Natural Frequency Characteristics of Laminated Composite Structures Reinforced by a Wavy CNT

This study investigates the influence of auxiliary piers on the natural frequency, deformation characteristics, displacements of the related parts, and internal forces of a long‐span heterogeneous steel‐structured main tower cable‐stayed bridge. Taking the Guohe Third Bridge in Anhui Province as an example, the software ANSYS was used to establish a three‐dimensional finite element model of a cable‐stayed bridge, and the dynamic characteristics of a long‐span specially shaped hybrid steel structure main tower cable‐stayed bridge with auxiliary piers added to single span and double spans were analysed. The results show that when one or three pairs of auxiliary piers are added to a single span, the changes in the natural frequency and deformation characteristics are smaller than those when there are no auxiliary piers. When one or three pairs of auxiliary piers are added to each of the two spans, the natural frequency and deformation characteristics are relatively low. Auxiliary piers induce relatively large changes; the changes with 3 pairs of auxiliary piers for a single span is compared with those with 1 pair for a single span, and 3 pairs and 1 pair of auxiliary piers are added to both spans for comparison. The natural vibration frequency and deformation characteristics exhibit relatively small changes; the presence or absence of auxiliary piers and the number of auxiliary piers have a greater influence on the vertical displacement of the main girder and less influence on the vertical displacement of the main tower. An appropriate number of auxiliary piers are beneficial to the seismic resistance of a cable‐stayed bridge, and if the number of auxiliary piers is too large, the seismic capacity of the bridge is reduced; it is recommended that a pair of auxiliary piers be added to both spans to optimize the overall dynamic performance of a cable‐stayed bridge. This research method can be used on similar cable‐stayed bridges to optimize their dynamic characteristics by setting a certain number of auxiliary piers.

Effect of geometry on the natural frequency and seismic response characteristics of slopes subjected to pulse-like ground motions

In traditional magnetic coupling wireless power transfer (MC-WPT) systems, the combined use of magnetic induction, tuned circuits and resonant operating frequency has been a common theme for achieving the maximum transfer efficiency. However, that is not exactly true. By deeply analyzing the operating frequency characteristics and circuit natural frequency characteristics of transfer efficiency of MC-WPT systems, this paper discovers that: 1) the optimal operating frequency and optimal circuit natural frequencies for the transfer efficiency are two different concepts; 2) Only under certain parameters, is there an optimal operating frequency for the transfer efficiency, otherwise the transfer efficiency increases with an increasing operating frequency. Moreover, even if there is an optimal operating frequency for the maximum transfer efficiency, the optimal operating frequency is not equal to the circuit natural frequencies in the system; 3) With a fixed operating frequency, the transfer efficiency is maximized when the natural frequency of the receiver is equal to the operating frequency, regardless of the natural frequency of the transmitter. The simulation and experimental results have confirmed the validity of these conclusions.

Numerical investigation on natural vibration characteristics of ship propulsion shafting under uncertainty based on nonparametric approach

Natural frequency characteristics of a thin-walled multiple layered cylindrical shell under lateral pressure are studied. The multiple layered cylindrical shell configuration is formed by three layers of isotropic material where the inner and outer layers are stainless steel and the middle layer is aluminum. The multiple layered shell equations with lateral pressure are established based on Love’s shell theory. The governing equations of motion with lateral pressure are employed by using energy functional and applying the Ritz method. The boundary conditions represented by end conditions of the multiple layered cylindrical shell are simply supported-clamped(SS-C), free-clamped(F-C) and simply supported-free(SS-F). The influence of different lateral pressures, different thickness to radius ratios, different length to radius ratios and effect of the asymmetric boundary conditions on natural frequency characteristics are studied. It is shown that the lateral pressure has effect on the natural frequency of multiple layered cylindrical shell and causes the natural frequency to increase. The natural frequency of the developed multilayered cylindrical shell is validated by comparing with those in the literature. The proposed research provides an effective approach for vibration analysis shell structures subjected to lateral pressure with an energy method.

The paper proposes a method in finite element analysis for estimating natural frequencies of a disk tensioned by rolling, without the use of eigenvalue analysis. The natural frequencies of a disk vary when the localized plastic deformation caused by roll-tensioning induces residual stresses. Tensioning is used for improving the dynamic stability of circular saws; the optimal condition of rolling can be predicted from natural frequency characteristics. In the proposed method, the natural frequencies after rolling are easily estimated from the mode shapes of the disk before rolling and the stress distribution after rolling. The method is based on ideas similar to thermal stress and sensitivity analysis rather than on eigenvalue analysis. The effectiveness of the method is shown by comparing the natural frequency characteristics obtained by this method with those by eigenvalue analysis.

Energy method for the vibration of two types of cylindrical shells, namely thin-walled homogeneous isotropic and manifold layered isotropic cylindrical shells under uniform external lateral pressure is presented. The study is carried out based on strain-displacement relationship from Love’s shell theory with beam functions as axial modal function. A manifold layered cylindrical shell configuration is formed by three layers of isotropic material where the inner and outer layers are stainless steel and the middle layer is aluminum. The homogeneous cylindrical shell is made-up of isotropic one layer with stainless steel. The governing equations with uniform external lateral pressure for homogeneous isotropic and manifold layered isotropic cylindrical shells are obtained using energy functional by the Lagrangian function with Rayleigh-Ritz method. The boundary conditions that are presented at the end conditions of the cylindrical shell are simply supported-simply supported, clamped-clamped and free-free. The influences of uniform external lateral pressure and symmetrical boundary conditions on the natural frequency characteristics for both homogeneous and manifold layered isotropic cylindrical shells are examined. For all boundary conditions considered, the natural frequency of both cylindrical shells with symmetric uniform lateral pressure increases as h/R ratio increases and those considering natural frequency of the both cylindrical shells with symmetric uniform lateral pressure decrease as L/R ratio increases.

This paper presents the study on natural frequency characteristics of a thin-walled functionally graded material (FGM) cylindrical shell with rings support under symmetric uniform interior pressure distribution. The FGM properties are graded along the thickness direction of the shell. The FGM shell equations with rings support and interior pressure are established based on first-order shear deformation theory. The governing equations of motion were employed, using energy functional and by applying the Ritz method. Ten boundary conditions represented by end conditions of the FGM shell are the following: simply supported-simply supported, clamped-clamped, free-free, clamped-free, clamped-simply supported, free-simply supported, sliding-sliding, sliding-simply supported, sliding-free and sliding-clamped. This problem was solved with computer programming using MAPLE package for numerical investigation. Comparison of the results is carried out to verify the validity of the proposed procedure with published works. The influence of interior pressure, ring support position and number of rings support, and effect of the ten boundary conditions on natural frequency characteristics are studied. The results presented can be used as an important benchmark for researchers to validate their numerical methods when studying natural frequencies of shells with ring and pressure.

Through a series of experiments of dynamic deformation and destruction under time series loading on an indoor real model bridge, Ground-based real-aperture radar interferometry (GB-InRAR) discovered that before the structure of the bridge was damaged, its amplitude and acceleration increased with the increase of load; After its structure was damaged or cracked, such dynamic characteristics as natural frequency, damping ratio, stiffness and bearing capacity decreased obviously. Moreover, GB-InRAR dynamic load monitoring of Xiangtan Railway Bridge and Inter-city Railway Bridge. In the process of vehicle dynamic load, such important parameters as bridge deflection, natural frequency and damping ratio conform to the bridge loading procedures and dynamic characteristics. The results show that the GB-InRAR can accurately measure the deflection changes, natural vibration frequency and spectrum characteristics of bridges, and it can be used as effective means of the dynamic characteristics analysis in the safety detection and health evaluation of bridges.

In this technical brief, the resonance problem of a robot joint is analyzed. By establishing the electromechanical coupling dynamic equation of the robot joint, the natural vibration characteristics of the electromechanical coupling system are calculated, and the resonance is analyzed by combining the modal energy and Campbell diagram. It is found that when the meshing frequency coincides with the seventh- and eighth-order natural frequencies, resonance is easy to occur. The influence of different parameters on natural characteristics is analyzed. The increase of torsional stiffness and meshing stiffness will increase the natural frequency. Different control algorithms will have different impacts on the transmission system, and fuzzy control is better than double closed-loop control.

A new type of U‐shaped steel‐concrete composite floor is analyzed in detail. The experimental test and finite element analysis of the floor are conducted to study the natural frequency and serviceability characteristics of the new composite floor structure. The natural frequency of the floor is measured under the environmental random vibration stimulating method, and the peak acceleration of the floor is measured under pedestrian‐induced load. The experimental test results show that the U‐shaped steel‐concrete composite floor has better antiseismic behaviors and meet the specified serviceability requirements. The finite element analysis results indicate the constraints have a great impact on the calculation results. The experimental tests and FEM results of the floor are compared based on the modal assurance criterion, and the results are in good agreement. The experimental test acceleration curves demonstrate that the peak values meet the requirements of Chinese specification.

Research on pendulum-type tunable vibration energy harvesting

A remarkable example of how to quantitatively explain the nonlinear performance of many phenomena in physics and engineering is the Van der Pol oscillator. Therefore, the current paper examines the stability analysis of the dynamics of ϕ6-Van der Pol oscillator (PHI6) exposed to exterior excitation in light of its motivated applications in science and engineering. The emphasis in many examinations has shifted to time-delayed technology, yet the topic of this study is still quite significant. A non-perturbative technique is employed to obtain some improvement and preparation for the system under examination. This new methodology yields an equivalent linear differential equation to the exciting nonlinear one. Applying a numerical approach, the analytical solution is validated by this approach. This novel approach seems to be impressive and promising and can be employed in various classes of nonlinear dynamical systems. In various graphs, the time histories of the obtained results, their varied zones of stability, and their polar representations are shown for a range of natural frequencies and other influencing factor values. Concerning the approximate solution, in the case of the presence/absence of time delay, the numerical approach shows excellent accuracy. It is found that as damping and natural frequency parameters increase, the solution approaches stability more quickly. Additionally, the phase plane is more positively impacted by the initial amplitude, external force, damping, and natural frequency characteristics than the other parameters. To demonstrate how the initial amplitude, natural frequency, and cubic nonlinear factors directly affect the periodicity of the resulting solution, many polar forms of the corresponding equation have been displayed. Furthermore, the stable configuration of the analogous equation is shown in the absence of the stimulated force.

A gradient of a blood flow velocity on the surface of a blood vessel is one of the clinical medicine concerns from the view point of prevention of the arteriosclerosis. In previous study, we formulated a relationship between the pressure and a flow velocity based on the coupled wave theory of elastic pipes and Newtonian fluids [1]. In addition, a flow velocity distribution and a wall shear stress are estimated by using the blood pressure data, which are non-invasively obtained by the tonometry method. This method is quasi-analytical method to apply the coupled wave theory for industrial flow field inside steel pipes proposed by Urata [4] to blood vessel, and has the advantage of systematic estimator compared with the numerical calculation. However, the coupled wave theory has applied to the elastic pipes that were assumed to be infinitely long. In addition, a single wave was assumed to be dominant within the elastic pipes and the Newtonian fluids. Therefore, in order to apply various length vessels in clinical field, the boundary of the blood vessels that varies from site to site, and the natural vibration characteristics that depend on the boundary conditions, could not be reflected in the wall shear stress estimation. In general, in order to solve the forced vibration with the boundary condition, it is necessary to clarify natural frequency and natural mode as natural vibration characteristics of structure. In this study, we introduce the spring supported elastic pipes to the coupled wave theory and formulated a relationship between the natural vibration characteristics and the boundary conditions. In this proposed method, the spring-supported elastic pipe has a feature that can be treated as an arbitrary boundary condition of an artery by giving an appropriate spring coefficients. Therefore, it is easy to apply to various types of blood vessels clinically. By investigating the natural vibration characteristics of blood vessels that varies from site to site, it may be possible to clarify fluctuations of blood flow in response to blood pressure with some frequency-bands. In addition, natural angular frequencies and natural modes of the spring supported elastic pipes and the Newtonian fluids were estimated for general blood vessel based on the coupled wave theory. In the result, the natural angular frequencies and the natural modes that reflect the clinical vibration characteristics to some extent can be estimated. On the other hand, particular modes may not reflect boundary condition, and further examination of the relationship between natural vibration characteristics and boundary condition is needed.

The free and forced response of spinning, viscoelastic, Rayleigh shafts is studied. Viscoelasticity is included using the three parameter solid model. The closed form polynomial frequency equation and integral expressions for the response to a general forcing function are derived. A convenient decay parameter is described. Results are given for natural frequencies and decay rates as functions of shaft rotation speed, stiffness, and viscosity. It is found that shaft materials are possible which have desirable damping and natural frequency characteristics. A parameter case is discussed in which natural frequency and damping simultaneous increase, while stiffness is held constant. Also, the special case of forced response to a step load is derived and used to illustrate the combined effects of viscoelasticity and gyroscopic forces.