Optimal Structural Modifications of a Gun Tripod for Desired Natural Frequencies

Sensitivity analysis and structural modification techniques are used to investigate the structural modifications of a machine gun tripod which suffers from severe vibration during firing due to the resonance. The finite element analysis and modal test techniques are used to determine the natural frequencies of the machine gun. The sensitivities of natural frequencies with respect to the structural parameters of the tripod are obtained by the method of sensitivity analysis, and they can be used as an indication for the structural modification of the tripod so as to shift the natural frequencies effectively. By the structural modification techniques, finally, the optimal structural modifications of the tripod for desired natural frequencies are made to avoid the resonance, and this optimal structural modification is verified by re-analysis of the modified structure and the vibration contrast between original structure and modified structure. The research resulted in a successful structural modification for desired natural frequencies, which can avoid the resonance and thereby greatly improve the shooting precision of the machine gun during firing.

Determination of Natural Frequencies of Multilayered Plates by Mixed Finite Elements

Natural frequencies for multilayer plates are calculated by mixed finite element method. The main object of this paper is to use the mixed model for multilayer plates, analyzing each layer as an isolated plate, where the continuity of displacements is achieved by Lagrange multipliers （representing static variables）. This procedure allows us to work with any model for single plate （so as to ensure the proper behavior of each layer）, and the complexity of the multilayer system is avoided by ensuring the condition of displacements by the Lagrange multipliers （static variables）. The plate is discretized by finite element modeling based on a primary hybrid model, where the domain is divided by quadrilateral, both for the displacement field and static variables. This mixed element for plates was implemented and several examples of vibrations have been verified successfully by the results obtained by other methods in the literature.

A Structural Damage Detection Method Using XGBoost Algorithm on Natural Frequencies

Structural damage detection and monitoring are vital in product lifecycle management of aeronautic system in space utilization.In this paper,a method based on vibration characteristics and ensemble learning algorithm is proposed to achieve damage detection.Based on the small volume of modal frequency data for intact and damage structures,the extreme gradient boosting algorithm enables robust damage localization under noise condition of wing-like structures on numerical data.The method shows satisfactory performance on localizing damage with random geometrical profiles in most cases.

Effect of vehicle weight on natural frequencies of bridges measured from traffic-induced vibration

Recently,ambient vibration test(AVT)is widely used tu estimate dynamic characteristics of large civil struc- tures.Dynamic characteristics ean be affected by various envirnnmental factors such as humidity,intensity of wind,and temperature.Besides these environmental conditions,tire mass of vehicles may change the measured valnes when traffic-in- duced vibration is used as a source of AVT tor bridges.The effect of vehicle mass on dynamic characteristics is investigated through traffic-induced vibration tests on three bridges;(1)three-span suspension bridge(128m+404m+128m),(2) five-span continuous steel box girder bridge(59m+3@ 95m+59m),(3)simply supported plate girder bridge(46m). Acceleration histories of each measurement location under normal traffic are recorded for 30 minutes at field.These recor- ded histories are divided into individual vibrations and are combined into two groups aceording to the level of vibration;one by heavy vehicles such as trucks and buses and the other by light vehicles such as passenger cars.Separate processing of the two groups of signals shows that,for the middle and long-span bridges,the difference can be hardly detected,but,for the short span bridges whose mass is relatively small,the measured natural frequencies can change up to 5.4%.

Investigation of Microstructure, Natural Frequencies and Vibration Modes of Dragonfly Wing

In the present work, a thorough investigation on the microstructural and morphological aspects of dragonfly wings was carried out using scanning electron microscope. Then, based on this study and the previous reports, a precise three-dimensional numerical model was developed and natural frequencies and vibration modes of dragonfly forewing were determined by finite element method. The results shown that dragonfly wings are made of a series of adaptive materials, which form a very complex composite structure. This bio-composite fabrication has some unique features and potential benefits. Furthermore, the numerical results show that the first natural frequency of dragonfly wings is about 168 Hz and bending is the predominant deformation mode in this stage. The accuracy of the present analysis is verified by comparison of calculated results with experimental data. This paper may be helpful for micro aerial vehicle design concerning dynamic response.

Natural frequencies analysis of a composite beam consisting of Euler-Bernoulli and Timoshenko beam segments alternately

Present investigation is concerned with the free vibration property of a beam with periodically variable cross-sections.For the special geometry characteristic,the beam was modelled as the combination of long equal-length uniform Euler-Bernoulli beam segments and short equal-length uniform Timoshenko beam segments alternately.By using continuity conditions,the hybrid beam unit(ETE-B) consisting of Euler-Bernoulli beam,Timoshenko beam and Euler-Bernoulli beam in sequence was developed.Classical boundary conditions of pinned-pinned,clamped-clamped and clamped-free were considered to obtain the natural frequencies.Numerical examples of the equal-length composite beam with 1,2 and 3 ETE-B units were presented and compared with the equal-length and equal-cross-section Euler-Bernoulli beam,respectively.The work demonstrates that natural frequencies of the composite beam are larger than those of the Euler-Bernoulli beam,which in practice,is the interpretation that the inner-welded plate can strengthen a hollow beam.In this work,comparisons with the finite element calculation were presented to validate the ETE-B model.

Determination of the natural frequencies of axially moving beams by the method of multiple scales

The natural frequencies of an axially moving beam were determined by using the method of multiple scales. The method of second-order multiple scales could be directly applied to the governing equation if the axial motion of the beam is assumed to be small. It can be concluded that the natural frequencies affected by the axial motion are proportional to the square of the velocity of the axially moving beam. The results obtained by the perturbation method were compared with those given with a numerical method and the comparison shows the correctness of the multiple-scale method if the velocity is rather small.

ON THE REPEATED NATURAL FREQUENCIES FOR TORSIONAL VIBRATION OF SHAFTS

To investigate the repeated frequency condition (RFC) for torsional vibration of shafts' system, the transfer matrix method was adopted. Firstly, the transfer relationship from the boundary to engaging disks of double shafts' system (DSS) was constructed. Secondly, the RFC of DSS was deduced out and the methods to select mode shape were presented. Finally, the relationship was extended to multilevel transmission system (MTS), and the RFC of this system was explored. The conclusions is this: 1) the necessary RFC requires the existence of joint engaging couple (JEC); 2) for DSS, the sufficient is the number of boundary transfer factors (f(B)) larger than 2; 3) the whale system can be split into independent groups, the total multiplicity is the sum of independent solution number of every group, the latter is the number of independent f(B), = 0 inside the group minus 1.

Natural frequencies of rotating functionally graded cylindrical shells

Love＇s first approximation theory is used to analyze the natural frequencies of rotating functionally graded cylindrical shells. To verify the validity of the present method, the natural frequencies of the simply supported non-rotating isotropic cylindrical shell and the functionally graded cylindrical shell are compared with available published results. Good agreement is obtained. The effects of the power law index, the wave numbers along the x- and O-directions, and the thickness-to-radius ratio on the natural frequencies of the simply supported rotating functionally graded cylindrical shell are investigated by several numerical examples. It is found that the fundamental frequencies of the backward waves increase with the increasing rotating speed, the fundamental frequencies of the forward waves decrease with the increasing rotating speed, and the forward and backward waves frequencies increase with the increasing thickness-to-radius ratio.

The Coupled Effect of Temperature Changes and Damage Depth on Natural Frequencies in Beam-Like Structures

A significant amount of research is concerned with dynamic modal parameters for damage detection of structural conditions due to their simplicity in use and feasibility.However,their use for damage detection should be performed with special attention,particularly in operational and environmental conditions subjected to temperature changes.Beams in construction industries experience different loading types,such as temperature changes leading to crack initiation and propagation.Changed physical and dynamic properties such as natural frequencies and mode shapes indicate that damage has occurred within the structures.In this study,vibration analysis of cantilever and cantilever simply supported beams has been carried out on intact and damaged beams to investigate the coupled effect of temperature changes and damage depth on natural frequencies.A numerical analysis of beams is completed using ANSYS software.The results of numerical simulation are validated using two other studies from literature.Numerical results revealed that in order to perform a successful damage assessment using the frequency shift,the vibration modes should be selected properly.In addition,an increase in temperature results in a decrease in structural frequencies.The assessment of the effect of damage depth on natural frequencies also confirms that when damage depth is increased,there is a significant decrease in natural frequency responses.

Geometry and size optimization of stiffener layout for three-dimensional box structures with maximization of natural frequencies

Based on the growth mechanism of natural biological branching systems and inspiration from the morphology of plant root tips,a bionic design method called Improved Adaptive Growth Method(IAGM)has been proposed in the authors’previous research and successfully applied to the reinforcement optimization of three-dimensional box structures with respect to natural frequencies.However,as a kind of ground structure methods,the final layout patterns of stiffeners obtained by using the IAGM are highly subjected to their ground structures,which restricts the optimization effect and freedom to further improve the dynamic performance of structures.To solve this problem,a novel post-processing geometry and size optimization approach is proposed in this article.This method takes the former layout optimization result as start,and iteratively finds the optimal layout angles,locations,and lengths of stiffeners with a few design variables by optimizing the positions of some specific node lines called active node lines.At the same time,thick-nesses of stiffeners are also optimized to further improve natural frequencies of three-dimensional box structures.Using this method,stiffeners can be successfully separated from their ground structures and further effectively improve natural frequencies of three-dimensional box structures with less material consumption.Typical numerical examples are illustrated to validate the effectiveness and advantages of the suggested method.

Natural vibration and critical velocity of translating Timoshenko beam with non-homogeneous boundaries

In most practical engineering applications,the translating belt wraps around two fixed wheels.The boundary conditions of the dynamic model are typically specified as simply supported or fixed boundaries.In this paper,non-homogeneous boundaries are introduced by the support wheels.Utilizing the translating belt as the mechanical prototype,the vibration characteristics of translating Timoshenko beam models with nonhomogeneous boundaries are investigated for the first time.The governing equations of Timoshenko beam are deduced by employing the generalized Hamilton's principle.The effects of parameters such as the radius of wheel and the length of belt on vibration characteristics including the equilibrium deformations,critical velocities,natural frequencies,and modes,are numerically calculated and analyzed.The numerical results indicate that the beam experiences deformation characterized by varying curvatures near the wheels.The radii of the wheels play a pivotal role in determining the change in trend of the relative difference between two beam models.Comparing the results unearths that the relative difference in equilibrium deformations between the two beam models is more pronounced with smaller-sized wheels.When the two wheels are of equal size,the critical velocities of both beam models reach their respective minima.In addition,the relative difference in natural frequencies between the two beam models exhibits nonlinear variation and can easily exceed 50%.Furthermore,as the axial velocities increase,the impact of non-homogeneous boundaries on modal shape of translating beam becomes more significant.Although dealing with non-homogeneous boundaries is challenging,beam models with non-homogeneous boundaries are more sensitive to parameters,and the differences between the two types of beams undergo some interesting variations under the influence of non-homogeneous boundaries.

Research on Automatic Test System of Engine Blade Natural Frequency

Blades are one of the important components on aircraft engines.If they break due to vibration failure,the normal operation of the entire engine will be offected.Therefore,it is necessary to measure their natural frequency before installing them on the engine to avoid resonance.At present,most blade vibration testing systems require manual operation by operators,which has high requirements for operators and the testing process is also very cumbersome.Therefore,the testing efficiency is low and cannot meet the needs of efficient testing.To solve the current problems of low testing efficiency and high operational requirements,a high-precision and high-efficiency automatic test system is designed.The testing accuracy of this system can reach ±1%,and the testing efficiency is improved by 37% compared to manual testing.Firstly,the influence of compression force and vibration exciter position on natural frequency test is analyzed by amplitude-frequency curve,so as to calibrate servo cylinder and fourdimensional motion platform.Secondly,the sine wave signal is used as the excitation to sweep the blade linearly,and the natural frequency is determined by the amplitude peak in the frequency domain.Finally,the accuracy experiment and efficiency experiment are carried out on the developed test system,whose results verify its high efficiency and high precision.

A novel virtual material layer model for predicting natural frequencies of composite bolted joints

A novel virtual material layer model based on the fractal theory was proposed to predict the natural frequencies of carbon fiber reinforced plastic composite bolted joints.Rough contact surfaces of composite bolted joints are modeled with this new proposed approach.Numerical and experimental modal analyses were conducted to validate the effectiveness of the proposed model.A good consistence is noted between the numerical and experimental results.To demonstrate the necessity of accurately modeling the rough contact surfaces in the prediction of natural frequencies,virtual material layer model was compared with the widely used traditional model based on the Master-Slave contact algorithm and experiments,respectively.Results show that the proposed model has a better agreement with experiments than the widely used traditional model(the prediction accuracy is raised by 8.77%when the pre-tightening torque is 0.5 N·m).Real contact area ratio A*of three different virtual material layers were calculated.Value of A*were discussed with dimensionless load P*,fractal dimension D and fractal roughness G.This work provides a new efficient way for accurately modeling the rough contact surfaces and predicting the natural frequencies of composite bolted joints,which can be used to help engineers in the dynamic design of composite materials.

Influence factors on natural frequencies of composite materials

Compared with traditional materials, composite materials have lower specific gravity, larger specific strength, larger specific modulus, and better designability structure and structural performance. However, the variability of structural properties hinders the control and prediction of the performance of composite materials. In this work, the Rayleigh–Ritz and orthogonal polynomial methods were used to derive the dynamic equations of composite materials and obtain the natural frequency expressions on the basis of the constitutive model of laminated composite materials. The correctness of the analytical model was verified by modal hammering and frequency sweep tests. On the basis of the established theoretical model, the influencing factors, including layers, thickness, and fiber angles, on the natural frequencies of laminated composites were analyzed. Furthermore, the coupling effects of layers, fiber angle, and lay-up sequence on the natural frequencies of composites were studied. Research results indicated that the proposed method could accurately and effectively analyze the influence of single and multiple factors on the natural frequencies of composite materials. Hence, this work provides a theoretical basis for preparing composite materials with different natural frequencies and meeting the requirements of different working conditions.

Numerical Approach to Simulate the Effect of Corrosion Damage on the Natural Frequency of Reinforced Concrete Structures

Corrosion of reinforcing steel in concrete elements causes minor to major damage in different aspects.It may lead to spalling of concrete cover,reduction of section’s capacity and can alter the dynamic properties.For the dynamic properties,natural frequency is to be a reliable indicator of structural integrity that can be utilized in non-destructive corrosion assessment.Although the correlation between natural frequency and corrosion damage has been reflected in different experimental programs,few attempts have been made to investigate this relationship in forward modeling and/or structural health monitoring techniques.This can be attributed to the limited available data,the complex nature of corrosion,and the involvement of multidisciplinaryfields.Therefore,this study presents a numerical attempt to simulate the effect of corrosion damage on the natural frequency of the structure.The approach relies on simulating the time history response of the structure using a modified Bouc-Wen model that incorporates the nonlinear effects of corrosion.Then,modal analysis is utilized to assess the change in dynamic properties in the frequency domain.Tofinish up,regression algorithms are employed tofind optimal relationship between involved parameters,including corrosion damage as input,and natural frequency as output.The efficiency of the suggested framework is illustrated in thirteen buildings with cantilevered column lateral force-resisting system and different levels of corrosion.

A NEW METHOD FOR FINDING THE NATURAL FREQUENCY SET OF A LINEAR TIME-INVARIANT NETWORK

This paper presents a new method for finding the natural frequency set of a linear time invariant network. In the paper deriving and proving of a common equation are described. It is for the first time that in the common equation the natural frequencies of an n th order network are correlated with the n port parameters. The equation is simple and dual in form and clear in its physical meaning. The procedure of finding the solution is simplified and standardized, and it will not cause the loss of roots. The common equation would find wide use and be systematized.

Calculation,Simulation,and Testing for the Natural Frequency of a Micro Accelerometer

A calculation and test method for the natural frequency of a high-g micro accelerometer with complex structures is presented. A universal formula for natural frequency, which can significantly simplify the structural design process, is deduced and confirmed by experiment. A simplified analytical model is established to describe the accelerometer＇s mechanical behavior and deduce the formula for the natural frequency. Finite element modeling is also conducted to evaluate the natural frequency of the micro-accelerometer and verify the formula. The results obtained from the analytical model and the finite element simulation show good agreement. Finally, a shock comparison method designed for acquiring the high frequency characteristics of the accelerometer is introduced to verify the formula by testing its actual natural frequency.

A New Method for Calculation of Natural Frequency of Suspended Pipeline

The buried pipelines are widely used in oil transportation. The pipelines become suspended in the river with flushing of floodwater. If the frequency of vortex shedding is near to the nature frequency of pipelines, it will cause resonance of the suspended pipeline and result in the damage of pipelines. In this paper, the buried parts of pipeline in soil are treated as the half unlimited long beam placed on the elastic foundations. The vibration partial differential equations of suspended pipe and the parts buried in soil are derived respectively. The iterative calculation method is then presented. The results obtained from the suggested method are proved to be identical with the measured values.

Experimental and numerical study of effecting core configurations on the static and dynamic behavior of honeycomb plate with aluminum material

The sandwich panel incorporated a honeycomb core,a widely utilized composite structure recognized as a fundamental classification of composite materials.Comprised a core resembling a honeycomb,possessing thickness and softness,and is flank by rigid face sheets that sandwich various shapes and materials.This paper presents an examination of the static and dynamic analysis of lightweight plates made of aluminum honeycomb sandwich composites.Honeycomb sandwich plate samples are 300 mm long,and 300 mm wide,the heights of the core have been varied at four values ranging from 10 to 25 mm.The honeycomb core is manufactured from Aluminum material by using a novel technique namely resistance spot welding(RSW)instead of using adhesive material,which is often used when an industrial flaw is detected.Numerical optimization based on response surface methodology(RSM)and design of experiment software(DOE)was used to verify the current work.A theoretical examination of the crashworthiness behavior(maximum bending load,maximum deflection)and vibration attributes(natural frequency,damping ratio,transient temporal response)of honeycomb sandwich panels with different design parameters was also carried out.In addition,the finite element method-based ANSYS software was used to confirm the theoretical conclusions.The findings of the present work showed that the relationship between the natural frequency,core height,and cell size is direct.In contrast,the relationship between the natural frequency and the thickness of the cell wall is inverse.Conversely,the damping ratio is inversely proportional to the core height and cell size but directly proportional to the thickness of the cell wall.The study indicates that altering the core height within 10-25 mm leads to a significant increase of 82%in the natural frequency and a notable decrease of 49%in the damping ratio.These findings are based on a specific cell size value of 0.01 m and a cell wall thickness of 0.001 m.Also,the results indicate that for a given set of cell wall thickness and size values,an increase in core height from(0.01-0.025)m,leads to a reduction of the percentage of maximum response approX imately 76%.Conversely,the increasing thickness of the wall of cell wall,ranging 0.3-0.7 mm with a constant core height equal to 0.015 m,resulted in a de crease of maximum transient response by 7.8%.