Beam Structure Research Articles

Bamboo (Dendrocalamus Asper) as an Eco-Friendly Sustainable Material: Optimising Mechanical Properties and Enhancing Load-Bearing Capacity for Environmental Architectural Design

This study will assess the utilisation of Bamboo (a Thai vernacular material) in the construction industry. Bamboo is a sustainable and environmentally friendly material which provides a suitable alternative to traditional construction materials. This research will examine its mechanical strength properties as determined by a review of the existing literature and an examination of the bearing area variations of bamboo nodes. The research data and ensuing experiments facilitated the simulation of the load-bearing capacities of bamboo columnar and beam structures via optimisation. Additionally, this study examined the limitations of bamboo-based structures. The assimilation of mechanical property data and bamboo strength was imperative for the production of load-bearing simulations for bamboo columns and beams within ANSYS software. In many countries, bamboo is a commonly employed construction material because of the many benefits it provides such as its rapid growth speed. The compressive strength tests conducted in this study revealed that the middle nodes could withstand up to 64.9 kN, which was the highest value amongs the three samples tested. These findings will contribute to ongoing optimisation and research regarding the damage mechanisms affecting column and beam structures under load. Notably, this damage was prevalent at the junctures of column and beam interfaces. The intention is to conduct additional research that will enhance the current understanding and ensure the sustainability of bamboo as an architectural building material.

Method for Constructing a Compact Component Mode Synthesis Model for Analyzing Nonlinear Normal Modes of Structures with Localized Nonlinearities

Abstract Nonlinear dynamics analysis is a crucial topic in mechanical and aerospace engineering. The analysis of nonlinear normal modes (NNMs) provides an effective mathematical tool for interpreting complex nonlinear vibration phenomena. Unlike the invariant normal modes of linear systems, NNMs often exhibit frequency-energy dependence and cannot be computed using the traditional eigen-decomposition method. Calculating NNMs relies on numerical methods that involve expensive iterative computations, especially for systems with numerous degrees-of-freedom. To relieve computational costs, this paper proposes a mode selection method for the component mode synthesis (CMS) technique to enable compact reduced-order modeling of structures with localized nonlinearities. The reduced-order model is then combined with a numerical continuation scheme to establish a low-cost NNM analysis framework. This framework can efficiently predict the NNMs of high-dimensional finite element models. The proposed framework is demonstrated on an I-shaped cantilever beam with localized nonlinear stiffness. The results show that the proposed approach can identify the key modes in the CMS modeling procedure. The NNMs of the nonlinear I-shaped beam structure can then be analyzed with a significant reduction in computational costs.

Enhanced Subspace Iteration Technique for Probabilistic Modal Analysis of Statically Indeterminate Structures

In structural stochastic dynamic analysis, the consideration of the randomness in the physical parameters of the structure necessitates the establishment of numerous stochastic finite element models and the subsequent computation of their corresponding vibration modes. When the complete analysis is applied to calculate the vibration modes for each sample of the stochastic finite element model, a substantial computational expense is incurred. To enhance computational efficiency, this work presents an extended subspace iteration method aimed at rapidly determining the vibration modal parameters of statically indeterminate structures. The essence of this proposed method revolves around efficiently constructing reduced basis vectors during the subspace iteration process, utilizing flexibility disassembly perturbation and the Krylov subspace. This extended subspace iteration method proves particularly advantageous for the modal analysis of finite element models that incorporate a multitude of random variables. The proposed modal random analysis method has been validated using both a truss structure and a beam structure. The results demonstrate that the proposed method achieves substantial savings in computational time. Specifically, for the truss structure, the calculation time of the proposed method is approximately 1.2% and 65% of that required by the comprehensive analysis method and the combined approximation method, respectively. For the beam structure, on average, the computational time of the proposed method is roughly 2.1% of a full analysis and approximately 48.2% of the Ritz vector method’s time requirement. Compared to existing stochastic modal analysis algorithms, the proposed method offers improved computational accuracy and efficiency, particularly in scenarios involving high-discreteness random analyses.

Finite element modeling to explore static bending responses of four-layer FG beam structures considering sliding motions

Finite element modeling to explore static bending responses of four-layer FG beam structures considering sliding motions

Research on Damage Detection of Dual-Rotor Synchronous Excitation Mine Screen Beams Based on Strain Mode Difference Vibration Mode Analysis

The frame beam structure of the mine screen, subjected to various excitations, is a critical component of mining machinery. Its stress is intricate, the operational environment is severe, and damage can lead to catastrophic failures resulting in machinery destruction and fatalities. Based on the characterization of the vibration response of mine screen frame beams with varying degrees of damage at the same location and with the same degree of damage but at different locations, this paper develops a method of strain modal difference vibration pattern analysis and damage feature extraction for the detection of structural damage in beams. This method is based on the sensitivity of the sudden change in vibration strain modal difference to small deformations. This method solves the problem of using the conventional structural finite element analysis or experimental modal analysis methods to obtain the displacement mode, intrinsic frequency, and other characteristics, which make it difficult to effectively identify the actual engineering, with the damage conditions of the damage state and damage location of the mine screen frame beam problems. The feasibility and validity of the engineering application of the concept are demonstrated through instances.

Structural Damage Detection Using PZT Transmission Line Circuit Model

Arrangements of piezoelectric transducers, such as PZT (lead zirconate titanate), have been widely used in numerous structural health monitoring (SHM) applications. Usually, when two or more PZT transducers are placed close together, significant interference, namely crosstalk, appears. Such an effect is usually neglected in most SHM applications. However, it can potentially be used as a sensitive parameter to identify structural faults. Accordingly, this work proposes using the crosstalk effect in an arrangement of PZT transducers modeled as a multiconductor transmission line to detect structural damage. This effect is exploited by computing an impedance matrix representing a host structure with PZTs attached to it. The proposed method was assessed in an aluminum beam structure with two PZTs attached to it using finite element modeling in OnScale® software to simulate both healthy and damaged conditions. Similarly, experimental tests were also carried out. The results, when compared to those obtained using a traditional electromechanical impedance (EMI) method, prove that the new approach significantly improved the sensitivity of EMI-based technique in SHM applications.

Chaotic control of a simply supported beam in a multidimensional system

In this work, a control strategy based on fuzzy sliding mode control (FSMC) is applied to effectively manage the large-amplitude chaotic vibrations exhibited by a simply supported beam. The analysis considers the nonlinear beam structure, which is subjected to an external load. Hamilton’s principle is employed, and the equations of motion are derived for the studied structure. The 3rd Galerkin discretization is employed to derive the ordinary differential governing equation of the structure. A control strategy is presented to decrease the response of the obtained multidimensional system. The vibration of a one-dimensional system is compared with that of the derived multidimensional system. As shown throughout the study, a multidimensional nonlinear system of the structure must be considered for accurate dynamic estimation. By using the recurrent neural network (RNN) model, we can accurately predict chaotic motion and effectively apply control strategies to suppress chaotic motion. The efficacy and suitability of the employed control strategy have been demonstrated by controlling chaos in the beam’s multidimensional system.

Quantification and Sensitivity Analysis of the Model Uncertainty in the Projectile-Barrel Coupled Artillery Dynamics System Based on Random Matrix Theory

Simplifications in the engineering of artillery firing dynamics modeling introduce model uncertainty, which seriously affects the model’s predictive performance. To this end, a typical variable-section hollow cylindrical cantilever beam structure in artillery firing dynamics is investigated in this paper. The statistical approximation methods quantify parameter and model uncertainty separately, and their respective confidence intervals were calculated and compared. The results show that the traditional parameter uncertainty approach overestimates the parameter uncertainty ranges, and introducing the model uncertainty approach dramatically improves the model prediction performance. Additionally, a projectile-barrel coupled artillery dynamics model considering model uncertainty is established, and its effectiveness is validated through the actual launch experiments. The sensitivity of the dynamic responses to the system matrix, namely model uncertainty, is further analyzed. This paper provides theoretical references for the study of uncertainty in artillery launch dynamics and proposes effective methods to enhance the predictability of computational models for complex structural systems.

The failure of edge-cracked hard roof in underground mining: An analytical study

Hard roof is the primary concern of strata control in underground mining. Various techniques have been utilized to fracture the hard roof and control the failure of strata. Understanding the impact of cracks on strata behaviour is vital for optimizing strata control strategies. In this study, the hard roof was regarded as a beam structure with different loading, support, and boundary conditions. The equivalent spring model was adopted to represent the edge-cracked section of the hard roof, which allows additional rotation at the crack location. A piecewise-defined function was developed for solving equations of hard roof in the vicinity of the crack section. By combining the hard roof beam model and the equivalent spring model, the impact of a crack on the hard roof can be measured. A case study was carried out to explore the impacts of crack location and crack depth on the mechanical state of the hard roof. Results showcase the failure of the hard roof controlled by the crack depth and greatly influenced by the crack location. From the perspective of coal burst prevention, roof fracturing should be implemented at the high-stress area of strata, whereas it has been challenging in practice to determine such a location precisely. To address this challenge, it was suggested that hard roof fracturing should be carried out before coal seam de-stressing, increasing the likelihood of a crack occurring in a high-stress area. By adopting the proposed method, the mechanical state of the edge-cracked hard roof can be quantified.

Analytic solutions for equatorial, Kelvin, Rossby, and Yanai beams

Wind-driven equatorial Kelvin, Rossby, and Yanai waves are known to propagate vertically, as well as zonally, and packets of them can form “beams” that descend into the deep ocean along ray paths consistent with wave-group theory. Here, we obtain analytic solutions to a simplified ocean model that provide a more complete description of beam properties and dynamics than in previous studies.The model is a linear, continuously stratified (LCS) system, in which the bottom is ignored and the background Vaisala frequency Nb is constant. Solutions are forced by an oscillatory wind stress, τα=τoαXxexp−iσt, where: α is x or y; Xx is confined to the region −L<x<L and increases and decreases monotonically; and τα enters the ocean as a body force with the profile Zz=2/πh/z2+h2. Under these restrictions, solutions can be represented as cosine transforms in z that can be readily inverted.Beam solutions for all three wave types have similar mathematical forms, and hence share many properties. Among other things, the solutions show how the structure and amplitude of beams depend on the above model parameters. Potential impacts of processes neglected in the solutions are noted.

Efficient layerwise multiphysics spectral element model for delaminated composite strips with PWAS transducers

Efficient structural element-based models are essential for fast simulations of wave propagation in composite structures for model-based and physics-informed data-driven structural health monitoring. This article introduces the first efficient multiphysics time-domain spectral structural element for wave propagation analysis of beam and panel-type composite structures with piezoelectric transducers (patch or full layers) containing delaminations. A general framework is presented to model multiple delaminations and transducer patches located arbitrarily. The intact host and patch transducer-bonded laminates and sub-laminates between delaminations are modelled separately using an electromechanically coupled efficient layerwise zigzag theory (ZIGT) for kinematics and a piecewise quadratic variation for the electric potential across piezoelectric layers. The high-order spectral element (SE) features a virtual electric node to model equipotential surfaces of piezoelectric transducers apart from the usual physical nodes having mechanical and internal electric degrees of freedom. A hybrid point-least squares continuity approach is employed to maintain continuity at the intersections of delaminated sub-laminates or the patch-bonded laminate with the host laminate. The model’s performance in capturing electroelastic waves’ interaction with delamination is examined with reference to the conventional finite element (FE) solution based on the ZIGT, continuum-based FE solutions, and the SE solution based on a non-layerwise version of the laminate theory. Finally, the model is used to examine the impact of interfacial location and size of delaminations on wave propagation behaviour.

Research on fatigue life of carbon fiber reinforced polymer strengthened single-sided butt welded joints utilizing resin pre-coating for strong adhesive bonding

Single-sided butt welding is a common connection method used in box beam structures such as excavator booms. Single-sided butt weld joints are prone to fatigue failure since the structures are subjected to cyclic loads over extended periods. The purpose of this study is to improve the fatigue performance of single-sided butt welded joints. Carbon fiber reinforced polymer (CFRP) strengthened single-sided butt welded joint specimens with permanent backing plates were prepared by pre-coating method, and constant-amplitude tension–tension fatigue tests were carried out on the specimens. The effects of welding groove parameters and CFRP reinforcement on fatigue life were studied. The test results show that the CFRP-strengthened specimens without blunt edges and with a groove angle of 40° show the highest average fatigue life. The single-sided bonding of 10 layers of CFRP sheets effectively inhibits the propagation of fatigue cracks and significantly improves the fatigue life of welded joints. In the CFRP/welded joint composite structure, the strain monitoring results show that the peak strain of the interface is the largest in the middle position, and the peak strain rises sharply in the rapid crack propagation stage, which indicates that the real-time interface strain peak can reflect the fatigue crack propagation. It provides an early warning method for real-time monitoring of fatigue life failure of welded structures in practical engineering.

Analysis of Strengthening Beam Structure Case Study on Food Court Building of Ruang Terbuka Hijau (RTH) Project at Alun-Alun Kota Kediri

The Green Open Space (RTH) construction in Kediri City includes a food court building utilizing reinforced concrete structures. During construction, cracking issues occurred in several beam structures due to the inability to bear the design loads effectively, necessitating a strengthening approach. This study aims to develop and evaluate a strengthening method for cracked beam structures by employing concrete jacketing. The specific objective is to improve the structural integrity and load-bearing capacity of these beams to ensure the durability and safety of the building. A concrete jacketing technique was used to reinforce the cracked beams, utilizing K-300 ready-mix concrete and additional reinforcing steel. The study involved structural analysis to assess the load-bearing capacity before and after jacketing, and on-site evaluation was conducted to monitor the method's effectiveness. The findings indicate that the jacketing method significantly increased the beams' bending moment capacity and overall structural strength, successfully addressing the cracks and enhancing the beams' ability to bear the intended loads. The reinforced beams showed improved load distribution and structural resilience performance. Concrete jacketing proved to be an effective method for strengthening the cracked beam structures in the Green Open Space project. The study provides valuable insights for similar future construction projects, suggesting that concrete jacketing can be a reliable reinforcement technique to enhance the durability and safety of building structures.

Open-loop swept frequency response of nonlinear structures subjected to weak coupling

AbstractThe present study demonstrates a common behaviour of a forced nonlinear structure with smooth nonlinearity, while coupled dynamics are apparent, originating from the attached electrodynamic shaker. This appears as a variation in the transmitted forcing amplitude and is often subjected to a hysteretic (multi-state) behaviour for up and down open-loop sweeping. This situation differs from the ideal constant amplitude harmonic excitation, on which parameter extraction and engineering comprehension are based on. Untreated or ignored, this can lead to the misinterpretation of the underlying dynamics through the measured nonlinear frequency response curves and their force-normalised version, often called quasi-frequency response function. In this paper, a post-processing solution is introduced for the correct interpretation of frequency response curves at constant forcing amplitudes through the open-loop construction and resectioning of the so-called frequency response surface. The phenomenon and the proposed methodology are demonstrated using a two-degrees-of-freedom model on a shaker-nonlinear beam structure. First, open-loop frequency sweeps are executed on the mechanical system to create the nonlinear frequency response surface, where their actual amplitudes and hysteresis widths are significantly different from the ideal constant forcing amplitude case. The response surface is then sectioned at the assumed constant forcing values by using an appropriate interpolation law. These resectioned curves represent the forced nonlinear standalone structure under ideal constant harmonic excitation. The frequency response surfaces are characterised and resectioned on a nonlinear structure with stiffening and softening cases. Furthermore, an improvement in the operational resonance decay (ORD) method in its filtering and automation is shown to extract the backbone curves (BBCs). The BBC and the resectioned surface provide a complete picture and cross-validation of the underlying dynamics. Finally, the BBC and its distortion are also shown in the response surfaces in relation with the excitation normalization.

Evaluation of Inherent Damping Feature of Beam Structure Based on Complex Modulus

Structural damping, which has been widely used to quantify the energy dissipation of engineering structures, plays an important role in dynamic analysis during the design phase and the assessment of existing structures. However, the development of an accurate damping model remains an open question due to the unclear mechanism. In this study, structural damping was identified based on loss factors for beam structures, which were used for presenting the damping behavior during vibrations. The equation of motion for the bending deformation of a Timoshenko beam was derived, accounting for the material damping. To identify the loss factor of the beam from the response signals at a limited number of measurement points, an inverse algorithm based on wave coefficient estimation was developed, considering the numerical stability for data interpretation. Based on the proposed loss factor identification method, several beam models with different shapes of cross-sections were investigated, focusing on the feasibility of the method of varying cross-section cases. Comparing the spectral element model with the loss factor and the finite element model with Rayleigh damping, it was confirmed that the loss factor can better describe the actual energy dissipation behavior of the structure. It provides a more accurate theoretical model for estimating structural damping in practical engineering.

Mode selective damping behavior of additively manufactured beam structures

AbstractAdditive manufacturing, with its inherent process-related degrees of freedom, offers significant potential for manufacturing high-performance parts. This allows effects to be integrated that enable completely new solution mechanisms for existing conflicting objectives, which means that the degrees of design freedom make it possible to optimize the application-specific behavior of a part. In addition to the thermal or electrical properties, the dynamic behavior of a part can also be optimized, for example. This article focuses on the integration of the particle damping effect, which can contribute significantly to increased part damping. Unfused powder inside the part leads to energy dissipation through impact and friction mechanisms. However, the particle damping effect is not yet fully explored, lacking essential knowledge for application in product design. Therefore, test specimens with particle dampers, manufactured using laser powder bed fusion by laser beam from 1.2709 tool steel, are investigated, with variations in the position and size of the particle-filled cavities. To determine damping, the samples are freely supported and excited with an impulse. The damping ratio is calculated based on the recorded decay behavior. The results show an increase in damping ratio of up to a factor of 70, with the extent of improvement strongly dependent on the cavity’s volume and, crucially, its position relative to the part’s mode shape. A linear relationship between the damping ratio and the displacement of the volume of the cavities of the beams is shown.

Mechanical loading-induced alveolar bone remodeling is suppressed in the diabetic state via the impairment of the specificity protein 1/vascular endothelial growth factor (SP1/VEGF) axis.

Orthodontic treatment involves alveolar bone remodeling in response to mechanical loading, resulting in tooth movement through traction-side bone formation and compression-side bone resorption. However, there are conflicting reports regarding alveolar bone resorption during the orthodontic treatment of patients with diabetes. Diabetes was induced in 8-week-old C56BL/6J mice using streptozotocin (STZ). Four weeks after the injection of STZ, a mechanical load was applied between the first and second molars on the right side of the upper jaw using the Waldo method with orthodontic elastics in diabetic (DM) and normal (N) mice tooth movement, gene expression, osteoclast counts, alveolar bone residual volume, and bone beam structure were evaluated. The duration until spontaneous elastic loss was significantly longer in the DM group, suggesting that tooth movement may be inhibited in the diabetic state. The number of osteoclasts at 7 days after mechanical loading and the alveolar bone resorption were both significantly lower in the DM group. The gene expression levels of vascular endothelial growth factor (VEGF), a protein related to alveolar bone remodeling, and specificity protein 1 (SP1), a transcription factor of the VEGF gene, were significantly lower in the DM group than in the N group on the compression side of mechanical loading. Mechanical loading-induced alveolar bone remodeling is suppressed in the diabetic state. Our results suggest that VEGF is a key molecule involved in impaired bone remodeling under mechanical loading in the diabetic state.

Damage detection and localization in a cantilever beam structure via regression-and-classification-based machine learning

Damage detection and localization in a cantilever beam structure via regression-and-classification-based machine learning

A novel high-Q Lamé mode bulk acoustic resonator

This study introduces a novel high-Q Lamé mode MEMS resonator, optimized through support beam structures and etching hole distributions to minimize anchor losses and thermal elastic dissipation (TED). Fabricated using a Silicon-On-Insulator (SOI) process, the resonators achieved Q values of 129,200 and 102,100 in different designs, demonstrating significant improvements in vacuum conditions and highlighting air damping as a key loss mechanism. Nonlinear analysis revealed material nonlinearity dominance. These findings offer valuable guidelines for developing high-end MEMS devices, such as low phase noise oscillators and high-resolution sensors, by showcasing substantial reductions in energy dissipation and enhanced Q factors through structural optimizations.

Analysis of reinforcement effect of different anchoring forces on slope stabilised by prefabricated anchorage cable frame beams

Prefabricated anchorage cable frame beams represent a new approach to slope reinforcement, displaying distinct deformation and stress patterns under varying anchoring forces compared to traditional cast-in-place frame beams. This renders the traditional theories and engineering practices of cast-in-place beams inapplicable. Field tests and sophisticated finite-difference simulation models were established to examine the mechanical performance of prefabricated beams under different anchoring forces. Initially, field test results validated the simulation models against measured and theoretical data. Subsequently, the impact of different anchoring forces on slope deformation, structural deformation, and stress in frame beams were explored. The beam pressure at the anchoring point of prefabricated beams was 24 % lower than that of cast-in-place beams, exhibiting a linear relationship with increasing anchoring forces and heightened initial sensitivity. Prefabricated beams showed a 20–30 % reduction in anchoring force loss over traditional beams when the anchoring force is not greater than 40 t. Notably, tensile stress emerges in prestressed prefabricated beams when anchoring forces exceed 50 t. The slope deformation with the increasing of anchoring force can be described by a power function. A new deflection deformation index for frame beams was proposed, showing a 70 % reduction compared to cast-in-place beams. During sliding face degradation, deformation differences between adjacent prefabricated beams weaken the reinforcement effect compared to continuous cast-in-place beams. However, applying sufficient anchoring forces significantly mitigates this effect. A well-calibrated anchoring force ensures superior performance of prefabricated anchorage cable frame beams, with enhanced crack resistance, reduced anchoring force loss, minimal deflection deformation. Moreover, the prefabricated beam structure is easy for local replacement and maintenance. This study can make a reference for the application and design of prefabricated structures for slope stabilisation.