Values Of Natural Frequencies Research Articles

Differential Quadrature Method for Vibration Analysis of Prestressed Beams

This paper investigates natural frequencies of free transverse vibrations of prestressed beams, and the governing equations and natural frequencies of the free vibration in related literatures are discussed and corrected. The differential quadrature methods (DQ) are applied directly to the corrected governing equations to get the the values of natural frequency numerically. Under the simple supported boundary conditions, the natural frequencies of model beam are numerically studied, and the physical parameters of the beam are analyzed respectively. The numerical results show that the natural frequency values increase with the growth of concrete strength and eccentricity of prestressed steels. But with the increase of the span length of beam and values of original prestressing force, the natural frequency values decrease.

The dynamical problem for the infinite elastic layer with a cylindrical cavity

The wave field of an infinite elastic layer weakened by a cylindrical cavity is constructed. The ideal contact conditions are given on the upper layer’s face and bottom face is rigidly fixed. The normal dynamic tensile load is applied to a cylindrical cavity’s surface at the initial moment of time. The Laplace and finite sin- and cos- Fourier integral transforms are applied successively directly to axisymmetric equations of motion and to the boundary conditions, on the contrary to the traditional approaches, when integral transforms are applied to solutions’ representation through harmonic and biharmonic functions. This operation leads to a one-dimensional vector inhomogeneous boundary value problem with respect to unknown displacements’ transformations. The problem is solved using a matrix differential calculus, which leads to an integral equation solved with a method of orthogonal polynomials. The field of initial displacements is derived after application of inverse integral transforms. The case of the steady-state oscillations was investigated. The normal stress on the rigidly fixed face of the elastic layer is constructed and investigated depending on the mechanical and dynamic parameters. Formulas for determining the normal stress for large values ​​of natural vibration frequencies were constructed.

Hybrid cross-tie system with passive dampers study

The authors have investigated the use of passive vibration dampers through the implementation of concentrated masses in the hybrid cross-tie system of a cable-stayed bridge. A 3D model of a cable-stayed bridge was built in ANSYS suite. The authors have studied the stress-strain behavior and dynamic characteristics of the model under the gravity load. The study has shown that the most effective model appears to be the one with passive dampers implemented by means of six concentrated masses. The increased stiffness of links of the concentrated masses had stronger effect on the model with passive dampers implemented by means of ten concentrated masses, however the model where passive dampers were implemented by six concentrated masses displayed comparable values of natural vibration frequencies with deflections in the spans being 3% lower, displacements of the towers being 8% lower, and longitudinal forces in the main cable being 6% lower. The results obtained by the authors allow for the conclusion that all models of a hybrid cross-tie system with passive dampers reviewed have high aerodynamic stability.

High Order Accurate Numerical Simulation of Vortex-Induced Vibrations of a Cooled Circular Cylinder Case using Solution Dependent Weighted Least Square Gradient Calculations

In this paper, the fluid-structure interaction problem: vortex-induced vibration of a cooled circular cylinder involving thermal buoyancy is numerically investigated. The elastically mounted cylinder having a temperature lower than the flowing fluid is modelled using mass-spring-damper hence allowed to vibrate in the transverse direction to the flow direction. The gravity is acting opposite to the flow direction. In-house fluid-structure interaction solver is developed based on Harten Lax and van Leer with contact for artificial compressibility Riemann solver. The arbitrarily Lagrangian-Eulerian formulation is employed here, and the mesh is dynamically moved using radial basis function-based interpolation. The solution-dependent weighted least squares based gradient calculations are developed to achieve higher-order accuracy over unstructured meshes. The laminar incompressible flow at Reynolds number, Re = 200, and Prandtl number, Pr = 0.71, is simulated for the mass ratio of 1 and reduced damping coefficient of 0.001. The flow is investigated for Richardson number (-1, 0) and over a wide range of natural frequencies of the cylinder. The heat transfer characteristics from a cylinder are captured and compared with the existing literature results. From the study, it can be observed that in the presence of the thermal boundary layer, the oscillation of the cylinder increases to its maximum amplitude, particularly for values of natural frequencies (0.063 – 0.3).

Динамічна втрата стійкості складеною нанокомпозитною оболонкою

Free oscillations and dynamic instability due to supersonic airflow pressure are investigated in a functional-gradient compound composite conical-cylindrical shell made of a carbon nanotubes-reinforced material. Nanocomposite materials with a linear distribution of the volumetric fraction of nanotubes over the thickness are considered. Extended mixture rule is used to estimate nanocomposite’s mechanical characteristics. A high-order shear deformation theory is used to represent the shell deformation. The assumed-mode technique, along with a Rayleigh-Ritz method, is applied to obtain the equations of the structure motion. To analyze the compound structure dynamics, a new system of piecewise basic functions is suggested. The pressure of a supersonic flow on the shell is obtained by using the piston theory. An example of the dynamic analysis of a nanocomposite conical-cylindrical shell in the supersonic gas flow is considered. The results of its modal analysis using the Rayleigh-Ritz technique are close to the natural frequencies of the shell obtained by finite element analysis. In this case, finite element analysis can only be used for shells made of material with a uniform distribution of nanotubes over the thickness. The dependence of the natural frequencies of a compound shell on the ratio of the lengths of the conical and cylindrical parts is studied. The dependence of the critical pressure of a supersonic flow on the Mach numbers and the type of carbon nanotubes reinforcement is investigated. Shells with a concentration of nanotubes predominantly near the outer and inner surfaces are characterized by higher values of natural frequencies and critical pressure than the shells with a uniform distribution of nanotubes or with a predominant concentration of nanotubes inside the shell.

A comparative dynamic analysis of rotor involving three engineering materials applying finite element analysis (FEA) simulation

The purpose of this study is to facilitate engineering applications and allied researches by presenting a detailed comparative picture based on dynamic analysis of Jeffcott rotor, diameter 32 mm for three materials, namely low carbon steel, SAE1045, and SAE5120 employing finite element analysis simulation software, ANSYS. The authors covered modal, harmonic response, and transient analyses along with natural frequencies and whirling speeds at different modes. Resonance occurrence speeds are also analyzed using the Campbell diagram. The harmonic response is investigated, with added material (0.1 kg) on the disc, to reveal the stresses and deformation. Transient analysis is performed with time-varying loads to work out stresses. FEA is carried out to estimate critical speeds for these three materials. The result highlights that SAE5120 exhibits the least resonance with a high value of natural frequency. Similarly, Campbell diagrams reveal no instabilities with a majority of critical speeds at the backward whirl, thus modal-based analysis confirms the superiority of SAE5120. Stress analysis involving harmonic responses also supports SAE5120 as the stress values are very high for both SAE1045 and SAE5120. The transient analysis involving equivalent, principal, and shear stresses supports the above results. The study compares and establishes the overall usefulness of SAE5120 for rotor applications among three materials.

RESEARCH TO IMPROVE POWERTRAIN NOISE, VIBRATION AND HARSHNESS CHARACTERISTICS

The paper presents a research algorithm consisting of: a developed methodology for selection of target values for natural frequencies and localization of vibration-loaded area of the powertrain based on calculation (simulation) and experimental research of resonant frequencies of the powertrain in operating modes and disturbances from two types of roads, calculation and experimental methodology for research of natural frequencies and oscillation modes of the powertrain, developed methodology for powertrain design refinement in terms of natural frequencies up to compliance with the target values and reduction of structural noise. Results of calculation and experimental research of resonant frequencies of the powertrain in operating modes and in case of disturbance from two types of roads are provided. There is also a justification given for selection of the target value for the powertrain natural frequency. Calculation of powertrain natural frequencies and oscillation modes was performed using the finite element method; experimental verification of the calculation was carried out as well. Using the verified calculation (simulation) model, design changes were introduced to reach the target values for natural frequencies and to reduce structural noise. Comparative calculation studies of the frequency response confirming the efficiency of the design changes are carried out.

Experimental Investigation on the Anticollision Performance of Corrugated Steel‐Reinforced Composites for Bridge Piers

To reduce the loss of life and property caused by the collision of a ship against a bridge pier, this study proposes a new type of anticollision facility. The facility uses corrugated steel plates and corrugated steel pipes (CSPs), or ordinary steel plates and corrugated steel pipes (OSPs), as structural elements to form a honeycomb structure, which can greatly improve the impact resistance of bridge piers and reduce any damage to ships. To evaluate the anticollision performance of the proposed anticollision facility, this work uses the CSPs and OSPs as study objects in the impact test research. A pendulum impact test system was utilized to compare and analyze the column with CSP and OSP specimens and the column without any anticollision facilities. Test results show that the CSP and OSP specimens have a relatively high energy dissipation effect. When the impact energy is small, the energy dissipation effect of the OSPs with the same plate thickness is stronger than that of the CSPs. When the impact energy is large, the energy dissipation effect of the CSPs with the same plate thickness is stronger than that of the OSPs. In addition, the extreme value analysis method is used to analyze the relationship curve between the peak value of the D1 lateral displacement and the specimen’s plate thickness, weight, and natural frequency; the optimal thickness, weight, and natural frequency values of the CSP and OSP specimens are also deduced. Taking the optimal value of the specimen’s natural frequency as a target, the structure of the CSP and OSP specimens is optimized. When the optimized plate thickness is 2.50 mm, the ratios of the optimal value of the specimen plate thickness, weight, and natural frequency to the optimal calculation value are all in the range of [0.80, 1.12]. OSP and CSP specimens are found to have the best energy dissipation effect. The peak value of the D1 lateral displacement of the top of the column equipped with the CSPs is at least 88.37% lower than that of the column without any anticollision facilities. For the top of the column equipped with the OSPs, the peak value of the D1 lateral displacement is at least 80.37% lower than that of the column without any anticollision facilities. Optimization results show that the extreme value analysis method is suitable for the optimal design of anticollision facilities for piers.

A finite element study on modal analysis of lightweight pipes

Pipes are mainly used in waste, drain and vent systems as well as transporting various liquids that might be corrosive, flammable, explosives, volatile, reactive, or sometimes hazardous to human health. Though pipes are used at the underground or above ground, all of them are exposed to vibration because of external factors. In this study, we focused on topology optimization of steel and PVC (Polyvinyl Chloride) pipes to get lighter ones which will lead to using less material during manufacturing, less CO2 emission while transporting them to usage areas by vehicles and easier assembling process. Firstly, new lightweight pipe designs were modeled, and then these novel pipe designs with lattice wall thickness were analyzed by using Ansys finite element program in clamped-free, hinged-hinged, and clamped-clamped boundary conditions to obtain the natural frequencies, mode shapes, and displacement values. Moreover, obtained finite element results for steel and PVC pipes were compared with analytical results calculated by using the equation to check and compare with the finite element results. Finite element results were found similar to analytical results at an acceptable level. The results show that lightweight pipes have similar natural frequency values to the commonly used pipe which has fully solid wall thickness and some significant results about displacement values were attained. Lastly, the effect of pipe material on vibration behaviors of pipes was investigated in depth.

Earthquake-induced liquefaction in the coastal zone, Case of Martil city, Morocco

According to historical documents and Moroccan earthquakes catalogs, the coastal zone has suffered in the past from several earthquakes. Understanding how sedimentary basins respond to seismic-wave energy generated by earthquake events is a significant concern for seismic-hazard estimation and risk analysis. The main goal of this study is to determine the distribution of the natural frequency value (F), the amplification factor value (A), and the soil vulnerability index (Kg) were carried out as an indicator for liquefaction potential sites in the Martil city based on the microtremor measurements. Liquefaction assessment was done at 96 stations using the HVSR approach provided by Nakamura (1989). According to the analysis results, the predominant frequency values range from about 0.31 to 5.63 Hz, and the amplification factor values range from 3 to 15. Based on these parameters, the vulnerability index Kg is determined, which can be used as a parameter in calculating the liquefaction potential of an area. This study shows supporting evidence for the first time that the HVSR of microtremors can be an excellent alternative indicator for an area's potential for liquefaction.

Sloshing Behavior in Rigid and Flexible Propellant Tanks: Computations and Experimental Validation

Liquid-propellant slosh occurrence in spacecraft continues to introduce instability-induced failures. Current mechanical models are insufficient in predicting differences in slosh frequencies for varying tank structure flexibilities. This paper is focused on 3-D high-fidelity computational simulation of sloshing in liquid-filled tanks under dynamic loads using the arbitrary Lagrangian–Eulerian method and their experimental validation. Varying fill levels and tank thicknesses that represent flexibility were studied. The computational results were compared with in-house experiments for the same fill levels and thicknesses. Fast Fourier transform analysis was performed on the acceleration data to determine the natural frequencies due to slosh. Comparisons were also made between experiments and simulations in terms of wave height and resonance observed in acceleration time histories. It was found that the natural frequency values after the first mode compared well between simulation and experiment. The computational simulation was capable of predicting the differences in frequency values due to the tank-thickness-induced flexibility and varying fill levels. It is concluded that a high-fidelity computational model is capable of capturing these differences and is necessary to accurately characterize the nonlinear behavior of propellant slosh in flexible tanks as opposed to the mechanical models in use.

Characterization of the Quality Factor Due to the Static Prestress in Classical Caputo and Caputo-Fabrizio Fractional Thermoelastic Silicon Microbeam.

The thermal quality factor is the most significant parameter of the micro/nanobeam resonator. Less energy is released by vibration and low damping, which results in greater efficiency. Thus, for a simply supported microbeam resonator made of silicon (Si), a thermal analysis of the thermal quality factor was introduced. A force due to static prestress was considered. The governing equations were constructed in a unified system. This system generates six different models of heat conduction; the traditional Lord–Shulman, Lord–Shulman based on classical Caputo fractional derivative, Lord–Shulman based on the Caputo–Fabrizio fractional derivative, traditional Tzou, Tzou based on the classical Caputo fractional derivative, and Tzou based on the Caputo–Fabrizio fractional derivative. The results show that the force due to static prestress, the fractional order parameter, the isothermal value of natural frequency, and the beam’s length significantly affect the thermal quality factor. The two types of fractional derivatives applied have different and significant effects on the thermal quality factor.

Research of dynamic influence from technological equipment on work of reinforced concrete slabs of overlapping

This article presents full-scale experimental measurements of the parameters of the elements of the load-bearing structures of thebuilding in real time with their subsequent processing and determination of the dynamic characteristics of such elements and the structure as awhole for further modeling and calculation ofbuilding elements.The research is based on an approach based on the hypothesis of considering systems of complex structure, which has a dynamic impact, as a single system with corresponding dynamic characteristics. Within the framework of such a review of the system, it is necessary to identify and assess the impact of various origins.As a dynamic criterion for assessing the condition of load-bearing structures were used the values of natural frequencies of oscillations, their actual measurement on different floors of the existing building.The research was performed by determining the integral dynamic parameters with subsequent analysis and establishment of causal relationships. In the course of the research, records of continuousfixation of dynamic action parameters were used directly on load-bearing structures. The obtained data were processed using ZETLAB SEISMOsoftware using spectral analysis.The obtained spectra were analyzed in order to determine the numerical values of the oscillation frequencies, which correspond to the main peakson the spectrograms and are a consequence of the design response to the sources of dynamic influence.The obtained data will be used to assess the stress state of fiber concrete slabs.

Numerical algorithm for searching for layouts of electroelastic bodies with external electric circuits for obtaining the best damping properties

This paper presents an algorithm which allows finding such layouts of electromechanical systems that provide the best vibration damping whether for one mode or a set of vibration modes within some continuous frequency ranges. The basis for the algorithm is the problem solution about natural vibrations. An elastic structure with a piezoelectric element located on its surfaces, which electrodes are connected to a passive external electric circuit, is treated as an electromechanical system. The piezoelectric elements shunted with an electric circuit are the devices where energy dissipation occurs, thus leads to damping of vibrations. A change in damping properties of such systems can be reached by a proper choice of parameters of the electric circuits and corresponding location of the piezoelectric element, which provides the highest energy withdrawal into the electric circuit. The paper presents the mathematical formulation of the natural vibrations problem for piecewise-homogeneous electroelastic bodies shunted with passive external electric circuits. Within the proposed mathematical statement, the problem solution of natural vibrations for such objects is based on values of complex natural vibration frequencies. Real parts of the complex natural vibration frequencies are the circular frequency of vibrations, and the imaginary parts are the damping indices of vibrations. We proposed techniques aimed at determining the location of the piezoelectric element and selecting parameters of shunting the external electric circuit. These approaches are based on values of the complex natural vibration frequencies obtained as results of solving the natural vibrations problem. The proposed approach is demonstrated using a specimen of a thin-walled shell in the semi-cylinder form. The piezoelectric element has a form of a segment of a ring made of PZT-4 piezoceramics. Electrodes of the piezoelectric element are connected to the series resonant RL -circuit. The formulated problem is solved numerically using the finite element method and ANSYS commercial package.

Model and Material Analysis of Gokart Chassis

The present study of this paper is to select the best material for manufacturing the Go-Kart. To meet this designing of go-kart chassis done by using CAD software CATIA tool and simulate with ANSYS work-bench. To select the best material, strength to weight ratio plays major role on it. Steel is considering to existing material another two materials Aluminum-6061, Kevlar selected. The main reason behind choosing Aluminum-6061, Kevlar materials is two materials are having less density and high yield limit values, and this factor can increase the strength/weight ratio compare to existing material steel. In this project material selection is one of the main design decisions that greatly increase the safety, reliability and performance. The material selection is choosen after my extensive research with various parameters like strength, weight and cost. We are comparing Aluminum-6061and Kevlar materials with mild steel. In this process boundary conditions applied on each material and calculated results like deformation, stress, strain, safety factor, natural frequency values, by knowing all these results, concluded with optimum material.

Nonlinear dynamic behavior and bifurcation analysis of a rotating viscoelastic size-dependent beam based on non-classical theories

In this paper, the free and harmonically forced vibrations of a viscoelastic rotating microbeam have been analyzed by exploiting non-classical theories, such as the Modified Couple Stress Theory and Modified Strain Gradient Theory (MSGT). A continuous model is derived and reduced to a well-known Duffing–Rayleigh system via a Galerkin projection; then, the Multiple Scales Method is used to obtain amplitude equations. Free and forced nonlinear oscillations are studied via classical and non-classical theories, and their corresponding results are compared with each other. An expression for natural frequency is obtained in which the effects of the internal damping and small-scale parameters are obvious. It is observed that the natural frequency obtained using the MSGT has the highest value, while the Classical Theory (CT) predicts the lowest natural frequency value. Also, it is seen that by increasing the hub radius, the influence of rotational speed on natural frequency is increased. According to obtained results, the responses corresponding to the CT become completely stable for the lowest value of the excitation force and the highest value of the external damping coefficient. For MSGT, responses are stable when the values of the excitation force and external damping coefficients are highest and lowest, respectively. It is shown that for the MSGT, the system is stable when the internal damping coefficient is small, while for the CT, the beam is stable for the highest value of the internal damping coefficient. The system parameters—such as the detuning parameter, damping coefficients, and excitation force—affect the solution, such a way that the system may possess one or two stable spirals depending on the values of those parameters, as shown in phase plane portraits.

Optimization of Dynamic and Buckling Behavior of Thin-Walled Composite Cylinder, Supported by Nature-Inspired Agorithms.

The paper presents the optimization of stacking sequence (the lamination angles in subsequent composite layers) of the composite cylinder in order to simultaneously maximize the values of the first natural frequency and the first buckling force . The optimization problem involves either two objective functions or one which combines both problems using a coefficient whose optimal value is also being searched for. The main idea of the paper is the application of two neural network metamodels which substitute very time- and resource-consuming Finite Element (FE) calculations. The metamodels are created separately through a novel iterative procedure, using examples obtained through Finite Element Method (FEM). The metamodels, once ready, are able to assess the values of and instantly and thus enable the application of nature-inspired Genetic Algorithm (GA) minimization with reasonable calculation times. Obviously, the maxima of and may be located in different points of the design parameters (i.e., lamination angles) space, the considered optimization task is to find a solution for which both and simultaneously reach values as close to their maxima as possible. All the investigated optimization examples are repeated several times and basic statistical analysis of the results is presented.

Closed Form Solutions for Predicting Lateral Response of Tripod Suction Pile for Offshore Wind Turbine Foundation

This study presents a simplified analysis technique capable of predicting the dynamic behavior of a tripod suction pile subjected to a horizontal load. The first natural frequency of the system, horizontal displacement, and allowable rotation angle at the pile head were set as target physical quantities in accordance with substructure design requirements. In consideration of the physical characteristics of the tripod suction pile, the analysis was extended to the single pile-multi-pile-tripod-tower part to derive the influence factors. A possible displacement response function that could be applied to the intermediate pile range was also proposed. Thereafter, a detailed design was determined using an integrated load analysis, which included a turbine based on the basic design of simplified analysis method. Furthermore, the dynamic behavior of the offshore wind turbine at each installation stage was predicted using a numerical analysis and measured via field tests. The displacement at the pile head and the predicted value of the first natural frequency of the system were compared using the field-measured and numerical analysis values. The first natural frequency value produced by the simple analysis method showed an error range within 1%, and the displacement at the pile head also satisfied the structural design requirements. Therefore, this method provides a quick and accurate solution to the lateral response of tripod suction piles as foundations for offshore wind turbines.

Dynamic behavior of the macauba palm (Acrocomia aculeata) fruit-rachilla system using the stochastic finite element method

The search for alternative energy sources has fomented the study of several crops. The macauba palm crop, for instance, has been highlighted because of its particular relevance in Brazil due to its wide distribution across Brazilian territory and its potential for yielding high amounts of oil per cultivated hectare. However, the species is still most commonly harvested via extractivism, which results in low yields. Therefore, we aimed to analyze the dynamic behavior of the fruit-rachilla system when subjected to mechanical vibration to gather baseline information for the subsequent development of macauba harvesting machines. The fruit-rachilla system of the species was modeled for different fruit maturation stages and plant accessions. Natural frequencies and modes of vibration were determined by the stochastic finite element method (FEM), adopting the specific mass and the modulus of elasticity of the system as random variables, which enabled us to compile a dataset of natural frequencies based on the variability of the system properties. The mean values of the natural frequencies obtained in the vibration assays were 26.02 Hz at the green maturation stage and 21.22 Hz at the ripe maturation stage. The mean values of natural frequencies found in the simulation by stochastic FEM, referring to the third mode of vibration, were 26.05 Hz at the green maturation stage and 21.23 Hz at the ripe maturation stage. We concluded that the natural frequencies of the macauba fruit-rachilla system on the basis of different plant accessions showed a decreasing behavior during fruit maturation. The modes of vibration characterized by pendulum displacement did not differ among plant accessions or between fruit maturation stages.

Dynamic Response of Machine Foundation Resting on End Bearing Piles

Herein, a finite element software (ANSYS. 11) is adopted which provides an effective tool for dynamic analysis and structural design of machine-foundations. As a case study, machine foundation on piles in sandy soil is investigated. Machine foundations supported by end-bearing piles are introduced. Sinusoidal dynamic load is applied. A study of parameters is conducted to investigate the influence of a number of parameters that include: geometry of the piles below the foundation, the dynamic load amplitude, damping ratio and frequency of the load. Linear elastic model is adopted for modeling the piles and their cap for machine foundation using eight node isoparametric (solid 65) element, while elastic model is adopted to model the soil behavior and eight node isoparametric elements are used to model the soil through (solid 45) element. It is concluded that the frequency ratio decreases with increase of spacing between piles values due to increase in natural frequency, except in the case of 3 m spacing where it increases due to decrease in natural frequency as the mass was increased obviously. The increase in spacing caused the increase of natural frequency by about 6% in the model having 1.5 m spacing more than the 1.25 m case and by about 3% for the 1.75 m spacing more than the 1.5 m reference case. The increase in pile cap length caused the natural frequency to decrease by about 18% for the 3.75 m pile cap length as compared with the reference case and by 29% in the case of 5 m less than the reference case. In the case of increasing pile cap thickness, there was only a slight difference in the values of natural frequency.