-Green elastic solid

Shear stresses for a two-dimensional (2D) beam are calculated modifying the classical method developed by Jouravski, for the case the linearized strain tensor is assumed to be a nonlinear function of the Cauchy stresses. Two problems are studied, namely, the case of a cantilever beam with a point load on its free edge (considering a rectangular and a circular cross-section) and the three-point flexural test for a beam of rectangular cross-section. Numerical results are obtained for the particular case of a bimodular constitutive model for rock, and the results for the shear stresses are compared with the predictions of the classical theory of strength of materials for such problems, assuming a linearized elastic body.

FIB line marking as a tool for local erosion/deposition/fuzz formation measurements in ASDEX Upgrade during the He campaign

Tungsten (W) is the prime candidate for the plasma facing material in present and future fusion devices. When exposed to a plasma containing He ions, W can exhibit creation of sub-surface nano-bubbles leading to formation of nano-tendrils called fuzz. Formation of W fuzz was confirmed by many laboratory experiments including He loading in linear plasma devices. There is, however, limited experience related to the parameter space for fuzz formation and re-erosion in a tokamak environment. For this reason, a dedicated experiment was carried out in ASDEX Upgrade (AUG) during its 2022 He campaign to study the evolution of fuzz-like W structures.Twelve tungsten samples were mechanically polished to a mirror-like surface finish. Six of them were subsequently exposed to a He plasma in the PSI-2 linear device in order to establish a fuzz layer with a thickness of 600 – 800 nm. Before exposure in AUG, all samples were pre-characterized by Focused Ion Beam (FIB) cross-sectioning. In total 48 FIB cross-sections with line markings for quantification of local erosion, deposition and fuzz formation were prepared – 4 on each sample. The samples were placed in two parallel poloidal rows spanning a range of 20 cm around the outer strike line position (OSP). They were subsequently exposed in AUG to a series of 14 consecutive discharges, 8 in H-mode and 6 in L-mode.Detailed analysis by means of electron microscopy revealed on the samples regions of erosion, deposition and fuzz formation. Below the H-mode OSP, homogeneous co-deposits containing W and O, with a thickness up to 400 nm, were found. In the close vicinity of the H-mode OSP, significant erosion of pre-exposure PSI-2 fuzz was observed. The erosion reached up to 100 – 250 nm, depending on the location. In addition, the initially polished samples did not show any newly formed fuzz in that zone. Above the H-mode OSP, new fuzz was formed with a thickness of up to 1 μm. There was no Mo found in the newly formed fuzz. Pre-exposure PSI-2 fuzz was either removed or modified.

Influence of flexural-torsional couplings and rotational effects on vibration behaviour of tapered thin-walled anisotropic biconvex beam

Accurate modelling and prediction of dynamic characteristics for rotating thin-walled blades have drawn attention as it is an essential part of structural health monitoring for various engineering and civil applications such as wind turbine, helicopter and aeroplane blades. With the advent of structural tailoring techniques, various non-classical effects and couplings implicitly affecting the behaviour of such structures are yet not fully explored. In this regard, the present work proposes a numerical model for finding the free vibration characteristics of anisotropic tapered biconvex closed cross-section beam under rotating conditions. The model is derived based on energy method following the Ritz approximation. Circumferentially asymmetric stiffness (CAS) ply configuration is considered in order to study the impact of flexural torsional coupling on the vibration characteristics. Transverse shear effects, primary and secondary warping were also included in the current model. Mode switching phenomenon is dissected elaborately for the first few frequencies under rotating and nonrotating conditions. The impact of rotational effects like centrifugal acceleration, centrifugal warping, inertial warping on the first few frequencies is also demonstrated. An iterative technique is adapted to solve the equations having these rotational effects. Modal Assurance Criterion (MAC) is done in order to judge the consistency of the modes at different rotating speeds.