Values Of Natural Frequencies Research Articles

MODAL ANALISIS PADA ROTARY KILN DENGAN MENGGUNAKAN METODE ELEMEN HINGGA

This research is based on the general damage to the rotary kiln due to continuous use. Then the results from the burned in a Rotary Kiln So we need a prevention to overcome it. Testing the vibration mode on a rotary kiln machine is a solution to overcome the limit on the use of the finite element menthod. With the completion procedure of finite element software with the step of Rotary Kiln Geometry Modeling Process, Rotary Kiln Geometry Import Process, Rotary Kiln Geometry Import Process, Material Data Input Process, Meshing Process, Determination of Boundary Conditions, Running Process, and Port Processing. The results of this study are from the finite element simulation obtained in the form of the frequency value of the natural response of the structure and the deflection due to vibrations that occur in the rotary kiln Indarung IV PT Semen Padang. And it was concluded that the vibration mode experienced by the rotary kiln has a natural frequency value, the vibration mode of the rotary kiln structure obtained a maximum value of 63.3 Hz, while the minimum value obtained a value of 41.805 Hz. The maximum deflection of the rotary kiln is obtained from the analysis results of 0.058981 mm while the minimum deflection value is 0.045 mm.

An Examination of the Vibrational Characteristics of a Diesel Engine Connecting Rod Using Modal Analysis

In this study, a connecting rod that belongs to a diesel test engine is examined with an experimental method and the Finite Element Method (FEM). The purpose of the experimental method is to obtain the Frequency Response Function. The graph of this function provides the necessary vibrational qualifications of the connecting rod. Obtained vibrational characteristics can be considered as natural frequencies, damping ratios and mode shapes that belong to these vibrational modes. While natural frequencies can be obtained with both of these methods, mode shapes could only be produced with FEM. The natural frequencies that are obtained with experimental method is determined for the first mode as 0,625 Hz, for the second mode as 4,38 Hz, and for the third mode as 8,13 Hz. The natural frequencies that are obtained with FEM is determined for the first mode as 0,04575 Hz, for the second mode as 8,3861 Hz, and for the third mode as 8,9434 Hz. Considering the frequency range of the connecting rod, this study shows that the natural frequency values which is determined from this study and any frequency value of the connecting rod while the engine is running would not coincide. Besides damping ratios are calculated for the first mode as 19,766 %, for the second mode as 8,0116 %, and for the third mode as 3,4839 %. It is determined which modes have bending and torsion mode shapes. The results provide the useful information about the weaknesses and the vibrational qualifications that has to be improved in terms of dynamical and structural analysis of the connecting rod or engine itself.

Experimental Study on the Influence of Micro-Abrasive and Micro-Jet Impact on the Natural Frequency of Materials under Ultrasonic Cavitation

The higher the natural frequency of the material is, the more resistant it is to deformation under impulse loading. To explore the influence of micro-abrasive and micro-jet impact on the natural frequency and resonance amplitude value of the material under ultrasonic cavitation, 18 sets of single-factor controlled variable ultrasonic cavitation experiments were carried out on a polished specimen of 6061 aluminum alloy (30 mm × 30 mm × 10 mm). With the increase of the abrasive content in the suspension, the natural frequency of the workpiece first increased, then decreased and remained stable. With the increase of the ultrasonic amplitude, the resonance amplitude value of the material increased, reaching the maximum at 0.1789 m·s−2 and then decreased. The effect of ultrasonic amplitude on the natural frequency of the material was greater than that of the abrasive content, and the effect of the abrasive content on the common amplitude value was greater than that of the ultrasonic amplitude. This research provides a certain reference significance for exploring the influence of power ultrasonic micro-cutting on material properties and avoiding the occurrence of resonance phenomenon of the workpiece under different working conditions.

KAJIAN RESPON JEMBATAN DI ACEH UTARA TERHADAP GEMPA BERDASARKAN DATA MIKROTREMOR

The parameters of the bridge's resistance to dynamic loads, such as natural frequency and damping ratio, were determined by theoretical and experimental modal analysis. Microtremor measurements were performed on two types of bridges: steel truss bridges and reinforced concrete bridges. The goal is to establish the value of the bridge's dynamic characteristics as well as the bridge's feasibility based on SNI 2833-2008's natural vibration period limit. The natural frequency of the dynamic test is used to compare natural frequencies to theoretical frequencies to determine the condition of the integrity and level of stiffness of the structure or structural elements. The HVSR (Horizontal to Vertical Spectral Ratio) approach is used to analyze microtremor data on the ground, while FSR (Floor Spectral Ratio) and RDM (Random Decrement Method) analysis is used to analyze microtremor data on bridges. According to the findings of the first case study, the natural frequency of the soil is 1.25–1.35 Hz. The steel truss bridge's natural frequency value from the FSR is 0.81–3.29 Hz, while the RDM values are 1.12–3.46 Hz, indicating that the frequency produced is less stable on the NS component. The damping ratio is 2.02–4.97% in this case. The same analysis was carried out on a different type of bridge in the second case study, with a natural ground frequency of 1.11 - 1.47 Hz. The reinforced concrete bridge's natural frequency value from the FSR is 2.21 - 3.62 Hz, and the RDM results are 2.30 - 3.62 Hz. In each component, the frequency found tends to be stable. The damping ratio result is 2.05 - 4.81%. The period of the experimental results shows identical results to the period of the theoretical calculation results, with the average experimental result period being 7.24% greater than the period of the theoretical calculation results. According to the experimental data, the bridge damping ratio is around 3.16% . This result is in accordance with the literature, which is around 2-5%.

KAJIAN RESPON GEMPA DAN KERENTANAN BANGUNAN PUBLIK BERDASARKAN DATA MIKROTREMOR DI ACEH UTARA

Analysis of building and soil interactions is an essential part of building construction appraisal. In this article, the response of buildings to earthquakes identified by determining the natural frequency of the soil and the value of the natural frequency of buildings on each floor, as well as examining the relationship between the natural frequency of the soil and the natural frequency of the building. This article will also identify attenuation factors for type of public buildings that have different functions, namely school and campus buildings, and determine the effect of resonance on building infrastructure. Analyzed public buildings include rest area buildings, elementary school buildings, junior high schools, and campuses. The variable number of floors is also an aspect that will be observed. Microtremor data research utilizes a near-broadband seismometer. The vibration recording device is placed on the ground, and the reviewed buildings are school and campus. Data collection was carried out when the condition of the building was not loaded, measurements were made on each floor of the building as many as 5 points on the floor and 1 point on the ground for 30 minutes at each measurement point. The methods used are Horizontal-to-Vertical Spectral Ratio (HVSR), Fast Fourier Transform (FFT), Floor Spectral Ratio (FSR), and Random Decrement Method (RDM). The calculation results show that the natural frequency value of the soil is in the range of 0.7 to 0.85 Hz except for the location of the campus building that the value reaches 6.868 Hz, the reason of this value is the type of soil in the area is dominated by hard rocks. The natural frequency of the building (f0) is in the range of 2.557 Hz to 4.292 Hz, a low frequency and meets the requirements of SNI, for the damping ratio of the building is in the range of 2.002 to 4.974%, the low category meets the attenuation standard of 2 to 5%, the five review buildings have a low resonance level, the natural vibration period of the building is in a safe limit according to SNI 17-02-2012 and the vulnerability index is low.

FAILURE ANALYSES OF TOWER CRANE USING FEM AND THEORETICAL STUDIES

This paper describes the technique to explicitly increase the tower crane’s stability during cyclones through modal analysis in FEM. For this, modal analyses of a boom, mast, and tower crane are carried out individually to minimize the tuning effect of natural frequencies. The study explains the methodology to increase the stiffness using bracings in the mast expressed in modal parameters. In FEM analysis, bracings are applied in fixed support along the vertical mast of the tower crane. For this purpose, a 1/10 scale model of “Potain MCi85 A/B” tower crane was modelled in Nx-Unigraphics. Theoretical analysis of the boom’s natural frequencies and its counterweight is assumed as cantilever beam and mast in form column. The values of natural frequencies of tower cranes under different boundary conditions are obtained through Galerkin and Dunkerley’s mathematical expressions. Theoretical and FEM results established similar trends of increasing stability as revealed in terms of natural frequencies of the tower crane.

Statistical investigation of the effect of different damage conditions on the modal frequency value of a steel beam

This study aimed to parametrically investigate the changes in modal frequency values on a steel beam caused by specified damaged schemes. In this context, the ANSYS Workbench software program was used to create a steel profile's finite-element model. A cantilever steel beam profile is created with a 60x60 mm cross-section and 3m length utilizing single-sided fixed support. In the finite-element model, the crack depth, width, and distance to the support were parametrically assigned as the damaged scheme to the steel profile. To investigate the effects of those damages on the modal frequency values of the steel profile, first of all, the modal frequency values for undamaged cases corresponding to the first ten-mode shapes were obtained. Then, the specified crack properties were determined parametrically, and the changes in frequency values for damaged cases were examined. In addition, a comparative evaluation of the effect of crack properties on the natural frequency of the steel element was performed by utilizing response surface and six sigma analysis. The analysis results demonstrated that specified crack schemes have different effects on different modal natural frequencies. The applied response surface and six sigma analysis provided important statistical data on the modal natural frequency values of the steel beam.

Analysis of mechanical properties of spatial truss structures sections

The paper presents the results of computational study of sections of spatial truss structures. They can form large supporting structures on spacecraft to place onboard equipment. The calculations were carried out by the finite element method in FEMAP with Nastran. The chosen section, the object of study, is a set of straight rods rigidly connected at the nodes in such a way that the cross section of the truss structure is a triangle. Calculation models, procedures for calculation and results analysis are presented. The purpose of the calculation is to determine how the relative position of the rods in the structural scheme affects the mechanical properties of the structure. The main criterion for strength estimating was the magnitude of the stresses derived by load. Stiffness was determined by the value of the first natural frequency. The sequential addition of rods and varying their connection allow modifying the structural schemes of truss structures. Next, the mechanical properties of the structure which effected by made modifications were evaluated again. Thus, six structural schemes of sections of the truss structure, obtained from the results of the study, have been developed. At the same time, the mass of the section, its shape and dimensions, the material and shape of the rods section as well as the initial and boundary conditions, remained unchanged. Based on the results of the analysis, someone can notice that each structure has unique mechanical characteristics. Thus, the paper gives recommendations for choosing a specific structural scheme of the section, depending on the required operating conditions and acceptable manufacturing technology. So, the criteria for choosing one of the above various sections of a truss structure or the principle of its building can be the complexity of manufacturing, maximum stiffness and strength, or minimum displacement. Structural schemes of sections with the highest strength and capability have been selected for use as part of spatial truss rods of spacecraft.

Influence of swirling flow parameters on frequency response of a simplified draft-tube in presence of cavitation

This paper focuses on investigating the influence of swirling flow parameters on frequency response of a simplified draft-tube under different cavitation numbers by using experimental approaches. The experiments are conducted for three swirl configurations featuring different swirl intensities conforming with the flow field in the draft-tube during high-load operation of a hydro-turbine. For this purpose, three stationary-blades swirl generators are used to generate axisymmetric swirling flows in a Venturi-tube with a diffuser resembling the draft-tube cone of a hydraulic turbine; and for each swirl configuration, the experiments are conducted over a wide range of cavitation numbers and flowrate values. Experiments include transient pressure measurements at different locations and high-speed visualization of cavitating flow in the Venturi. The results of transient pressure measurements are analyzed to identify the frequency spectrum of pressure fluctuations in the draft-tube. The first natural frequency of the draft-tube is identified for a wide range of operating conditions; and several correlations are established for its relationship with the flow parameters (cavitation number and swirl number). It is observed that the operating flowrate does not affect the natural frequency of the draft-tube. An unstable mode of cavitating flow is highlighted and a transition from stable to unstable modes is identified. Investigating the transition mechanism from the stable to the unstable modes of cavity led to identifying an excitation force for the onset of cavitation instability in the draft-tube. High-speed visualization of cavitation in the draft-tube is performed to capture the mean cavity volume and its fluctuations in time domain. The 1st natural frequency of the draft-tube is further predicted by analyzing the fluctuations of cavity volume. Furthermore, a 1D hydroacoustic model is also used to predict the local wave speed and the 1st natural frequency of the draft-tube. The obtained values of natural frequency from cavity visualization and 1D modelling are compared with the results of pressure measurements at the end.

Natural Vibration Characteristics Analysis of a High-Rise Reinforced Masonry Structure Based on Field Test Data

In structural response array observation, the vibration response of a structure during an earthquake or from the natural environment is recorded and stored using high-sensitivity strong motion seismographs, and the dynamic characteristics of the structure are analyzed and determined using random signal data processing technology. Due to the use of field test data for analysis, this may be the most accurate and effective way to obtain the actual characteristics of the structure, which can be further used to verify the accuracy of theoretical analysis, experimental results, and numerical simulations. Therefore, this technique plays an important role in earthquake prevention and disaster reduction, with the application of strong motion observation data. In this paper, field vibration tests were performed on the highest reinforced masonry structure in China. With the test environmental vibration data, the natural vibration frequency values and mode shapes of the structure were identified using the peak picking method. A numerical modal analysis was then performed to verify the accuracy of the field test results. In addition, the structural response records obtained during an earthquakes in Songyuan were also used to identify the natural vibration frequency of the structure and the changes in the natural vibration frequency before, during, and after the earthquake. The results showed that the structure was not damaged during the earthquake and remained in an elastic state.

A Prediction Model for Natural Frequencies on Kevlar/Glass Hybrid Laminated Composite using Artificial Neural Networks (ANN)

This paper aims to developa prediction model for the natural frequencies on Kevlar/Glass hybrid laminated composite plates using Artificial Neural Networks (ANN). Finite element simulations were performed to generate data for the natural frequencies under various lamination schemes and fibre angles. Rectangular symmetric and anti-symmetric hybrid laminated composite plates were modeled using commercial software, ANSYS, and meshed using shell elements. The Matlab-ANN tool was used to generate the prediction model, where the generated data (natural frequencies) from the finite element simulations were used for training and testing of the prediction model. The network adapted a two-layer feed-forward algorithm. The adequacy of using ANN in predicting natural frequencies was verified, where the coefficient of determination, R2, was found to be over 0.995. The overall results proved that ANN could be a useful tool, where the prediction model produced an error of less than 5%, when compared to the simulated values of natural frequency of various hybrid laminated composites using finite element analysis. These findings concluded that the current study had contributed significant knowledge in understanding the prediction of natural frequency on hybrid laminated composite using the ANN model.

ICAE 2021 - Preface

One of the applicable shell structures related to underwater systems, covering riser pipes, ice-breaking equipment, underwear noise migrations, ballast water components, and gliders, can be considered Linked Hemispherical-Conical Shell (LHCS) structures. Accordingly, the ensuing investigation is provided to compute the Natural Frequency Values (NFVs) of the LHCS, with the opening angle at starting part of the hemispherical structure (which will be studied for the first time) enhanced by graphene-based nanocomposite materials containing Graphene Nano-Platelet (GNP) and Graphene Oxide-Powder (GOP) nanocomposites. For this reason, the Halpin-Tsai approach and the rule of the mixture are engrossed in determining the productive functionally graded mechanical criteria of the graphene-based nanocomposite materials. To obtain the main formulations of the LHCS, Donnell's assumptions and First-Order Shear Deformation Theory (FOSDT) are also engaged. Additionally, Hamilton's technique is involved in finding the kinetic equations coupled with the hemispherical and the conical parts of the LHCS. Next, the distinguished approach, Generalized Differential Quadrature (GDQ) program, is applied to discrete the kinetic equations. Subsequently, the standard eigenvalue problem determines the NFVs related to the GNP and GOP nanocomposites LHCSs. At termination, the exactness of the suggested scheme is confirmed by comparing the provided outputs with the NFVs of the submitted work (which can be used as the benchmark) with responses determined by FEM commercial software and the only benchmark study that exists in the literature. Furthermore, some novel cases are solved to estimate the effects of different geometric criteria of the LHCS, such as the opening angle of the hemispherical, the Half-Apex (HA) angle of the conical segment, the thickness related to the structure, and also the effect of GNP and GOP scattering models spread in conjunction with the thickness of the LHCS on the NFVs coupled with the GNP and GNP nanocomposites LHCS.

Vibration Analysis and Human Comfort Assessment of Building Subjected to Wind Dynamic Loads

AbstractIn the last few decades, Brazilian cities have presented a substantial increasing associated to the design and construction of tall and slender buildings. However, this architectural trend has produced flexible structural systems, with low natural frequency values and, therefore, more susceptible to excessive vibrations problems, when subjected to the nondeterministic wind loadings. Having these ideas in mind, this research work aims to study the dynamic structural response and evaluate the human comfort of a 40‐storey reinforced concrete building with 150 m high and floor dimensions of 30 m by 60 m. In this research work the Spectral Representation Method (SRM) was adopted to generate the wind nondeterministic dynamic loadings, based on the use of pressure coefficients calculated through the use of different strategies such as the HFPI‐TPU and DEDM‐HRP databases, CFD modelling and the Brazilian design standard NBR 6123. The numerical model developed for the reinforced concrete building dynamic analysis, adopted the usual mesh refinement techniques present in finite element method simulations and implemented in the ANSYS program. The main conclusions obtained in this work aim to alert the civil engineers to the relevant modifications associated with the dynamic response, when different strategies are used to calculate the wind pressure coefficients on the building's facade.

Vibration Analysis of a Symmetric Double-Beam with an Elastic Middle Layer at Arbitrary Boundary Conditions

Vibration of double beams with an elastic connected layer has been studied in this paper by assuming that the beam is a Bernoulli-Euler beam. The natural frequencies equations of the symmetric double beam have been computed at arbitrary boundary conditions. The behavior of those frequencies has been investigated with a change in the stiffness of connected layer, modulus of elasticity of beam, length of beam, mass density of beam, and thickness of beam. The high effect of the elastic connected layer on the higher natural frequencies of a cantilever double beam is less than that in the clamped and free double beams. The increase in the thickness of upper and lower beams made a high increase in the values of lower natural frequencies in all types of beams. The change in the modulus of elasticity values of double beam becomes high on the lower natural frequencies but without enlarging the influence on the higher frequencies, especially in the cantilever double beam. The similar effect of change in the mass density of the beam resulted in the same influence on the higher and lower natural frequencies in all types of beams. The length of the beam enlarges the influence on the higher natural frequencies of clamped and free.

Wave frequency responses estimate of the nanocomposite linked hemispherical-conical shell underwater-like bodies with the impacts of two types of graphene-based nanofillers

One of the applicable shell structures related to underwater systems, covering riser pipes, ice-breaking equipment, underwear noise migrations, ballast water components, and gliders, can be considered Linked Hemispherical-Conical Shell (LHCS) structures. Accordingly, the ensuing investigation is provided to compute the Natural Frequency Values (NFVs) of the LHCS, with the opening angle at starting part of the hemispherical structure (which will be studied for the first time) enhanced by graphene-based nanocomposite materials containing Graphene Nano-Platelet (GNP) and Graphene Oxide-Powder (GOP) nanocomposites. For this reason, the Halpin-Tsai approach and the rule of the mixture are engrossed in determining the productive functionally graded mechanical criteria of the graphene-based nanocomposite materials. To obtain the main formulations of the LHCS, Donnell's assumptions and First-Order Shear Deformation Theory (FOSDT) are also engaged. Additionally, Hamilton's technique is involved in finding the kinetic equations coupled with the hemispherical and the conical parts of the LHCS. Next, the distinguished approach, Generalized Differential Quadrature (GDQ) program, is applied to discrete the kinetic equations. Subsequently, the standard eigenvalue problem determines the NFVs related to the GNP and GOP nanocomposites LHCSs. At termination, the exactness of the suggested scheme is confirmed by comparing the provided outputs with the NFVs of the submitted work (which can be used as the benchmark) with responses determined by FEM commercial software and the only benchmark study that exists in the literature. Furthermore, some novel cases are solved to estimate the effects of different geometric criteria of the LHCS, such as the opening angle of the hemispherical, the Half-Apex (HA) angle of the conical segment, the thickness related to the structure, and also the effect of GNP and GOP scattering models spread in conjunction with the thickness of the LHCS on the NFVs coupled with the GNP and GNP nanocomposites LHCS.

Influence of connection stiffness on static-dynamic behavior of steel frames

The growing problems of excessive vibration in steel structures due to human rhythmic activities and vibrating machinery have led to the need for increasingly rigorous dynamic analysis in order to verify excessive displacements and ensure the users’ comfort. The present work aimed to carry out, via numerical simulation in ANSYS Mechanical APDL software, static, modal and harmonic analysis in steel frames with two floors and two bays in order to investigate the influence of the connection’s stiffness on the behavior of the structure. The results obtained showed that the natural frequency value of the models increases as the stiffness of the beam-column connections is increased. However, due to the harmonic analysis performed, it was not possible to delineate a behavior between the stiffness of the connections and the amplification.

Layout optimization of pin-jointed truss structures with minimum frequency constraints

Controlling the frequency response of an engineering component or structure is important in the aerospace and automotive sectors and is a key consideration when seeking a new and more efficient design for a given component. In this contribution, the standard truss layout optimization procedure is modified to incorporate semidefinite constraints to limit the minimum value of the first natural frequency. Since this increases the computational expense and reduces the scale of the problem that can be solved, a bespoke algorithm incorporating an adaptive ‘member adding’ procedure is proposed and applied to a number of benchmark example problems. It is demonstrated that this allows problems to be solved with relatively fine numerical discretization, allowing modified structures with an acceptable minimum first natural frequency response to be successfully identified.

An investigation of the effect of tapered angle and boundary condition on natural frequency of different ceramic coated Ti-6Al-4V alloy with finite element analysis

In recent years, the interest in light metals has increased due to the increasing demand for components with high specific strength and long service life in the industry. In this context, titanium alloys have become very common and popular owing to their high strength/weight properties and superior refractory characteristics. In this study, the effect of boundary condition and tapered angle on the natural frequency and vibration behavior of the beam was investigated in Ti-6Al-4V beams coated with three different ceramic materials; Al2O3, AlN, and TiB2. Tapered angle values are considered as 0°, 0.2°, 0.4°, 0.6° and 0.8°. Besides, boundary conditions were evaluated in two conditions including left side fixed or both sides fixed. All analyzes were performed in the finite element-based Ansys APDL 19 program. According to the results obtained from the analyses, it was observed that there was a change in the natural frequency values according to the type of coating material, but no difference was found in terms of increase/decrease tendency. In addition, the resultant displacement values were determined for all samples. The results indicated that the resultant displacement values were severely affected by the tapered angle. A decreasing resultant displacement trend was observed in all samples with increasing tapered angle.

Диссипативные свойства трехслойных композитных структур. 4. Численный эксперимент

Object and purpose of research. The study is concerned with a three-layer plate formed by two rigid anisotropic layers and a soft medium isotropic layer of viscoelastic polymer. Each rigid layer presents anisotropic structure formed by a finite number of randomly oriented orthotropic viscoelastic layers of composites. The paper is intended to study the influence of reinforcement orientation of rigid layers, relative thickness of the soft layer of an isotropic viscoelastic polymer and the ambient temperature on values values of natural frequencies and mechanical loss factors of the coupled damped oscillations in symmetric and assymetric plates. Materials and methods. Numerical experiment using a computer program implementing the previously proposed method for solving coupled differential equations of damped oscillations in anisotropic three-layer plates [2]. Main results. It was shown that in unsupported globally monoclinic symmetrical three-layer rectangular plate a bendingtorsional interaction occurs, generating mutual transformations of the eigenforms of the coupled oscillation modes if at least in one of the directions of the plate one of the eigenforms is characterized by an even number of quarters of the wave, and the other eigenform is characterized by an odd number of quarters of the wave. In unsupported globally orthotropic asymmetric three-layer rectangular plate interaction of bending modes of oscillations occurs in two mutually orthogonal planes, if both eigenforms are characterized by either an even or an odd number of wave quarters in main directions of the plate. It was found that each mode of natural oscillations of both symmetric and asymmetric three-layer plates has its own effective relative thickness of the soft layer of an isotropic viscoelastic polymer corresponding to the maximum level of dissipative properties. A further increase in the relative thickness is often accompanied by a decrease in values of the mechanical loss factors. The significant influence of ambient temperature on natural frequencies values and mechanical loss factors of all considered oscillation modes of symmetric and asymmetric unsupported rectangular three-layer composite plates is demonstrated. Conclusion. It was found that coupled damped oscillations of a symmetric three-layer plate are described by two systems of differential equations, with structures close to that of the systems of corresponding differential equations describing the damped oscillations of a quasi-homogeneous monoclinic plate. At the same time, the coupled damped oscillations of an asymmetric three-layer plate are described by two systems of differential equations that coincide with the systems of corresponding differrential equations describing the damped oscillations of a globally orthotropic three-layer plate.

Dynamic Analysis of a Curved Beam With Tuning of Elastic Modulus and Mass Density in Circumferential Direction

Abstract Deformation and stress fields in a curved beam can be tailored by changing its mechanical properties such as the elastic modulus/mass density, which is typically done using functionally graded materials (FGM). Such functional gradation can be done, for instance, by using particles or fiber-reinforced materials with different volume fractions along the beam length. This article presents in-plane vibrations of functionally graded (FG) cantilevered curved beams. Both semi-analytical and finite element modeling are employed to find natural frequencies and mode shapes of such beams. The natural frequencies obtained from the analytical solution and finite element analysis are in close agreement with an error of 6.2% when the variance of material properties gradation is relatively small. In the analytical approach, the direct method is employed to derive the governing linear differential equations of motion. The natural frequencies and mode shapes are obtained using the Galerkin and the finite element methods. First, three natural frequencies and corresponding mode shapes are analyzed for different elastic modulus/mass density distribution functions. Furthermore, the natural frequencies of FG curved beams with a crack are also investigated. Our results indicate that larger cracks near the clamped side of the beam significantly decrease the first natural frequency. In the second and third vibration modes, cracks located in the area with a maximum moment result in the lowest natural frequency values. However, the second and third natural frequencies of the cracked curved beam are not affected by the presence of a crack, if the crack is located at the nodal points of the curved beam.