Deflection Of Cantilever Beam Research Articles

Research on the influence of applying counterweight on the deflection and stability of cantilever beam of machine tool

Abstract The deflection and stability of the cantilever beam of the machine tool are important factors that affect the machining accuracy of the machine tool. Because of the space size, it needs to be weighted within a limited size. By designing different weighting schemes, the static analysis and modal analysis are carried out by finite element analysis software, and the influence law of the deflection and stress of the beam is obtained, so the appropriate weighting scheme is selected. Through the analysis of different schemes, it is known that the deflection of the beam is the smallest under the action of the arm of 900mm and the force of 1000N, and the machine tool structure is more compact, which is the key component of the subsequent machine tool.

High–Speed Laser Modulation for Low–Noise Micro–Cantilever Array Deflection Measurement

In this paper, an innovative approach is introduced to address the noise issues associated with micro–cantilever array deflection measurement systems employing multiple lasers. Conventional systems are affected by laser mode hopping during switching, resulting in wavelength instability and beam spot fluctuations that take several hundred milliseconds to stabilize. To mitigate these limitations, a high–speed laser modulation technique is utilized, leveraging the averaging effect over multiple modulation cycles within the sampling window. By driving the lasers with a high–frequency carrier signal, a low–noise and stable output suitable for micro–cantilever beam deflection measurement is achieved. The effectiveness of this approach is demonstrated by simultaneously modulating the lasers and rapidly observing the spectral and centroid variations during high–speed switching using a custom–built high–speed spectrometer. The centroid fluctuations are also analyzed under different modulation frequencies. The experimental results confirm that the high–speed modulation method can reduce the standard deviation of beam spot fluctuations by more than 90%, leading to significant improvements in noise reduction compared to traditional laser switching methods. The proposed high–speed laser modulation approach offers a promising solution for enhancing the precision and stability of multi–laser micro–cantilever array deflection measurement systems.

Numerical and experimental investigation on crack detection in a beam using maximal overlapping discrete wavelet transform

The present study is concerned with detecting a crack in the beam numerically and experimentally using maximal overlapping discrete wavelet transform (MODWT). Slope discontinuity in the beam elastic line can reveal the presence of a crack in a beam. The MODWT is used for locating the cracks in a beam. MODWT coefficients are compared with discrete wavelet transform coefficients at different noise levels. For the experimental validation, high-resolution measurements of the cantilever beam deflection are obtained using photographic measurements. The algorithm is tested for the detection of cracks away and near the ends of a beam. Crack detection near the end of the beam is difficult due to border distortion. Border distortion suppresses the signal in that region. Isomorphism is utilized to shrink the border distortion zone. It helps in the better visualization of the spike due to the crack located away from the ends. Moving averaging is applied to the MODWT-based results for better localization of the spike near the crack position.

Characterizing stress development and cracking of ceramic particulate coatings during drying

AbstractDuring drying, liquid‐applied particulate coatings develop stress and are consequently prone to stress‐induced defects, such as cracking, curling, and delamination. In this work, the stress development and cracking of coatings, prepared from aqueous silica and zinc oxide particle suspensions, were characterized using cantilever beam deflection with simultaneous imaging of the coating surface. Drying uniformity was improved and lateral or edge‐in drying was discouraged by using thin silicone walls around the perimeter of the cantilever. Coatings prepared from larger monodisperse silica particles (D50 ∼ 0.9 µm) dried uniformly but had a high critical cracking thickness (>150 µm) that prevented simultaneous study of stress development and cracking. Coatings prepared from smaller silica particles (D50 ∼ 0.3 µm) cracked readily at low thicknesses but exhibited edge‐in drying that complicated the stress measurement data. This drying nonuniformity was connected to the potential for these small particles to accumulate at the coating surface during drying. Hence, the selection of particle size and density was critical to drying uniformity when characterizing stress development and cracking. Coatings prepared from suspensions of zinc oxide particles (D50 ∼ 0.4 µm) were well‐suited for these studies, with uniform drying stress peaking at ∼1 MPa. Characteristic features in the stress development data above and below the critical cracking thickness (53 µm) were identified, demonstrating that cantilever beam deflection is a useful tool for studying the effectiveness of crack mitigation methods and the fundamentals of coating fracture during drying.

A correction method for large deflections of cantilever beams with a modal approach

Abstract. Modal-based reduced-order models are preferred for modeling structures due to their computational efficiency in engineering problems. One of the important limitations of the classic modal approaches is that they are geometrically linear. This study proposes a fast correction method to account for geometric nonlinearities which stem from large deflections in cantilever beams. The method relies on pre-computed correction terms and thus adds negligibly small extra computational efforts during the time domain response analyses. The accuracy of the method is examined on a straight-beam model and International Energy Agency (IEA) 15 MW wind turbine blade model. The results show that the proposed method increases the accuracy of modal approaches significantly in secondary deflections due to nonlinearities such as axial and torsional motions for the two studied cases.

Semi-Analytical Solution for Elastoplastic Deflection of Non-Prismatic Cantilever Beams with Circular Cross-Section

A solution for the elastoplastic deflection of cantilever beams with linearly variable circular cross-section loaded by shear force at the free end, which is suitable for practical use, has not yet been developed. A semi-analytical solution for such a problem is proposed in this paper. The solution involves beams made of homogenous and isotropic materials with bilinear elastoplastic strain hardening behavior. The Bernoulli–Euler formula is used for determining the elastic deflection. However, for the plastic domain of material behavior, the differential equation of beam bending does not have a solution in closed form. Therefore, an incremental procedure for determining the curvature of the plastified region of the beam is suggested. Deflection of the cantilever beam is calculated via integration of the approximated function of the beam curvature. The proposed semi-analytical solution is validated using experimental results of the seismic energy dissipation device components which have been selected as a sample of a real engineering system. Also, validation is done via finite element analysis of six different cantilever beam models with varying geometric and material characteristics. A satisfying agreement between the proposed semi-analytical results and the subsequent experimental and numerical results is herein achieved, confirming its reliability.

Being gradually softened approach for solving large deflection of cantilever beam subjected to distributed and tip loads

The solutions to small deflections of uniform cantilever beams have been obtained and widely used. However, when the deflections become large, it is quite challenging to derive the solutions due to the geometric nonlinearity, especially for non-uniform beams. To handle that, in this paper, a novel and an efficient method called being gradually softened approach (BGSA) is proposed to predict the large deflections of uniform and non-uniform cantilever beams subjected to distributed and tip loads. The cantilever beam is initially regarded as a rigid beam and then is gradually softened from the free end to the fixed end to solve the deflection of the cantilever beam. As new rigid units of the cantilever beam are softened, the direction of the force load acting on the previous softened units changes. Because of that, the deflections of the previous softened units need to be updated accordingly. Experimental results show that this method can solve the large deflections of uniform and non-uniform cantilever beams that experience distributed and tip loads with high accuracy.

Optimization algorithm-based approach for modeling large deflection of cantilever beam subject to tip load

The modeling of beam mechanisms, especially non-uniform beams, becomes complicated due to the geometric nonlinearity that is proved to be significant with large deflection. A new method, called optimization algorithm-based approach (OABA), is proposed to predict the large deflection of uniform and non-uniform cantilever beams, in which an optimization algorithm is exploited to find the locus of the beam tip. The Euler-Bernoulli beam theory is employed here. With the derived locus of the beam tip, the deflection curve of the cantilever beam can be calculated. The optimization algorithm in this paper is embodied in a particle swarm optimization (PSO) algorithm. Experimental results show that the proposed method can precisely predict the deflection of the uniform and non-uniform cantilever beams. The maximum error is limited to 4.35% when the normalized maximum transverse deflection reaches 0.75. To demonstrate the effectiveness of this method in analyzing compliant mechanisms, we also exploited this method to predict the deformation of a compliant parallel-guiding mechanism.

Influence of Piping on On-Line Continuous Weighing of Materials inside Process Equipment: Theoretical Analysis and Experimental Verification

Due to the continuity and complexity of chemical systems, piping and operating conditions will have a significant effect on the on-line continuous weighing of materials inside process equipment. In this paper, a mathematical model of the weighing system considering piping and operating conditions was established based on the gas–liquid continuous heat transfer weighing process. A theoretical criterion which can be extended to any continuous weighing system of the materials inside equipment with connected piping is obtained through the mechanical derivation between the material mass, the cantilever beam deflection, the strain gage deformation, and the bridge output voltage. This criterion can effectively predict the influence of piping on weighing results with specific accuracy, and provide a basis for engineering optimization design. On this basis, a set of gas–liquid continuous contact weighing devices was built. The static/dynamic experimental results showed that the accuracy of the system meets the set requirements.

Novel photostrictive 0-3 composites: A finite element analysis

Simultaneous action of photovoltaic effect and converse piezoelectric effect will induce the photostrictive effect. In contrast to the naturally occurring photostrictive material, the present study proposes a 0-3 photostrictive composite. The current photostrictive composite comprises of poly{4,8-bis[5-(2-ethyl-hexyl) thiophen-2-yl] benzo[1,2-b:4,5-b′] dithiophene-2,6-diyl-alt-3-fluoro-2-[(2-ethyl-hexyl) carbonyl] thieno[3,4-b] thiophene-4,6-diyl} (PTB7-Th) as organic photovoltaic polymer matrix and Pb(Mg1/3Nb2/3)O3-0.35PbTiO3 (PMN-35PT) as the particulates. The current study shows that the present 0-3 photostrictive composite is a suitable alternative for the most popular lead-based photostrictive material. While evaluating all the effective elastic, dielectric, piezoelectric, and pyroelectric properties of 0-3 photostrictive composite, the effect of local fluctuations was incorporated in representative volume element (RVE) using the finite element method. A finite element formulation using a degenerated shell element is derived to simulate the actuation response of the proposed 0-3 photostrictive composite. Numerical studies have been performed on cantilever and simply supported beams. The maximum tip and center deflection of cantilever beam and simply supported beam bonded with 0-3 photostrictive patch is mm and mm, respectively. The maximum value of the effective piezoelectric coefficient effective thermal expansion coefficient effective Young’s modulus and effective pyroelectric coefficient of proposed 0-3 photostrictive composite are m/V, 4.59 1.63 N/m2, and 7.57 C/m2 K, respectively, obtained at 25% volume fraction of particulates. This study opens possibilities of photostrictive coupling in composites.

Drag reduction of a blunt body through reconfiguration of rear flexible plates

We investigate the quasi-static reconfiguration of rear parallel flexible plates on the drag coefficient of a blunt body. The drag coefficient, plates deformation, and main features of the turbulent wake are characterized experimentally in a towing tank. It is found that increasing the flexibility of plates leads to an important drag reduction, induced by the progressive streamlining of the trailing edge due to plates deformation. The study of the Vogel exponent is adopted here to evaluate the limit on the potential drag reduction at large values of the Cauchy number, which is shown to be mainly caused by the growth in the vibrating amplitude response of plates. The plates deformation is analyzed by means of image processing, showing that their shapes mainly follow the first modal form of a cantilever beam deflection, although a slight concavity develops toward the plates tip for large Cauchy numbers. To further analyze this process, the empirical flow loading along the plates is estimated by a modified beam theory assuming a distributed load given by a power law. The experimental fitting shows that for large flexibility, the load diminishes at the rear tip. Besides, the progressive deformation of plates is shown to weaken the shedding of vortices and reduce the size of the recirculation bubble. Finally, an affine direct relationship between recirculation bubble aspect ratio and drag coefficient has been proposed in order to quantify the linkage between near wake modifications and hydrodynamic improvement provided by the trailing edge streamlining.

Adaptive Polynomials for the Vibration Analysis of an L-Type Beam Structure with a Free End

Vibration analysis using the component mode method has been less popular than before, since computers are powerful enough to solve complicated structures by a single large finite model. However, many structural engineers designing local structures on a ship still need simple tools to check anticipated vibration problems during their design work. Since most of local structures on a ship are simple enough to consist of several substructures, the component mode method could be of use as long as good, natural mode functions can be provided so that reasonable natural frequencies can be yielded. In this study, since mode polynomials based on static deflection of cantilever beams fail to work to cover the various configurations of L-type beams with a free end, two alternatives are suggested. One is based on more flexible mode functions—we call them adaptive polynomials. The other is a purely mathematical approach, which makes realistic mode functions unnecessary. Suggested alternatives yield very good numerical results.

Fatigue life prediction of cfrp composites in plane bending by modal analysis

This is investigation of the fatigue behaviour of carbon fiber reinforced polymer laminates under various angles of deflections of cantilever beam in bidirectional (R=-1) plane bending. The Unidirectional 45˚ carbon fiber oriented CFRP composite were tested at different cantilever bending angles at frequency of 8 Hz. The non- destructive modal testing is conducted to evaluate reduction in structural stiffness in fully reversed plane bending in terms of natural frequency. The modal test at specific intervals is conducted by interrupting the fatigue test. The curve fitting technique for prediction of fatigue life over experimental analysis is used to formulate behaviour of CFRP in plane bending fatigue. It is shown that A Non-destructive Testing method (Modal Test) can be applied for the fatigue life estimation of CFRP laminates. The natural frequency reduction model is able to represent the overall reduction in stiffness due to fully reversed plane bending fatigue.

Cost‐Effective and Ultraportable Smartphone‐Based Vision System for Structural Deflection Monitoring

This work demonstrates the viability of using a smartphone‐based vision system to monitor the deflection of engineering structures subjected to external loadings. The video images of a test structure recorded by a smartphone camera are processed using the state‐of‐the‐art subset‐based digital image correlation (DIC) algorithm to extract the vertical image displacement of discrete calculation points defined on the test object. The measured vertical image displacement can be converted to deflection (vertical displacement) by easy‐to‐implement scaling factor determination approaches. For accuracy validation, laboratory experiments using a cantilever beam subjected to external loadings were performed. The deflection and inherent frequency of the test cantilever beam measured by the proposed smartphone‐based vision system were compared with those measured by conventional dial gauges and a dynamic strain gauge. The relative errors were estimated as 1% and 0.15% for deflection and inherent frequency, respectively. Outdoor real bridge deflection monitoring tests were also carried out on an overpass with subway passing by, and the measured deflection‐time curves agree well with actual situations. The cost‐effective, ultraportable, and easy‐to‐use smartphone‐based vision system not only greatly decreases the hardware investment and complexity in deflection measurement system construction, but also increases the convenience and efficiency of deflection monitoring of engineering structures.

Simulation of Mechanical Behaviour of Materials Using Constant Boundary Elements - A Discussion on the Accuracy of Results for Beams

The Boundary Element Method (BEM) is one among the most popular simulation techniques employed to simulate mechanical behaviour of materials, including smart engineering materials. Although BEM is a quite well-established numerical technique, literature tells that the method may not be well suited to simulate structures where one or two of the dimensions is much smaller than the remaining dimension/s (for a 3D problem). Hence in this work, deflection of a cantilever beam is simulated using constant boundary elements to get a feel of the accuracy of the BEM when used to simulate such type of structures. Although the concept is not new, the study assumes significance because studies which list the results in detail are not readily found in the literature. In this study, the results are obtained for different mesh resolutions also. The results indicate that - as expected - constant boundary elements are not a good choice for simulating the mechanical behaviour of smart materials when the structural member to be simulated is thin. Although it is a known fact that constant boundary elements converge very slowly, the present study helps to get a clearer picture on the accuracy and the convergence rate that one can expect from constant boundary elements. This paper heavily borrows content from this author’s PhD thesis [1]. The geometry considered in this paper is a beam. One may also note that the author is publishing another paper [2] (“Simulation of Mechanical Behaviour of Materials using Constant Boundary Elements - A Discussion on the Accuracy of Results for Bars”) that is very similar to this paper except that the geometry considered in that paper is a bar.

A three dimension lattice-spring model with rotational degree of freedom and its application in fracture simulation of elastic brittle materials

Applying parameter mapping theory, this paper establishes a new three dimension lattice-spring model with rotational degree of freedom (3D-LSMR). This 3D-LSMR contains nearest neighbor, next nearest neighbor and third nearest neighbor which highly increases the accuracy of system. Compared with the general lattice spring model, 3D-LSMR adds the rotational and tangential degrees of freedom, whose spring parameters are obtained by finite element parameter mapping. The traditional lattice spring model only considers the normal interaction between two points (the Poisson’s ratio is fixed), which limits the application of the lattice spring model in a wider range of materials. Some scholars proposed to add shear spring into the traditional model to solve the problem of fixed Poisson’s ratio, but the rotation invariance could not be maintained. The main reason is that the shear spring can’t distinguish the difference of tangential velocity (or displacement) between the two particles due to the common rotation or shear. Therefore, the rotation of the whole rigid body may cause incorrect generation of additional strain energy inside the shear spring. 3D-LSMR model is able to maintain rotation invariance and reproduces different Poisson’s ratios because of the spring parameters with rotational degrees of freedom and the rotation effect of lattice points. In this paper, the finite element stiffness matrix with rotational freedom is derived by using 3D-LSMR as the basic mechanical model, and the parameter mapping theory of spring stiffness coefficient is introduced. By means of numerical simulation, the large deflection of slender cantilever beam, elastic symmetrical collision and the simulation of dynamic fracture for concrete L-specimen are checked and calculated respectively, and then the correctness of the model is verified.

Lattice spring model with angle spring and its application in fracture simulation of elastic brittle materials

Lattice Spring Model with Angle Spring (LSMA) is a novel type of lattice model. Compared with the general lattice spring model, LSMA adds the rotational and tangential degrees of freedom, whose spring parameters are obtained by finite element parameter mapping. The traditional lattice spring model only consider the normal interaction between two points (the Poisson’s ratio is fixed), which limits the application of the lattice spring model in a wider range of materials. Some scholars proposed to add shear spring into the traditional model to solve the problem of fixed Poisson’s ratio, but the rotation invariance could not be maintained. The main reason is that the shear spring can not distinguish the difference of tangential velocity (or displacement) between the two particles due to the common rotation or shear. Therefore, the rotation of the whole rigid body may cause incorrect generation of additional strain energy inside the shear spring. LSMA model is able to maintain rotation invariance and reproduce different Poisson’s ratio because of the spring parameters with rotational degrees of freedom and the rotation effect of lattice points. In this paper, the finite element stiffness matrix with rotational freedom is derived by using LSMA as the basic mechanical model, and the parameter mapping theory of spring stiffness coefficient is introduced. By means of numerical simulation, the deflection and rotation Angle of cantilever beam, shear wave and compressional wave velocity of stress wave and the simulation of compact tensile test are checked and calculated respectively, and the correctness of the model is verified.

Functionally graded wood filler–recycled polypropylene composite: Effect of mechanical loading on deflection of cantilever beam

Structures made from natural fiber–polypropylene composite material usually have uniform mechanical properties throughout. In some applications, such as in products with snap-fit assembly, it is desirable to have lower stiffness in some parts of the structure while having significantly higher stiffness at other parts of the same structure. In this research, the effect of changing the material arrangement and composition in a cantilever beam made from functionally graded natural filler–recycled polypropylene (FGNF-RPP) composite on the deflection behavior was investigated under static mechanical loads. The composite material was made using 10%, 20%, 30%, and 40% waste wood sawdust as a filler and arranged in different sequences to fabricate beams having 30–40, 20–30–40, and 10–20–30–40 hybrid sections along the length. The deflection behavior was investigated by both experiment and finite element modeling. The results showed that the 30–40 setup produced the least deflection when the 40% end of the beam was fixed, while the 10–20–30–40 setup produced the highest stiffness when fixed at the 40% section. The study has shown that the FGNF-RPP structure can be custom-designed to obtain different stiffness along the same structure, thus making it possible to design products with varying stiffness.

Experimental and theoretical investigation of static deflection and natural frequency of stepped cantilever beam

ABSTRACT A maximum static deflection and natural frequency of aluminium cantilever stepped beam (two steps) were investigated experimentally and theoretically for different values of small and large diameters and for different lengths of larger diameter step. Eighty samples of aluminium beams were manufactured using turning machine. The range of the beam diameter was 12–20 mm and the length of beam was 45 cm. Classical Rayleigh method, modified Rayleigh method and finite element using ANSYS software method were adopted to calculate the maximum static deflection and the natural frequency. A good agreement was found for the static deflection at different positions of applied load between the experimental results and the theoretical results, ANSYS and modified Rayleigh method. The experimental results of the natural frequency showed that there was a consistent with the theoretical results particularly when there is a minor difference between the larger and smaller diameters of the stepped beam.

Enhancement of Micro cantilever’s Rectangular and Triangular Beam for Improvising the Sensitivity of Biosensor – a Comparative Study

Micro-Electro-Mechanical Systems (MEMS) is the mixing of factors like mechanical, sensors, actuators, and electronics on a common substrate through the consumption of micro-fabrication era or micro-technology. A type of beam is called “cantilever” which provides assistance at only one end. This work affords to have a look on MEMS based entirely micro cantilever beama which are employed in medical software systems and are a component to slicing region reasonably evolved sensors. The beams of the Cantilever are the most omnipresent systems within the area of micro-electromechanical structures (MEMS). MEMS cantilevers are normally made from silicon (Si), silicon nitride (Si3N4), or poly-silicon. A procedure on growth in deflection of micro cantilever beam is essential for enhancing the sensitivity of biosensor. The sensitivity level of a microcantilever biosensor relies upon on its deflection that occurs because of the antigen-antibody interplay. The deflection can be elevated by way of growing the length or lowering the thickness of micro cantilever beam but it’ll minimize the reverberating frequency of the beam. This minimizes the resonant frequency and that makes the cantilever vulnerable to thermal noise and low frequency vibrations which immediately affect the size of deflection. In this method, the rectangular and triangular shapes are taken into consideration and the comparative evaluation is established. The outcomes display that the deflection of triangular beam is two times extra than rectangle fashioned beam.