Free Vibration Analysis of Rectangular Plate with Cutouts under Elastic Boundary Conditions in Independent Coordinate Coupling Method

Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.

B-Spline Wavelet on Interval Finite Element Method for Static and Vibration Analysis of Stiffened Flexible Thin Plate

A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.

Size dependent free vibration analysis of functionally graded piezoelectric micro/nano shell based on modified couple stress theory with considering thickness stretching effect

Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform temperature rising.Size dependency is included in governing equations based on the modified couple stress theory.Hamilton’s principle is used to derive governing equations of the cylindrical micro/nano shell.Solution procedure is developed using Navier technique for simply-supported boundary conditions.The numerical results are presented to investigate the effect of significant parameters such as some dimensionless geometric parameters,material properties,applied voltages and temperature rising on the free vibration responses.

Vibration analysis of fluid- structure interaction in water hammer based on transfer matrix method

In consideration of the problem that the effect of conduit structure on water hammer has been ignored in the classical theory,the Poisson coupling between the fluid and the pipeline was studied and a fourteen-equation mathematical model of fluid-structure interaction(FSI)was developed.Then,the transfer matrix method(TMM)was used to calculate the modal frequency,modal shape and frequency response.The results were compared with that in experiment to verify the correctness of the TMM and the results show that the fluid-structure coupling has a greater impact on the modal frequencies than the modal shape.Finally,the influence on the response spectrum of different damping ratios was studied and the results show that the natural frequency under different damping ratios has changed little but there is a big difference for the pressure spectrum.With the decreasing of damping ratio,the damping of the system on frequency spectrum is more and more significant and the dispersion and dissipation is more and more apparent.Therefore the appropriate damping ratio should be selected to minimize the effects of the vibration of the FSI.The results provide references for the theory research of FSI in the transient process.

Static and free vibration analysis of four-parameter continuous grading elliptical sandwich plates

In the present study,the static and dynamic analyses of elliptical functionally graded sandwich(FGS)plates are investigated.The constituent materials of the sandwich plates are ceramic and metal so that the core is made of pure metal,while the face sheets consist of a combination of metal and ceramic according to a four-parameter power-law distribution.Different material profiles such as classic,symmetric,and asymmetric can be obtained using the applied generalized power-law distribution relation.The analysis is performed based on the classical laminated plate theory(CLPT)and the Ritz method.The effects of four parameters in the material distribution relation as well as different geometric parameters on the deflection and natural frequencies of elliptical FGS plates are studied.The results of this study show that with a proper distribution of materials,the optimal static and dynamic behavior can be achieved.The results also indicate that the generalized power-law distribution has significant effects on the natural frequencies of elliptical FGS plates.For example,although the frequency parameter of a plate with ceramic face sheets is more than the one with metal face sheets,the use of larger amounts of ceramic does not necessarily increase the natural frequency of the structure.

Nonlinear vibration analysis of pipeline considering the effects of soft nonlinear clamp

Soft nonlinear support is a major engineering project,but there are few relevant studies.In this paper,a dynamic pipeline model with soft nonlinear supports at both ends is established.By considering the influence of the Coriolis force and centrifugal force,the dynamical coupling equation of fluid-structure interaction is derived with extended Hamilton’s principle.Then,the approximate analytical solutions are sought via the harmonic balance method.The amplitude-frequency response curves show that different effects can be determined by approximate analysis.It is demonstrated that the increase in the fluid velocity can increase the amplitude of the pipeline system.The frequency range of unstable response increases when the fluid pressure raises.The combination of the soft nonlinear clamp and the large geometrical deformation of the pipeline affects the nonlinear vibration characteristic of the system,and the external excitation force and damping have significant effects on the stability.

A Simplified Model for Vibration Analysis of Diesel Engine Crankshaft System

A spatial finite element model for vibration analysis of crankshaft system was proposed. The crankshaft body was simplified as spatial rigid frame by using beam elements based on Timoshenko beam theory. The main bearings in system were simplified as linear springs and dashpots. The natural frequencies of the crankshaft system of a four in-line cylinder engine were calculated and compared with the analytical and experimental values available in other publications. In order to simulate the motion of operating crankshaft system, the gas forces, rotating masses and reciprocating masses were considered, the crankshaft and main bearings were coupled in a rotating coordinate system, and a dynamic model for vibration analysis of crankshaft system was established. By applying the dynamic model, the influence of the mass and moment of inertia of front pulley on the behavior of crankshaft vibration was investigated.

Vibration Analysis of Beams by Spline Finite Element

In this paper,the spline finite element method is developed to investigate free vibration problems of beams.The cubic B-spline functions are used to construct the displacement field.The assembly of elements and the introduction of boundary conditions follow the standard finite element procedure.The results under various boundary conditions are compared with those obtained by the exact method and the finite difference method.It shows that the results are in excellent agreement with the analytical results and much more accurate than the results obtained by the finite difference method,especially for higher order modes.

Vibration Analysis of Fetching Carton Mechanism of Square Carpets Packaging

In this paper,according to the cantilever beam of fetching carton mechanism in square packaging machine, considering the impact of motion of air cylinder on it,its dynamics model and finite element model are built by using ANSYS. This paper not only acquires the deformation distribution,stress distribution and natural frequency of the cantilever beam in the static state; but also gets the dynamic response curve in the maximum deformation and the dynamic stress response curve in the near of the maximum stress during the motion of air cylinder. Result shows that no matter static state or dynamic state,deformation of the cantilever in the fetching carton mechanism is acceptable. The design of mechanism is reliable and its motion is also stable; no resonance can occur on the cantilever beam.

Parametric CAD Modelling of Aircraft Wings for FEA Vibration Analysis

Excessive vibration of aircraft wings during flight is harmful and may cause propagation of existing cracks in the material, leading to catastrophic failures as a result of material fatigue. This study investigates the variations of modal characteristics of aircraft wings with respect to changes in the structural configurations. We develop parametric Computer-Aided Design (CAD) models to capture new design intend on the aircraft wing architectures. Subsequent Finite Element Analysis (FEA) based vibration analysis is performed to study the effects of architecture changes on the wing’s natural frequencies and mode shapes. It is concluded that the spar placement and the number of ribs have significant influence on the wing’s natural vibration properties. Integrating CAD modelling and FEA vibration analysis enables designers to develop alternative wing architectures to implement design requirements in the preliminary design stage.

Vibration Analysis and Fatigue Assessment of Floors.Part I:Human Rhythmic Activities

Structural problems associated with excessive vibration of building floor systems when subjected to human rhythmic activities have been frequent.In this context,this research work aims to develop an analysis methodology to evaluate the human comfort and assess the fatigue performance of steel-concrete composite floors when subjected to human rhythmic activities(aerobics).The investigated structural model corresponds to a steel-concrete floor with dimensions of 10 m×10 m and a total area of 100 m^(2).The numerical model developed for the dynamic analysis of the floor adopted the usual mesh refinement techniques present in finite element method(FEM)simulations implemented in the ANSYS program.The investigated floor dynamic response was calculated through the consideration of people practicing rhythmic activities on the structure,in order to verify the occurrence of excessive vibration and to assess the human comfort.The fatigue assessment is based on a linear cumulative damage rule through the use of the Rainflow-counting algorithm and S-N curves from traditional design codes.The results indicated that,in several analysed situations,the investigated floor presents excessive vibration and user’s discomfort.On the other hand,the structure service life values were higher than those proposed by the design codes,ensuring that the members,connections and joints will not fail by fatigue cracking.

Frequency Features Based Fuzzy System for Rotating Machinery Vibration Analysis Using Smartphones Low-Cost MEMS Sensors

Smart devices have become an important entity for many applications in daily life activities. These devices have witnessed a rapid improvement in its technology to fulfill the increasingly diverse usage demands. In the meanwhile, rotating machinery vibration analysis based on low-cost sensors has gained a considerable attraction over the last few years. For a long time, the vibration analysis of machines has been accepted as an effective solution to detect and prevent failures in complex systems to avoid the sudden malfunction. The objective of this work is to use MEMS accelerometer measurements to monitor the different level of vibration of a machine. This work presents a new technique for rotating machinery vibration analysis. It uses Fast Fourier Transformation as a feature extraction algorithm and Fuzzy Logic System (FLS) as the classifier algorithm. A smartphone accelerometer is used to collect the data from the vibrating machine. The performance of the proposed technique is tested using data from different vibration resources at a different speed of operations. The results are discussed to illustrate the various vibration levels.

Shape Control and Vibration Analysis of Pi-ezolaminated Plates Subjected to Electro-Mechanical Loading

Shape control and free vibration analysis of piezolaminated plates subjected to electro mechanical loading are evaluated using finite element method. First order shear deformation theory is employed in the analysis. Both extensions as well as shear actuators are considered for piezolaminated plates. Rectangular four node isoparametric element is used in the finite element formulation. Variation of temperature is neglected for the orthotropic layers of the laminate and for piezolayer. Annular circular plates and rectangular plates with piezoelectric layers mounted and/or integrated are analysed for various parameters. Numerical results are presented for varying the actuator voltage for annular plates with different thicknesses of piezo patches. In case of rectangular plate shear actuator is considered for vibration analysis.

The semi-analytical modeling and vibration reduction analysis of the cylindrical shell with piezoelectric shunt damping patches

By considering electromechanical coupling, a unified dynamic model of the cylindrical shell with the piezoelectric shunt damping patch(PSDP) is created. The model is universal and can simulate the vibration characteristic of the shell under different states including the states in which PSDP cannot be connected, partially connected, and completely connected to the shunt circuit. The equivalent loss factor and elastic modulus with frequency dependence are proposed to consider the electrical damping effect of resistance shunt circuits. Moreover, the semi-analytical dynamic equation of the cylindrical shell with PSDP is derived by the Lagrange equation. An experimental test is carried out on the cylindrical shell with PSDP to verify the vibration suppression ability of PSDP on the cylindrical shell and the correctness of the proposed model. Furthermore, the parameter analysis shows that determining the appropriate resistance value in the shunt circuit can achieve a good vibration suppression effect.

An active high-static-low-dynamic-stiffness vibration isolator with adjustable buckling beams:theory and experiment

High-static-low-dynamic-stiffness(HSLDS)vibration isolators with buckling beams have been widely used to isolate external vibrations.An active adjustable device composed of proportion integration(PI)active controllers and piezoelectric actuators is proposed for improving the negative stiffness stroke of buckling beams.A nonlinear output frequency response function is used to analyze the effect of the vibration reduction.The prototype of the active HSLDS device is built,and the verification experiment is conducted.The results show that compared with the traditional HSLDS vibration isolator,the active HSLDS device can broaden the isolation frequency bandwidth,and effectively reduce the resonant amplitude by adjusting the active control parameters.The maximum vibration reduction rate of the active HSLDS vibration isolator can attain 89.9%,and the resonant frequency can be reduced from 31.08 Hz to 13.28 Hz.Therefore,this paper devotes to providing a new design scheme for enhanced HSLDS vibration isolators.

Vibration analysis and control technologies of hydraulic pipeline system in aircraft:A review

Vibrations in aircraft hydraulic pipeline system,due to multi-source excitation of high fluid pressure fluctuation and serious vibration environment of airframe,can cause the pipeline system vibration failures through overload in engineering field.Controlling the vibrations in hydraulic pipeline is a challenging work to ensure the flight safety of aircraft.The common vibration control technologies have been demonstrated to be effective in typical structures such as aerospace structures,shipbuilding structures,marine offshore structures,motor structures,etc.However,there are few research literatures on vibration control strategies of aircraft hydraulic pipeline.Combining with the development trend of aircraft hydraulic pipeline system and the requirement of vibration control technologies,this paper provides a detailed review on the current vibration control technologies in hydraulic pipeline system.A review of the general approaches following the passive and active control technologies are presented,which are including optimal layout technique of pipeline and clamps,constrained layer damping technique,vibration absorber technique,hydraulic hose technique,optimal pump structure technique,and active vibration control technique of pipeline system.Finally,some suggestions for the application of vibration control technologies in engineering field are given.

Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting.The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule(GDQR) method.The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation.Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS,and good agreement is found.The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam.It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam,i.e.,generating more voltage outputs over a wide frequency range,absorbing vibration,and being less weight.

Chebyshev-Lagrange Multipliers Technique for Vibration Analysis of Functionally Graded Material Beams using Various Beam Theories

In this paper,a new technique for analysing functionally graded material(FGM)beams using the Chebyshev polynomials and Lagrange multipliers with various beam theories is presented.By utilizing the inner products and the Chebyshev polynomials’orthogonality properties incorporated with Lagrange multipliers,we can combine the governing equation and boundary conditions to yield the matrix equations with explicit weighting coefficients.Numerical examples are provided for vibration analysis of various beam theories and assumptions.Based on numerical evaluations,it is revealed that the proposed technique can efficiently achieve good agreement with those of the references.

Fault diagnosis of tractor auxiliary gearbox using vibration analysis and random forest classifier

Accurate detection of mechanical components faults is an essential step for reduction of repair cost,human injury probability and loss of production.Using intelligent fault diagno-sis systems in tractor could prevent secondary damage,thereby avoiding heavy conse-quences.In this study,fault diagnosis of tractor auxiliary gearbox is presented.Vibration signals of healthy and faulty pinions gear under three different operational conditions(Rotational speeds of 600 RPM,1350 RPM and 2000 RPM)were collected,and discrete wave-let transform(DWT)was used as signal processing.Useful statistical features were calcu-lated from collected signals.Correlation-based feature selection(CFS)method was used to find the best features.Random forest(RF)and multilayer perceptron(MLP)neural net-works were employed to classify the data.The overall accuracy of RF classifier without using feature selection were 86.25%,at 600 RPM.The corresponding values of RF trained with the optimal 6 features by using CFS was 92.5%.The best results obtained at 1350 RPM,since the detection accuracy was 95%.The results of this study demonstrated the effectiveness and feasibility of the proposed method for fault diagnosis of tractor auxiliary gearbox.

Vibration Characteristics Analysis and Structure Optimization of Catenary Portal Structure on Four-Wire Bridge

The portal structure is the support equipment in the catenary,which bears the load of contact suspension and support equipment.In practical work,with the change of external forces,the support equipment bears complex and changeable loads,so it has higher requirements for its reliability and safety.In order to study the dynamic characteristics of catenary portal structure on continuous beam of four-way bridge,taking the catenary portal structure on Dshaping four-way bridge as the research object,the portal structure simulation model of bridgenetwork integration was established in Midas Civil.The maximum point of deformation and stress was determined by finite element analysis of catenary hard span equipment,and the frequency and mode of natural vibration of hard span were obtained by modal analysis.Secondly,through the field dynamic stress acquisition test,combined with the results of finite element analysis,the fault location is determined,and the vibration characteristics are analyzed.Finally,based on the results of modal analysis and vibration analysis,the method that the vibration of portal structure beam is affected by structural stiffness and vibration frequency amplitude is proposed.The torsional vibration of the portal structure beam was suppressed by increasing the stiffness of the beam and reducing the vibration conduction between the trolley and the beam,and the hard cross beam was optimized by strengthening the hanging column and the connecting beam and adding diagonal support between the pillar and the portal structure beam.By comparing the values of shear,bending moment,displacement and dynamic stress on the hard span before and after optimization,the amplitude peak after structural optimization is reduced by about 25%,and the application of oblique support and reinforcement of the beam can significantly improve the portal structure vibration.