Beam Theory Research Articles

Simulation of Concrete Fracture Using ABAQUS

This paper discusses the analytical simulation of crack propagation using the Fictitious Crack Model for notched and unnotched Portland Cement Concrete beam specimens. Parameters such as those controlling the loading conditions, mesh fineness, aspect ratio in the vertical or horizontal directions, and notch to beam thickness ratio are considered. The commercial program ABAQUS is used, and simulations are compared to previous analytical and experimental results. A linear elastic investigation is first conducted to test the agreement of the results with the Timoshenko beam theory. Subsequently, an investigation is conducted to test the built-in fracture mechanics capabilities of ABAQUS for tracking crack propagation. Since these built-in capabilities are found to be inadequate, the creation of a model from basic elements is pursued. This is accomplished by introducing JOINTC elements along the crack plane to model joint interactions. Several series of tabulated results are used to illustrate the advantage of using finite element simulation over conducting laboratory experiments, reflected in the time, effort, and money saved. The application of fracture mechanics to understanding concrete pavement cracking is found to be desirable, practical and feasible. It is argued that the development of a truly mechanistic design procedure hinges on the elimination of long-held empirical concepts, including statistical transfer functions.

Design of a novel buckling-type quasi-zero stiffness isolator

Based on the significant geometric nonlinearity associated with large deformations in beams, this paper presents the design of a buckling-type quasi-zero stiffness (BQZS) isolator using slender beams with positive and negative stiffness. This design achieves a characteristic output of nonlinear load-bearing combined with linear stiffness. The elliptic integral method is employed to solve the mechanical equations of the large deformation beams. Through numerical simulations and theoretical calculations, the mechanical properties of the large deformation beams are obtained. A prototype was designed for validation, and its manufacturing and experimental studies are presented. The results demonstrate that the designed BQZS isolator effectively attenuates the system’s vibration response, achieving a 95% reduction at 5 Hz vibration excitation. Additionally, the natural frequency of the isolator with BQZS is less than 1 Hz.

Predictive Model for Deformation of Adjacent Pipelines Caused by Tunnel Boring in Twin-Lane Tunnels in Soft Ground Layers

To create a discretized prediction model for the deformation of an adjacent pipeline, the pipeline structure is discretized, the differential equations governing the longitudinal deformation of the pipeline are inferred, and the displacement expressions and the solution methods of the virtual nodes of each unit are provided after discretization. This approach is based on the Pasternak foundation beam theory. It aims to address the issue of the difficulty in predicting the deformation of the adjacent pipeline caused by shield tunneling in a saturated soft ground layer in the Yangtze River Delta. The deformation pattern of the surrounding soil is determined and confirmed through additional numerical simulation, and the discretized prediction model is contrasted with the conventional Winkler foundation beam model and the Pasternak foundation beam model. The findings demonstrate that the discrete prediction model is simpler to solve and more accurately describes the deformation characteristics of the adjacent pipeline as well as the deformation distribution law. The calculated deformation characteristics primarily appear as the adjacent pipeline’s deformation due to the double tunnel boring exhibiting a “mono-peak shape” with a large middle and small ends, which is consistent with the actual situation. The two main factors influencing the pipeline deformation are the shield tunneling distance and pipeline spacing; the former has a negative correlation with the pipeline deformation, while the latter has a positive correlation. This work can offer a straightforward deformation prediction technique for shield tunneling in the Yangtze River Delta’s saturated soft ground next to existing pipelines.

A modified spectral collocation method for vibration of sandwich beams based on a higher-order layer-wise beam theory

A modified spectral collocation method for vibration of sandwich beams based on a higher-order layer-wise beam theory

Trigonometric Higher‐Order Shear Deformation Theory on Exact Solution for Lateral and Longitudinal Dynamic Response of Magneto‐Electric Carbon Nanotube‐Reinforced Composite Beams Under Two Moving Loads Resting on Winkler–Pasternak Foundation

This paper aims to analyze the transverse and axial dynamic response of magneto‐electric carbon nanotube‐reinforced composite (CNTRC) beams under two moving constant loads resting on an elastic foundation. The governing equations of the magneto‐electric CNTRC beam are obtained based on Mantari’s shear deformation beam theory, Hamilton’s principle, and Laplace transforms to solve the derived differential equations. The beams, which include a Winkler spring and shear layer, are considered as resting on the elastic foundation. The boundary conditions for this work are simply supported. This marks the inaugural instance in which a precise analytical approach rooted in mathematical principles has been employed to examine these constructions. The drawback inherent in this technique lies in its reliance on a simply supported boundary condition, stemming from the challenge associated with performing Laplace inversion on the Coupled equations. A comparison with previous studies has been conducted, which is a valuable contribution. Several examples were used to analyze the magnetic, voltage, and spring constant factors, the volume fraction of carbon nanotubes (CNTs), the velocity of a moving constant load, and their influence on the transverse and axial dynamic responses and maximum deflections.

Long-time dynamics for a coupled system modeling the oscillations of suspension bridges

<p>This paper is concerned with a coupled system modeling the oscillations of suspension bridges, which consists of a beam equation and a viscoelastic string equation. We first transformed the original initial-boundary value problem into an equivalent one in the history space framework. Then we obtained the global well-posedness and regularity of mild solutions by using the semigroup theory. In addition, we employed the perturbed energy method to establish a stabilizability estimate. By verifying the gradient property and quasi-stability of the corresponding dynamical system, we derived the existence of a global attractor with finite fractal dimension.</p>

Synchronous detection of multiple micro-substances with a single output channel using a weakly coupled resonator array

Abstract In this paper, a multiple micro-substances sensing scheme with a single output channel using a weakly coupled resonator array is proposed. An analytical model of the resonator using the Euler-Bernoulli beam theory has been developed, as well as the dynamic behavior has been further explored using the Galerkin method. We have discovered numerically that, in the weakly coupled cantilever array, the A-f (amplitude-frequency) curve of any cantilever physically reflects the vibration features of other cantilevers. Hence, by measuring the output signal of a single cantilever, multiple substances applied on each cantilever respectively can be identified and detected synchronously. A single output channel via a weakly coupled micro-resonator array is constructed and validated numerically for picogram level mass detection. Equivalent experiments with a macro coupled five-cantilever array have been further conducted for verification. Under a common sweep-driven signal, the five analytes applied on each cantilever with masses at microgram level can be detected synchronously and independently by measuring the frequency shifts of the five resonant peaks of the center cantilever. Multiple substances sensing with a single output channel and a single driving signal is thus realized with low relative errors and high linearities. By enhancing the driving voltage, the mass resolution can also be improved via Duffing bifurcation. This work not only reveals a new coupled vibration behavior but also provides a new avenue for multiple analytes detection.

Analyzing the Vibration Response of Adhesively Bonded Composite Cantilevers.

In this study, we investigated the vibration of adhesively bonded composite cantilevers consisting of two beech wood lamella and a bondline of flexible polyurethane. The beams had a constant total height, while the thickness of the adhesive layer varied. We analyzed both the driven and free vibration of a single cantilever beam and a cantilever with an additional mass attached to its end. The eigenfrequencies were determined using Fourier analysis of a sweep load response, the response to an impact load excited using an impact hammer, and the response observed via the manual displacement of the beam's tip. The system's damping was estimated according to the recorded logarithmic decrement. Theoretical estimates of the fundamental natural frequency were obtained using the γ-method and employing a linear elastic theory of composite beams. A numerical modal analysis was carried out using the finite element method. Upon comparing the results of our experiments with the numerical estimates and theoretical predictions, a fair agreement was found.

An Echo Pressure Model Based on Mutil‐Gaussian Beam Theory for Measuring the Liquid Level in Special Field

ABSTRACTIn aviation, petroleum and chemical industries and other special areas of production, since the liquid in containers mostly are flammable, explosive, volatile, and corrosive mixtures, the accurate measurement of the liquid level is essential to the real‐time control and production process. In this study, an approximation algorithm based on echo pressure model for measuring the liquid level in special field is proposed in this paper. According to the model, a complete lateral incident ultrasonic measurement system is constructed for the inductive liquid level detection technology in special applications, an algorithm model of the echo pressure is established, which provides the determination of the liquid level relying on the characteristic curve of the echo pressure. The model in this study converts complex interaction problems of sound fields into the echo pressure calculation, which quickly determines performance parameters of sound fields, and a virtual reflection method is used to calculate the sound pressure of the receiving transducer in different states, which reduces computational complexity, finally, through the simulation and experiment, the algorithm is validated. The results are consistent with expectations, and the algorithm can be further applied in practice.

Dynamics characteristics of variable stiffness curvilinear fiber-reinforced layered composite beam under moving load by sinusoidal shear flexible beam model including nonlinear and thermal effects

In this study, the dynamic response behavior of curvilinear fibers based layered-composite beam under transversely moving load is investigated considering linear and nonlinear analyses. The formulation is developed applying sinusoidal shear flexible beam theory, geometrical nonlinearity based on von Kármán’s assumption, and the constitutive equation fulfilling the plane stress situation through the width of arbitrarily lay-up composite beam. The load on the beam is treated as moving with uniform velocity, acceleration and also oscillatory motion with time. The governing nonlinear dynamic equations are framed employing Hamilton’s principle and by adopting finite element approach. The response of beam in time domain is obtained solving the governing equations through direct time integration method by Newmark integration scheme. and the results are viewed through the frequency-amplitude relationship. A detailed parametric study involving curvilinear fiber path angles, lay-up ply angles, thickness ratio, moving load velocity, and acceleration, and forcing frequency is made on the dynamic behavior of variable stiffness beam with curvilinear fiber beam. The effect of thermal environment and boundary conditions on the vibrational response behavior of beam is also predicted.

Vibration Control of Tapering E-FGM Porous Wind Turbine Blades Using Piezoelectric Materials

Piezoelectric materials have many interesting applications thanks to their ability to generate an electrical voltage when subjected to mechanical pressure, and vice versa. In the field of vibration energy recovery, these materials can convert mechanical vibrations into electrical energy. For example, piezoelectric sensors integrated into roads or pavements can generate electricity from vibrations caused by vehicles or pedestrians. In the field of wind turbines, the vibratory control of wind turbine blades can increase the overall efficiency of these systems. Additionally, composite materials are being increasingly integrated into the construction of mechanical systems, and specifically FGM materials. This work focuses on the active vibration control of FGM beams with non-uniform cross-sections, using piezoelectric materials. Euler-Bernoulli beam theory combined with the FEM is applied to an FGM beam. The equation of motion is generated using Hamilton's principle.

A new shear deformation micro-beam model based on a nonlocal elasticity theory

In this article, a nonlocal refined shear deformation beam theory is proposed to analyze the free vibration behavior of FG nanobeams. The formulation is based on the nonlocal differential constitutive equations of Eringen that accounts for small scale effects. Material properties vary continuously through thickness according to a power law distribution. The study is performed within the framework of a new parametric shear deformation theory which provides parabolic transverse shear strains across the thickness direction and hence, does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the nanobeam are satisfied rigorously. Equations of motion of FG nanobeam are derived from both the nonlocal differential constitutive relations of Eringen and Hamilton’s principle. The system of differential equations is solved using the Navier solution technique. The parametric study is conducted to examine the effects of volume fraction index, length scale parameter and length ratio on the free frequencies of vibration of FG thin and thick nanobeams.

Polyurethane foam sandwich structures collapse modes under three-point bending

The aim of this analysis is to investigate the mechanical behavior of polyurethane foam sandwich sandwiches in three-point bending tests by varying the span length of test specimens and the core thickness. Theoretical models are represented that use foamed sandwich mechanics and classical beam theory. Tests were dispensed so as to seek out the link between the geometrical configuration of the sandwich and therefore the failure mechanism. The static bending tests created numerous collapse modes looking on support span distance and core layer thickness. Numerous failure modes and injury as well as indentation failure below the loading roller, core–upper skin delamination and core shear square measure reportable and mentioned the consequences of core thickness and span length on most static load and bending stiffness also are examined. it absolutely was ascertained that the span distance has important impact on the failure mode of the specimen.

Free vibration analysis of bidirectional functionally graded double-tapered beam using the p-version of the finite element method

In this paper, we conducted a frequency analysis of bidirectional functionally graded double-tapered beam (BDFG beam) using the p-version of the finite element method, the beam was modeled by the Euler Bernoulli beam theory, the global matrices of the equation of motion are determined by applying the Lagrange equation on the kinetic and deformation energies. The material properties are assumed to vary along the thickness and width directions according the power-law distribution. The numerical results are obtained by a developed Matlab code and compared with Ansys Workbench and Solidworks for a pure metallic tapered cantilever beam and with previous study for a unidirectional functionally graded tapered cantilever beam (UDFG beam), case studies were carried out to analyze the influence of tapering angles, the power law indeces, and boundary conditions on the natural frequencies of the beam; these studies demonstrate the advantage of the proposed bidirectional functionally graded tapered beam over the metallic and unidirectional functionally (UDFG) beams.

Size-dependent nonlinear bending of tapered cantilever microbeam based on modified couple stress theory

The Euler-Bernoulli beam theory is adopted in conjunction with modified couple stress theory (MCST) in this paper to formulate a beam element for size-dependent nonlinear bending analysis of a tapered cantilever microbeam subjected to end force/moment. The microbeam is considered to be linearly tapered in both the width and height directions. The element is derived in the context of the co-rotational approach in which the internal force vector and the tangent stiffness matrix are firstly derived in an element attached coordinate system and then transferred to the global one by the transformation matrices. An incremental/iterative procedure is adopted in conjunction with the arc-length method to compute the response of the microbeam. The obtained results show that the formulated element is efficient, and it is capable to model accurately the size-dependent nonlinear response of the microbeam by using just several elements. It is shown that the size effect plays an important role on the large deflection response, and the displacements of the microcantilever are overestimated by ignoring the influence of the micro-scale size effect. The effects of the material length scale parameter and the tapered ratio on the nonlinear behavior of the microbeam are studied in detail and highlighted.

Mandibular biomechanics of Acheroraptor temertyorum (Theropoda: Dromaeosauridae) with implications for the feeding ecology and behaviour

Acheroraptor temertyorum is a dromaeosaurid theropod, probably a saurornitholestine, found in the upper Maastrichtian Hell Creek Formation of Montana. This enigmatic dromaeosaurid is known from only a partial maxilla and dentary, as well as referred isolated teeth, making even the general aspects of its palaeobiology largely elusive. In this work, beam theory is applied to the lower jaw of Acheroraptor temertyorum to document the biomechanical properties of the mandible of this taxon and to infer the feeding mechanism of this dinosaur. This work suggests the lower jaw of Acheroraptor temertyorum is mainly adapted to produce rapid, slashing bites, as previously inferred for other dromaeosaurids. Intriguingly, despite having a closer phylogenetic affinity with Saurornitholestes langstoni, overall biomechanical properties of the lower jaw of Acheroraptor temertyorum are found to be weaker than the former taxon, but rather comparable to Asian velociraptorines. Such results may indicate Acheroraptor temertyorum preyed on smaller animals compared to other saurornitholestines, and suggest diets or predation methods of saurornitholestine dromaeosaurids might have been more diverse than previously assumed.

Modeling and Dynamic Analysis of Fish Robot with Soft Fluidic Actuation

A biomimetic robotic fish tailored for environmental monitoring and hydrographic exploration is examined in this study. Traditional fish robots, driven by tail oscillations, often grapple with constrained maneuverability in a single plane. This article focuses on mitigating these limitations through an exploration of the dynamic behavior of a bioinspired soft robotic fish. Unlike prior designs that employed similar actuators for the robot's tail, which either lacked the ability for out-of-plane motion or relied on other propulsion systems, the single propulsion design proposed in our model enables movement along three-dimensional trajectories, leading to improved efficiency and maneuverability due to tail oscillation dynamics. The proposed design integrates strategically positioned nozzles for out-of-plane movements, alongside parallel fluid channels on the tail's neutral plate. Actuation is achieved by manipulating the internal fluid pressure within these channels. To precisely model tail deflection, we introduce a novel method utilizing Euler–Bernoulli beam theory considering nonlinear characteristics arising from internal fluid stress. For instance, following the proposed approximate analytical method, we optimize the fluidic actuator, considering that the soft tail deformation increases by 65% as the channel shape transitions from a semicircular to a square cross-section. The comprehensive comparison with analytical nonlinear method, finite element method, and experimental-driven analytical method extends our approach as an effective tool in terms of accuracy and computation time, demonstrating the effectiveness of validation processes. This study unveils a simplified and robust fish robot design, outperforming traditional mechanisms in efficacy. Despite its simplicity, the proposed design delivers comparable performance, presenting an effective alternative for achieving requisite functionality in fish robots.

On the use of direct implicit integration with numerical Jacobian matrix in helicopter rotor dynamics

In recent years, geometrically exact beam theory is widely used in rotor structural dynamics to model composite blade undergoing large deflections. The corresponding differential equations based on this theory show strong nonlinearity and the aeroelastic terms are normally written in implicit format. It brings most difficulties to implicit integration methods since the analytical Jacobian matrix is hard to derive. In this paper, a trapezoidal integration utilizing numerical Jacobian matrix is introduced to solve the dynamic equations of rotor blade. Central difference method with Romberg extrapolation scheme is adopted to numerically calculate the Jacobian. Accuracy of the methods is evaluated on dynamic problems from one cantilevered beam and the other fully articulated rotor blade. Numerical stability and efficiency are also investigated by changing update policies of Jacobian matrix and mesh configurations of typical rotor blade. Numerical results show that both extrapolation scheme for partial derivatives and the integration method with numerical Jacobian perform well on predicting natural frequencies and transient responses in rotor dynamics.

Modeling and Analysis of Thermoelastic Damping in a Piezoelectro-Magneto-Thermoelastic Imperfect Flexible Beam

This research addresses the phenomena of thermoelastic damping (TED) and frequency shift (FS) of a thin flexible piezoelectro-magneto-thermoelastic (PEMT) composite beam. Its motion is constrained by two linear flexible springs attached to both ends. The novelty behind the proposed study is to mimic the uncertainties during the fabrication of the beam. Therefore, the equation of motion was derived utilizing the linear Euler–Bernoulli theory accounting for the flexible boundary conditions. The beam’s eigenvalues, mode shapes, and the effects of the thermal relaxation time (t1), the dimensions of the beam, the linear spring coefficients (KL0 and KLL), and the critical thickness (CT) on both TED and FS of the PEMT beam were investigated numerically employing the Newton–Raphson method. The results show that the peak value of thermoelastic damping (Qpeak−1) and the frequency shift (Ω) of the beam increase as t1 escalates. Another observation was made for the primary fundamental mode, where an increase in the spring coefficient KLL leads to a further increase in Ω. On the other hand, the opposite trend is noted for the higher modes. Indeed, the results show the possibility of using the proposed design in a variety of applications that involve damping dissipation.

Extending Generalized Explicit Terms and Applying Euler–Bernoulli Beam Theory to Enhance Dynamic Response Prediction in Receptance Coupling Method

This paper presents a theoretical framework to enhance the prediction of dynamic responses in complex mechanical systems, such as vehicle structures, by incorporating both translational and rotational degrees of freedom. Traditional receptance coupling methods often neglect rotational effects, leading to significant inaccuracies at higher frequencies. Additionally, approaches that implicitly include full dynamics frequently result in redundancy of generalized coordinates, especially at connection points. To address these limitations, the generalized receptance coupling method using Frequency-Based Substructuring is extended to explicitly account for rotational dynamics resulting in a refined GRCFBS approach. This extension enhances both the understanding and prediction of system responses, which are represented through the receptance matrix or Frequency Response Function. Building on Jetmundsen’s foundational work, the proposed framework introduces a practical, generalized formulation that explicitly incorporates full translational and rotational dynamics at each substructure node. This explicit definition provides deeper insights into system behavior, particularly for complex interactions between substructures under weak and strong coupling scenarios at interface points. The Euler–Bernoulli beam theory is employed to model rotational behavior at critical points, yielding reduced-order and explicit receptance matrices for substructures in the coupling process. The methodology’s accuracy and applicability in capturing resonance and anti-resonance modes are validated through two case studies: the coupling of two flexible subsystems and the integration of flexible and rigid components. Results are benchmarked against numerical finite element analysis, and all limitations and potential improvements are discussed. By directly incorporating rotational dynamics directly, this approach enables more reliable dynamic response predictions under multi-directional loading conditions, particularly for vehicle and machinery system design. The GRCFBS method offers a versatile and reliable tool for dynamic system analysis, with significant potential for vibration analysis over a broad frequency range.