Splines in vibration analysis of non-homogeneous circular plates of quadratic thickness

Mathematical model to account for non-homogeneity of plate material is designed, keeping in mind all the physical aspects, and analyzed by applying quintic spline technique for the first time. This method has been applied earlier for other geometry of plates which shows its utility. Accuracy and versatility of the technique are established by comparing with the well-known existing results. Effect of quadratic thickness variation, an exponential variation of non-homogeneity in the radial direction, and variation in density; for the three different outer edge conditions namely clamped, simply supported and free have been computed using MATLAB for the first three modes of vibration. For all the three edge conditions, normalized transverse displacements for a specific plate have been presented which shows the shiftness of nodal radii with the effect of taperness.

Vibration Energy Harvesting by Means of Piezoelectric Patches: Application to Aircrafts

Vibration energy harvesters in industrial applications usually take the form of cantilever oscillators covered by a layer of piezoelectric material and exploit the resonance phenomenon to improve the generated power. In many aeronautical applications, the installation of cantilever harvesters is not possible owing to the lack of room and/or safety and durability requirements. In these cases, strain piezoelectric harvesters can be adopted, which directly exploit the strain of a vibrating aeronautic component. In this research, a mathematical model of a vibrating slat is developed with the modal superposition approach and is coupled with the model of a piezo-electric patch directly bonded to the slat. The coupled model makes it possible to calculate the power generated by the strain harvester in the presence of the broad-band excitation typical of the aeronautic environment. The optimal position of the piezoelectric patch along the slat length is discussed in relation with the modes of vibration of the slat. Finally, the performance of the strain piezoelectric harvester is compared with the one of a cantilever harvester tuned to the frequency of the most excited slat mode.

Investigation of mechanical characteristics of braided carbon fiber

The use of composite materials in various branches of modern industry is rapidly increasing due to their high strength properties, low weight and good manufacturability. A wide variety of materials used, types of reinforcement and internal structures creates a need for studies of the static and dynamic properties of composite materials. Due to the latest advances in technology, composite materials are widely used in a variety of industrial applications. As a result, there is considerable interest in studying and understanding the behavior of composite structures. Analysis of composite structures, study of resonance frequencies, damping factors and modal shapes played an important role in determining the dynamic characteristics of the structure, detecting damage and monitoring the state of the composite structure. In this paper, the results of computational and experimental researches of the Young’s modulus, natural frequencies and modes of vibration, damping properties of the composite material are presented. The researches were carried out on samples of the woven ten-layer carbon fiber reinforced plastic. The investigated carbon fiber reinforced plastic has a plain weave. Samples were cut in three directions: warp (0 °), weft (90 °) and 45 °. Nine samples were prepared for each direction. To study the Young’s modulus, a tensile testing machine was used, and a vibration stand was used to determine the natural frequencies and modes of vibration. Damping properties are calculated by the Oberst method, based on the amplitude-frequency characteristics of the samples. Statistical processing of the experimental results was carried out and the values ​​of the mathematical expectation and variance were obtained. Geometric and finite element models of сarbon fiber reinforced plastic samples were built, their natural frequencies and vibration modes were determined. Comparison of the computational and experimental data with numerous calculations using the finite element method is carried out.

MODELING OF VIBRATION PROCESSES OF PASSENGER CAR BODY

The quality of rail transport largely depends on the comfortable and safe movement of passengers. By the method of computer modeling, the frequencies and modes of vibration of the body, which have a negative effect on the human body, were found.

Time Period of the Vibration of the Circular Plate with Circular Variation Both in Thickness and Density

An analysis was carried out to investigate the time period of the thermally induced vibration of clamped and simply supported circular plates with circular variation both in thickness and density. Prior to this study, the variations considered were either linear, quadratic, parabolic, or exponential in nature. To study thermal effect, one-dimensional linear temperature variation on the plates is taken into consideration. Rayleigh–Ritz method is applied to compute the time period of the first three modes of vibration for both plates by varying tapering parameter, thermal gradient, and density. Convergence study of frequency modes for both plates conducted suggests that the convergence rate in case of circular variation is faster than the other studies done. A comparison of time period with the available published results is done. The comparison done concludes that time period obtained in the present study by varying thermal gradient and tapering parameter is found to be less than the other studies done for the same set of parameters. This study helped to establish the fact that, by using circular variation in plate parameters, we can get less time period of frequency modes in comparison to other variations considered till date.

Modal Kinematic Analysis of a Parallel Kinematic Robot with Low-Stiffness Transmissions

Several industrial robotic applications that require high speed or high stiffness-to-inertia ratios use parallel kinematic robots. In the cases where the critical point of the application is the speed, the compliance of the main mechanical transmissions placed between the actuators and the parallel kinematic structure can be significantly higher than that of the parallel kinematic structure itself. This paper deals with this kind of system, where the overall performance depends on the maximum speed and on the dynamic behavior. Our research proposes a new approach for the investigation of the modes of vibration of the end-effector placed on the robot structure for a system where the transmission’s compliance is not negligible in relation to the flexibility of the parallel kinematic structure. The approach considers the kinematic and dynamic coupling due to the parallel kinematic structure, the system’s mass distribution and the transmission’s stiffness. In the literature, several papers deal with the dynamic vibration analysis of parallel robots. Some of these also consider the transmissions between the motors and the actuated joints. However, these works mainly deal with the modal analysis of the robot’s mechanical structure or the displacement analysis of the transmission’s effects on the positioning error of the end-effector. The discussion of the proposed approach takes into consideration a linear delta robot. The results show that the system’s natural frequencies and the directions of the end-effector’s modal displacements strongly depend on its position in the working space.

Fast-Slow Coupling Dynamics Behavior of the van der Pol-Rayleigh System

In this paper, the dynamic behavior of the van der Pol-Rayleigh system is studied by using the fast–slow analysis method and the transformation phase portrait method. Firstly, the stability and bifurcation behavior of the equilibrium point of the system are analyzed. We find that the system has no fold bifurcation, but has Hopf bifurcation. By calculating the first Lyapunov coefficient, the bifurcation direction and stability of the Hopf bifurcation are obtained. Moreover, the bifurcation diagram of the system with respect to the external excitation is drawn. Then, the fast subsystem is simulated numerically and analyzed with or without external excitation. Finally, the vibration behavior and its generation mechanism of the system in different modes are analyzed. The vibration mode of the system is affected by both the fast and slow varying processes. The mechanisms of different modes of vibration of the system are revealed by the transformation phase portrait method, because the system trajectory will encounter different types of attractors in the fast subsystem.

Assessment of stress state and dynamic characteristics of plane and spatial structure

This study is devoted to the assessment of the stress state and dynamic characteristics of various structures. The actual task at the design stage is to determine the parameters of a structure. In this article, a mathematical model was developed for assessing the stress state and dynamic characteristics of plane and spatial structures based on the Lagrange variational equation using the d’Alembert principle. The variational problem for the structures considered by the finite element method leads to the solution of nonhomogeneous algebraic equations or to the solution of algebraic eigenvalue problems. To assess the adequacy of the model and the accuracy of the numerical results obtained, a plane and spatial test problem with an exact solution was solved. Using the proposed model, the eigenfrequencies and modes of oscillations of the gravitational and earth dams (296 m high) of the Nurek reservoir were investigated. At that, it was revealed that in the natural modes of vibration of earth dams, the greatest displacements under low frequencies are observed at the crest part or at the middle of the slopes.

Analyzing behaviour of a rail wheel assembly with alumino thermite weldment with modal analysis simulations in ANSYS

The Free vibration response of the Railway track is an important area in the design of the Rail and its joints to improve the ride comfort of the passengers. In this study, the rail weld considered is alumino thermite weldment used in majority of Indian Railways network. This paper aims at the study of the vibration response of rail wheel assembly having an AT weld on as a rail joint subjected to free vibration and to find the Natural frequencies of vibration and mode shapes. The geometric model of rail and weldment with wheel and axle components is modelled using Space-claim which is a part of ANSYS package and analysed using numerical simulation package ANSYS 2020 Workbench. In this work, free vibration analysis or modal analysis of the rail weld is carried out to extract the first few modes of vibration. The Natural frequencies obtained along with the corresponding mode shapes of the rail weldment show that they are within the permissible range specified by the standards of railway department also for better ride comfort of the passenger.

Probabilistic methods for calculating seismic resistance of buildings

The article aims to assess possibilities of using probabilistic methods for calculating seismic resistan of buildings based on the laws of structural mechanics. The design schemes and models of buildings rigidly embedded in the base and with a seismic isolation device are described. Formulas developed on the basis of the law of energy conservation, namely the seismodynamic law, which allow to estimate the coefficient of dynamism, are presented. It is proposed to abandon the main modes of vibration in the calculations, i.e. the coefficient ηir of the waveform and the vibration frequency of the residential building and the foundation during earthquakes. Shear and bending calculations of a residential building are based on the design model developed. The values of seismic force are determined by the first and last modes of vibration. Based on these values, it is proposed to calculate internal forces and deformations in the bearing structures of buildings using the methods of structural mechanics.