Control and vibration analyses of a sandwich doubly curved micro-composite shell with honeycomb,truss,and corrugated cores based on the fourth-order shear deformation theory

Curved shells are increasingly utilized in applied engineering due to their shared characteristics with other sandwich structures,flexibility,and attractive appearance.However,the inability of controlling and regulating vibrations and destroying them afterward is a challenge to scientists.In this paper,the curve shell equations and a linear quadratic regulator are adopted for the state feedback design to manage the structure vibrations in state space forms.A five-layer sandwich doubly curved micro-composite shell,comprising two piezoelectric layers for the sensor and actuator,is modeled by the fourth-order shear deformation theory.The core(honeycomb,truss,and corrugated)is analyzed for the bearing of transverse shear forces.The results show that the honeycomb core has a greater effect on the vibrations.When the parameters related to the core and the weight percentage of graphene increase,the frequency increases.The uniform distribution of graphene platelets results in the lowest natural frequency while the natural frequency increases.Furthermore,without taking into account the piezoelectric layers,the third-order shear deformation theory(TSDT)and fourth-order shear deformation theory(FOSDT)align closely.However,when the piezoelectric layers are incorporated,these two theories diverge significantly,with the frequencies in the FOSDT being lower than those in the TSDT.

In-plane forced vibration of curved pipe conveying fluid by Green function method

The Green function method （GFM） is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping ratio are considered. The Laplace transform is used, and the Green functions with various boundary conditions are obtained subsequently. Numerical calculations are performed to validate the present solutions, and the effects of some key parameters on both tangential and radial displacements are further investigated. The forced vibration problems with linear and nonlinear motion constraints are also discussed briefly. The method can be radiated to study other forms of forced vibration problems related with pipes or more extensive issues.

Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass

In this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonlin- ear vibrations were investigated. Sinusoidal and parabolic type functions were used as curvature functions. Equations of motion have cubic nonlinearities because of elongations during vibrations. Damping and harmonic excitation terms were added to the equations of motion. Method of mul- tiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequen- cies were calculated exactly for different mass ratios, mass locations, curvature functions, and linear elastic foundation coefficients. Amplitude-phase modulation equations were found by considering primary resonance case. Effects of nonlinear terms on natural frequencies were calculated. Frequency-amplitude and frequency-response graphs were plotted. Finally effects of concentrated mass and chosen curvature function on nonlinear vibrations were investigated.

Simplified Method and Influence Factors of Vibration Characteristics of Isolated Curved Girder Bridge

The isolated curved girder bridge's vibration characteristics play a major part in the seismic responses of structures and anti-seismic properties.A clear analytic relationship between design parameters and the system's vibration characteristics could be established by its simplified dynamic analysis model,making it convenient for providing a reference to the optimization of design and safety analysis.A double-mass six-degree-of-freedom model for curved girder bridges with isolation bearings installed at the top of the bridge piers is built and a simplified analysis method for the vibration characteristics of the system is provided.Combined with the Matlab programming,the influences of radius of curvature,central angle,bridge deck width and damping ratio of the isolation layer and circular frequency of the isolation layer of isolated curved girder bridges on the pseudo-undamped natural circular frequency(called pseudo-frequency for short)and system damping ratio are systematically analyzed,and the sensitivity of vibration characteristics of isolated curved girder bridges is studied.The results show that the vibration characteristics of isolated curved girder bridges can be reflected well with this simplified model and calculation method.The pseudo-frequency of curved girder and system damping ratios increases with the increase of the isolation layer.The third-order vibration characteristic is more sensitive to the parameters of a curved girder,and the first-order vibration characteristic is sensitive to both central angle and radius of curvature to some extent while insensitive to the width of the bridge deck.Furthermore,the second-order vibration characteristic is not sensitive to the parameters of a curved girder.

APPROXIMATE VIBRATION ANALYSIS OF LAMINATED CURVED PANEL USING HIGHER-ORDER SHEAR DEFORMATION THEORY

An approximate analysis for free vibration of a laminated curved panel(shell)with four edges simply supported(SS2),is presented in this paper.The transverse shear deformation is considered by using a higher-order shear deformation theory.For solving the highly coupled partial differential governing equations and associated boundary conditions,a set of solution functions in the form of double trigonometric Fourier series,which are required to satisfy the geometry part of the considered boundary conditions,is assumed in advance.By applying the Galerkin procedure both to the governing equations and to the natural boundary conditions not satisfied by the assumed solution functions,an approximate solution,capable of providing a reliable prediction for the global response of the panel,is obtained.Numerical results of antisymmetric angle-ply as well as symmetric cross-ply and angle-ply laminated curved panels are presented and discussed.

Theoretical Study on the Potential Energy Curve and Vibration-rotation Spectra of BeF Radical

The potential energy curve （PEC） of BeF（X2Σ＋） radical is investigated by using the complete active space self-consistent field （CASSCF） method followed by the highly accurate valence internally contracted multireference configuration interaction （MRCI） approach over the internuclear separation range from 0.0522 to 2.0472 nm. The PEC is fitted to the analytic Murrell-Sorbie function, which is employed to accurately determine the spectroscopic parameters. The present D0, De, Re, ωe, ωeχe, αe and Be are 6.14 eV, 6.22 eV, 0.1372 nm, 1236.12 cm-1, 9.11 cm-1, 0.0175 cm-1 and 1.4651 cm-1, respectively. These parameters have been compared with those of previous investigations reported in the literature. With PEC determined at the present level of theory, a total of 75 vibrational states have been predicted for the first time by numerically solving the radial Schrdinger equation of nuclear motion using the Numerov method. For each vibrational state, the complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are determined for the first time. Comparing with the available experiments and other theories, we find that the present spectroscopic parameter and molecular constant results are more accurate and complete than the previous theoretical investigations.

Flow-Induced Vibration of A Nonlinearly Restrained Curved Pipe Conveying Fluid

Investigated in this study is the flow induced vibration of a nonlinearly restrained curved pipe conveying fluid. The nonlinear equation of motion is derived by equilibrium of forces on microelement of the system under consideration. The spatial coordinate of the system is discretized by DQM (differential quadrature method). On the basis of the boundary conditions, the dynamic equation is solved by the Newton Raphson iteration method. The numerical solutions reveal several complex dynamic motions for the variation of the fluid velocity parameter, such as limit cycle motion, buckling and so on. The result obtained also shows that the sub parameter regions corresponding to the several motions may change with the variation of some parameters of the curved pipe. The present study supplies a new reference for investigating the nonlinear dynamic response of some other structures.

Coupled Vibration of Long-Span Railway Curved Girder Bridges and Vehicles

The structure of a long curved girder bridge is represented with a three-dimensional curved finite element model. Each 4-axle ~vehicle is modeled by a dynamic system of 35 degrees of freedom. The random irregularities of the track are generated from a power spectral density function under the given track condition. The dynamic interaction between the bridge and train is realized through the contact forces between the wheels and track. Then based on these models, the coupled equations of motion are solved by applying the time-integration and iteration techniques to the coupled system. The proposed formulation and the associated computer program are then applied to a real curved girder bridge. The dynamic responses of the bridge-vehicle system and the derailments and offload factors related to the riding and running safeties of vehicles are computed. The results show that the formulation presented in this paper can well predict dynamic behaviors of both bridge and train with reasonable computation efforts.

Nonlinear Free Vibration Analysis of Thin-walled Curved Beam with Non-symmetric Open Cross Section

A finite element formulation was presented for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies were derived by the virtual principle. The energy function includes the effect of fiexural-torsional coupling, the torsion warping and the shear centre location. For finite element analysis, cubic polynomials were utilized as the shape functions of the two nodal thin-walled curved elements. Each node possesses seven degrees freedom including the warping degree of freedom. The nonlinear eigenvalue problem was solved by the direct iteration technique. The results are compared with those for straight beams as available in the literature. The results for nonlinear free vibration analysis of curved beams for various radii and subtended angle are presented.

WEIGHTED LEAST SQUARE METHOD FOR S-N CURVE FITTING

An S-N curve fitting approach is proposed based on the weighted least square method, and the weights are inversely proportional to the length of mean confidence intervals of experimental data sets. The assumption coincides with the physical characteristics of the fatigue life scatter. Two examples demonstrate the method. It is shown that the method has better accuracy and reasonableness compared with the usual least square method.

Analysis Approach to Durability Based on Material Initial Fatigue Quality and S-N Curve

Based on probabilistic fracture mechanics approach, a new concept of material initial fatigue quality （MIFQ） is developed. Then, the relation between S-N curve and crack propagation curve is studied. From the study, a new durability analysis method is presented. In this method, S-N curve is used to determine crack growth rate under constant amplitude loading and evaluate the effects of different factors on durability and then the structural durability is analyzed. The tests and analyses indicate that this method has lower dependence on testing, and higher accuracy, reliability and generality and is convenient for application.

Combine S-N curve and fracture mechanics for fatigue life analysis of welded structures

Based on the evolution of fatigue cracks in welded structures,the fatigue life of welded structures was defined as the sum of the crack initiation life Ni and the crack propagation life Np.Correspondingly,a fatigue-life analysis method combining S-N curves and fracture mechanics theory was proposed.The equivalent structural stress method and the lower 99%boundary of the master S-N curve were used to evaluate Ni,and cracks at the end of the initiation stage were considered as semi-elliptical surface cracks.Moreover,Paris equation and the stress intensity factor range of the cracks were used to evaluate Np.Furthermore,the fatigue test results obtained from the running girder of cranes were used as a reference for comparison and verification of the results.The results revealed that the equivalent structural stress is a good indicator for the crack initiation behavior of complex welded structures.In addition,the predicted fatigue life corresponded closely to the testing life.

Compression Properties and Energy Absorption of A Novel Double Curved Beam Negative Stiffness Honeycomb Structures

This paper presents the design of a novel honeycomb structure with a double curved beam.The purpose of this design is to achieve vibration isolation for the main engine of an offshore platform and reduce impact loads.An analytical formula for the force-displacement relationship of the honeycomb single-cell structure is presented based on the modal superposition method.This formula provides a theoretical basis for predicting the compression performance of honeycomb structures.The effects of structural geometric parameters,series and parallel connection methods on the mechanical and energy absorption properties are investigated through mathematical modeling and experimental methods.Furthermore,the study focuses on the vibration isolation and impact resistance performance of honeycomb panels.The results show that the designed honeycomb structure has good mechanical and energy absorption performance,and its energy absorption effect is related to the geometric parameters and series and parallel connection methods of the structure.The isolation efficiency of the honeycomb with 4 rows and 3 columns reaches 38%.The initial isolation frequency of the isolator is 11.7 Hz.

Reconstruction of probabilistic S-N curves under fatigue life following lognormal distribution with given confidence

When the historic probabilistic S-N curves are given under special survival probability and confidence levels and there is no possible to re-test, fatigue reliability analysis at other levels can not be done except for the special levels. Therefore, the wide applied curves are expected. Monte Carlo reconstruction methods of the test data and the curves are investigated under fatigue life following lognormal distribution. To overcome the non-conservative assessment of existent man-made enlarging the sample size up to thousands, a simulation policy is employed to address the true production where the sample size is controlled less than 20 for material specimens, 10 for structural component specimens and the errors matching the statistical parameters are less than 5 percent. Availability and feasibility of the present methods have been indicated by the reconstruction practice of the test data and curves for 60Si2Mn high strength spring steel of railway industry.

Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

Mechanical properties of disc-spring vibration isolators based on boundary friction

To ascertain the influence of the boundary friction on mechanical properties of disc-spring vibration isolators a load-displacement hysteresis curve formula of disc-spring vibration isolators is derived on the basis of the energy conservation law as well as considering the effect of the boundary friction.The formula is validated through the finite element analysis and static load tests.On this basis the effect of the boundary friction on the bearing capacity is researched. Then the dynamic performance of disc-spring vibration isolators is studied by dynamic tests.The experimental results indicate that the boundary friction can promise a larger damping with a ratio of 0.23 for disc-spring vibration isolators.Compared with the loading frequency the loading amplitude has a greater impact on the energy consumption dynamic stiffness and damping of vibration isolators.This research can provide valuable information for the design of disc-spring vibration isolators.

HOPF BIFURCATION OF A NONLINEAR RESTRAINED CURVED PIPE CONVEYING FLUID BY DIFFERENTIAL QUADRATURE METHOD

This paper proposes a new method for investigating the Hopf bifurcation of a curved pipe conveying fluid with nonlinear spring support.The nonlinear equation of motion is derived by forces equilibrium on microelement of the system under consideration.The spatial coordinate of the system is discretized by the differential quadrature method and then the dynamic equation is solved by the Newton-Raphson method.The numerical solutions show that the inner fluid velocity of the Hopf bifurcation point of the curved pipe varies with different values of the parameter, nonlinear spring stiffness.Based on this,the cycle and divergent motions are both found to exist at specific fluid flow velocities with a given value of the nonlinear spring stiffness.The results are useful for further study of the nonlinear dynamic mechanism of the curved fluid conveying pipe.

Structural Stress-Fatigue Life Curve Improvement of Spot Welding Based on Quasi‑Newton Method

ΔF-N curves are usually used to predict the fatigue life of spot welding in engineering,but they are time-consuming and laborious and not universal.For the purpose of predicting the fatigue life of spot welding accurately and efficiently,tensile-shear fatigue tests were conducted to obtain the fatigue life of spot-welded specimens with different sheet thicknesses combinations.These specimens were simulated by using the finite element method,and the structural stress was theoretically calculated.In the double logarithmic coordinate system,the structural stress-fatigue life(S-N)curve of spot welding was fitted by the least-squares method,based on the quasi-Newton method.The square of the correlation coefficient of the S-N curve was taken as the optimization objective,with the correction coefficients of force,bending moment,spot welding diameter,and sheet thickness as the variables.During the optimization process,three different ways were utilized to get three optimized spot welding S-N curves,which are suitable for different situations.The results show that the fitting effect of the S-N curve is improved,the data points are more compact,and the optimization effect is significant.These S-N curves can be used to predict the fatigue life,which provide the basis for practical engineering application.

Multireference configuration interaction potential curve and analytical potential energy function of the ground and low-lying excited states of CdSe

The potential energy curves （PECs） of the ground state （^3∏） and three low-lying excited states （^1∑, ^3∑,^1∏） of CdSe dimer have been studied by employing quasirelativistic effective core potentials on the basis of the complete active space self-consistent field method followed by multireference configuration interaction calculation. The four PECs are fitted to analytical potential energy functions using the Murrel-Sorbie potential function. Based on the PECs, the vibrational levels of the four states are determined by solving the Schrodinger equation of nuclear motion, and corresponding spectroscopic constants are accurately calculated. The equilibrium positions as well as the spectroscopic constants and the vibrational levels are reported. By our analysis, the ^3∏ state, of which the dissociation asymptote is Cd（^1S） ＋ Se（^3p）, is identified as a ground state of CdSe dimer, and the corresponding dissociation energy is estimated to be 0.39eV. However, the first excited state is only 1132.49cm^-1 above the ground state and the ^3∑ state is the highest in the four calculated states.

A bio-inspired spider-like structure isolator for low-frequency vibration

This paper proposes a quasi-zero stiffness(QZS)isolator composed of a curved beam(as spider foot)and a linear spring(as spider muscle)inspired by the precise capturing ability of spiders in vibrating environments.The curved beam is simplified as an inclined horizontal spring,and a static analysis is carried out to explore the effects of different structural parameters on the stiffness performance of the QZS isolator.The finite element simulation analysis verifies that the QZS isolator can significantly reduce the first-order natural frequency under the load in the QZS region.The harmonic balance method(HBM)is used to explore the effects of the excitation amplitude,damping ratio,and stiffness coefficient on the system’s amplitude-frequency response and transmissibility performance,and the accuracy of the analytical results is verified by the fourth-order Runge-Kutta integral method(RK-4).The experimental data of the QZS isolator prototype are fitted to a ninth-degree polynomial,and the RK-4 can theoretically predict the experimental results.The experimental results show that the QZS isolator has a lower initial isolation frequency and a wider isolation frequency bandwidth than the equivalent linear isolator.The frequency sweep test of prototypes with different harmonic excitation amplitudes shows that the initial isolation frequency of the QZS isolator is 3 Hz,and it can isolate 90%of the excitation signal at 7 Hz.The proposed biomimetic spider-like QZS isolator has high application prospects and can provide a reference for optimizing low-frequency or ultra-low-frequency isolators.