Showing papers on "Natural frequency published in 2021"

Application of nonlocal strain–stress gradient theory and GDQEM for thermo-vibration responses of a laminated composite nanoshell

Abstract: In this article, thermal buckling and frequency analysis of a size-dependent laminated composite cylindrical nanoshell in thermal environment using nonlocal strain–stress gradient theory are presented. The thermodynamic equations of the laminated cylindrical nanoshell are based on first-order shear deformation theory, and generalized differential quadrature element method is implemented to solve these equations and obtain natural frequency and critical temperature of the presented model. The results show that by considering C–F boundary conditions and every even layers’ number, in lower value of length scale parameter, by increasing the length scale parameter, the frequency of the structure decreases but in higher value of length scale parameter this matter is inverse. Finally, influences of temperature difference, ply angle, length scale and nonlocal parameters on the critical temperature and frequency of the laminated composite nanostructure are investigated.

Frequency-dependent damped vibrations of multifunctional foam plates sandwiched and integrated by composite faces

Abstract: This paper investigates damped vibrational behavior of a lightweight sandwich plate subjected to a periodic load within a limited time. The lightweight sandwich structure includes a thick polymeric porous core with either functionally graded or uniformly distributions of voids which is sandwiched by two thin layers of laminate composites. To investigate the effect of void distribution properly, the same void volume fraction has been considered while different types of core have been analyzed. Using the first-order shear deformation theory of plates, the governing equations for the free and forced vibrations have been developed. By involving structural damping, these equations which are able to treat thin to moderately thick plates have been solved by developing a computationally cost-effective finite element approach. An extensive sensitivity analysis has been performed to examine the effects of fiber orientation in composite layers, void’s volume and dispersion in core, and geometrical dimensions on the vibrational behavior of such porous composite sandwich plates (PCSPs). The results show that the use of foam in PCSPs considerably reduces the amplitude of vibrations and improves the fundamental frequency. Furthermore, it was found that the use of [45, −45]2 composite layers offers PCSPs with the highest natural frequency and the lowest amplitude of vibrations.

An efficient method for vibration and stability analysis of rectangular plates axially moving in fluid

Abstract: An efficient method is developed to investigate the vibration and stability of moving plates immersed in fluid by applying the Kirchhoff plate theory and finite element method. The fluid is considered as an ideal fluid and is described with Bernoulli’s equation and the linear potential flow theory. Hamilton’s principle is used to acquire the dynamic equations of the immersed moving plate. The mass matrix, stiffness matrix, and gyroscopic inertia matrix are determined by the exact analytical integration. The numerical results show that the fundamental natural frequency of the submersed moving plates gradually decreases to zero with an increase in the axial speed, and consequently, the coupling phenomenon occurs between the first- and second-order modes. It is also found that the natural frequency of the submersed moving plates reduces with an increase in the fluid density or the immersion level. Moreover, the natural frequency will drop obviously if the plate is located near the rigid wall. In addition, the developed method has been verified in comparison with available results for special cases.

Topology optimization of vibrating structures with frequency band constraints

Abstract: Engineering structures usually operate in some specific frequency bands. An effective way to avoid resonance is to shift the structure’s natural frequencies out of these frequency bands. However, in the optimization procedure, which frequency orders will fall into these bands are not known a priori. This makes it difficult to use the existing frequency constraint formulations, which require prescribed orders. For solving this issue, a novel formulation of the frequency band constraint based on a modified Heaviside function is proposed in this paper. The new formulation is continuous and differentiable; thus, the sensitivity of the constraint function can be derived and used in a gradient-based optimization method. Topology optimization for maximizing the structural fundamental frequency while circumventing the natural frequencies located in the working frequency bands is studied. For eliminating the frequently happened numerical problems in the natural frequency topology optimization process, including mode switching, checkerboard phenomena, and gray elements, the “bound formulation” and “robust formulation” are applied. Three numerical examples, including 2D and 3D problems, are solved by the proposed method. Frequency band gaps of the optimized results are obtained by considering the frequency band constraints, which validates the effectiveness of the developed method.

An experimental validation of a new shape optimization technique for piezoelectric harvesting cantilever beams

Abstract: The piezoelectric energy harvester efficiency depends on optimizing the cantilever geometry and tuning its natural frequency with vibration source frequency. Moreover, the effect of harvester parameters on natural frequency is vital in tuning the resonance frequency. So, a COMSOL Multi-physics finite element analysis, Eigen frequency study and analytical analysis using MATLAB were constructed to calculate the resonance frequencies and to analyze the harvester parameters effect. Five harvester different shapes, namely, the T-shaped, rectangular, L-shaped, variable width, and triangular cantilevers were optimized using the genetic algorithm. The simulation of the five shapes was implemented using COMSOL. The results indicated that the T- shaped cantilever produced the largest power. Due to its high power and inclusive shape, the T-shaped cantilever with variable width was optimized using the COMSOL optimization module (BOBYQA). Linking genetic algorithm and COMSOL optimization module has highly improved the output power. The COMSOL results were validated using an experimental setup of piezoelectric cantilevers. The experimental setup was employed to calculate the voltage of the base excited harvester with very low excitation frequencies from 0.5 to 10 Hz. Also, the experimental setup investigated the effect of the tip mass, length of the cantilever, and piezoelectric material volume on the output voltage.

Vibration Mode Analysis for a Suspension Bridge by Using Low-Frequency Cantilever-Based FBG Accelerometer Array

Abstract: In this article, we present a vibration measurement system based on low-frequency cantilever-based fiber Bragg grating accelerometers (CFAs) for a suspension bridge. Each accelerometer has an end-loaded cantilever beam, specifically tailored to achieve a uniform sensitivity for a frequency range of 0–4 Hz, a suitable detection range for the vibration analysis. In the field test, seven CFAs were installed at specific positions along the deck of a 110-m-long suspension bridge for synchronous multipoint vibration measurements. The reflection spectra of the CFA array were recorded and processed using the pseudo-high-resolution scheme to improve the signal quality and measurement accuracy. Three natural vibration frequencies: 1.15, 1.54, and 3.17 Hz have been identified from the measurement. Following that, the acquired time-domain signals were processed by a digital bandpass filter to retrieve the waveform at each natural frequency to determine the corresponding mode shapes. The results are in agreement with the phase difference between the frequency domain signal for each natural frequency. This investigation has shown the feasibility of the proposed measurement system for determining the mode shapes and dynamic frequency analysis of a suspension bridge. It is a potential method for structural health monitoring for other similar civil structures.

Control and dynamic releasing method of a piezoelectric actuated microgripper

Abstract: This paper proposes the control and dynamic releasing method of a symmetric microgripper with integrated position sensing. The microgripper adopted in this micromanipulation system is constructed by two L-shaped leverage mechanisms and the fingers of the microgripper is machined much thinner than the gripper body. A combined feedforward/feedback position controller is established to improve the motion accuracy of the microgripper in high frequency. The feedforward controller is established based on rate-dependent inverse Prandtl-Ishlinskii (P–I) hysteresis model. The inertial force generated in dynamic based releasing process is analyzed through MATLAB simulation. Open-loop experimental tests have been performed, and the results indicate the first natural frequency of the microgripper is 730 Hz. Then experiments in high frequency based on the developed combined controller are carried out and the results show the tracking error of a superimposed sinusoidal trajectory with the frequency of 100 Hz, 120 Hz and 130 Hz is 6.4%. Finally, the tiny objects releasing experiments are conducted where the combined controller is used to control the motion amplitude and frequency to achieve inertial force controllable to improve operation accuracy. And the results show that the dynamic releasing strategy is effective.

Stability Analysis of a Cantilever Structure using ANSYS and MATLAB

Abstract: The objective is to study the behavior of gallery in a concert hall under forced vibration (Man Induced Vibration) without damping to avoid deformations in the structure leading to potential damage. In order to execute this, it is vital to further find the (first three, in this case) natural frequencies and natural mode shapes of the cantilever corresponding to deformations of the beam in the x-y-plane in order to determine the stresses acting within the structure. The natural frequency of the Gallery of two proposed designs is then determined followed by finding the best design based on their natural frequencies by comparing with exact natural frequencies of a uniform cantilever beam to find the Transient Response for the given load at the tip of the Cantilever Beam. This technique has also been applied to shock wave theories that are applied underground using ultrasonic sensors to determine cracks within underground pipelines to avoid any leakage.

An analytical approach for nonlinear thermo-electro-elastic forced vibration of piezoelectric penta - Graphene plates

Abstract: This paper deals with the nonlinear forced vibration of imperfect penta – graphene plates integrated with piezoelectric actuator layers. The plate is subjected to combination of mechanical, thermal, and electrical loadings. Based on the first order shear deformation plate theory, the governing equations are established taken into account the effect of the von Karman type of geometrical nonlinearity, the Pasternak type elastic foundations, the damping and the piezoelectric – thermal effects. Four edges of the hybrid plate are assumed to be simply supported and immovable in the in-plane directions. The solution forms that satisfy the boundary conditions are assumed to be trigonometric. The closed form expressions of natural frequency, the frequency ratio – amplitude and the deflection amplitude – time curves are obtained by using the Galerkin and Runge – Kutta methods. The numerical results show positive effects of elastic foundations, negative effect of temperature increment and initial imperfection, considerable effect of geometrical parameters as well as small effect of applied voltage on the nonlinear forced vibration of piezoelectric penta – graphene plate.

Counterweight-pendulum energy harvester with reduced resonance frequency for unmanned surface vehicles

Abstract: In this paper, a novel electromagnetic pendulum energy harvester with a counterweight is designed to harvest low frequency vibration from ocean waves for unmanned surface vehicles. This design is the first of its kind, allowing the natural resonant frequency of the pendulum to be reduced without increasing its length, thereby maintaining a high power output from the energy harvester at lower frequencies than previously possible with pendulums of the same size. Implementing a novel mechanical rotation rectifier (MRR) system for a high energy conversion efficiency, this counterweight pendulum energy harvester can provide multi-watt-level power at frequencies lower than 1 Hz, with a primary pendulum arm length of just 195mm. When actuated at 0.1 g rms, the pendulum energy harvester with a counterweight produced electrical power of 0.997 W at 0.75 Hz, compared to 0.168 W without the counterweight. The average normalised power output of the system at this frequency is 95.8 W/g2, corresponding to a power density of 6.11 W/g2/kg. Testing of a range of configurations of the pendulum mass and counterweight shows a clear linear relationship between the ratio of lengths of the pendulum arms and the reduction of the natural frequency of the system. This demonstrates empirically that this device is capable of operating under conditions in which existing energy harvesters are unable to provide adequate power, and therefore provides a significant development in energy harvesting in an ultra-low frequency marine environment.

2D electrostatic energy harvesting device using a single shallow arched microbeam

Abstract: We propose to use a shallow arched microbeam to design a compact 2D energy harvesting device using a single electrostatic transducer. The proposed design can transform any in-plane applied acceleration into motion of a variable capacitor whose movable electrode is linked to the shallow arched microbeam. A secondary electrode is placed to directly apply a force on the microbeam in order to tune its natural frequency to increase the amount of harvested energy. We derive the governing equations of the coupled system using the Hamilton’s principle. The associated nonlinear differential equations are solved using a Galerkin technique. The frequency response curves are obtained for accelerations in different directions under several applied voltages. The model and the design are validated using a finite element model. In a second modeling approach, the system is coupled to a conditioning circuit based on pump-charge technique. The coupled system is solved for different excitation frequencies. It was observed that the input voltage can be doubled after a 16 s excitation, and that almost the triple of this value can be obtained for longer excitation times. The performance of the system is assessed by comparing its performances with other designs found in the literature.

Bending vibration control of pipes conveying fluids by nonlinear torsional absorbers at the boundary

Abstract: A nonlinear torsional absorber, which can overcome the influence of the fluid velocity on the natural frequency, is employed at the boundary to restrain the bending vibration of a pipe for the first time. By using the rotating angle at the end of the pipe, the bending vibration energy is pumped to the boundary absorber. The nonlinearly coupled pipe-absorber governing equations are obtained by the generalized Hamilton’s principle. Steady-state responses subjected to a basement excitation are discussed by the modal-correction-harmonic-balance-method. According to this method, the boundaries of the pipe are treated as the generalized governing equations. In this way, those nonlinearities and time-dependent terms in the boundary are involved in the response completely. A direct simulation method, called the differential quadrature element method (DQEM), is used to verify these analytical results. The investigation indicates that the nonlinear boundary absorber owns two outstanding advantages. The first one is that the natural characters remain the same and the absorber can capture the resonance of the pipe automatically. The second one is that the absorber works at all natural modes. Especially, by using the nonlinear damping, the absorber will not worsen the weak vibration in the non-resonance region. The parameters of the absorber are investigated to optimize the efficiency in detail. The result finds that good efficiency can be achieved with a tiny mass. Meanwhile, the efficiency becomes better as the damping increases. With the help of these investigations, the work provides a new strategy to protect pipes conveying fluids from being destroyed by the vibration.

On the modelling of the vibration behaviors via discrete singular convolution method for a high-order sector annular system

Abstract: This research presents a numerical investigation on the dynamic information of the axisymmetric sandwich annular sector plate via a higher-order continuum elasticity theory. The sandwich annular sector plate comprises multi-hybrid nanocomposite reinforced (MHCR) face sheets in the top, bottom layers, and a honeycomb core. For modeling the thermal situation and the thickness of the structure, three-kinds of thermal loading are presented. For simulating MHCR face sheets, the role of the mixture and Halpin–Tsai micromechanics model is utilized. For obtaining the governing equations and various boundary conditions, first-order shear deformation theory (FSDT), as well as Hamilton’s principle, are presented. For solving the equations and obtaining eigenvalue, and eigenvector of the current structure, discrete singular convolution method (DSCM) as a numerical one is investigated. Consequently, a parametric study is carried out to examine the impacts of honeycomb network angle, thickness to length ratio of the honeycomb, honeycomb to face sheet thickness ratio, fibers angel, outer to inner radius ratio, and weight fraction of CNTs on the dynamics of the current sandwich structure. The results show that for clamped edge and each th/lh, increasing $$\theta_{h} /\pi$$ is a reason for decreasing the natural frequency of the disk. Another consequence is that the impact of temperature changes on the frequency of the disk is hardly dependent on the fiber angle. It means that the effect of temperature changes on the frequencies of the current system is more considerable at 0.2 ≤ θf ⁄π ≤ 0.4 and 0.6 ≤ θf ⁄π ≤ 0.8.

A Self-Tuning S/S Compensation WPT System without Parameter Recognition

Abstract: In the application of wireless power transfer system, parameter drift of resonant tank is a general situation which induces that natural frequency of primary side or secondary side deviates from switching frequency. This frequency deviating phenomenon will deteriorate load-independent constant current characteristic and decrease output power capacity for a S/S compensation system. This paper illustrates the problems caused by frequency deviating through output characteristic analysis and addresses them by a self-tuning method based on switched capacitors (SCs). The proposed self-tuning method requires no resonant parameters such as compensation capacitance and coil self-inductance in advance. Primary and secondary natural frequencies can be both tuned to switching frequency continuously by SCs. The proposed method is verified by a simulation and a 500W S/S compensation experimental prototype. After the completion of self-tuning process, load-independent constant current characteristic is recovered and the output power capacity is boosted which are in consistence with the theoretical analysis of system output characteristic. The proposed method is also applicable to LCC/S and LCC/LCC topologies.

Size and layout optimization of truss structures with dynamic constraints using the interactive fuzzy search algorithm

Abstract: Optimizing truss structures considering natural frequency constraints can fundamentally enhance their dynamic behaviour under transient loadings. In this regard, the current investigation assesses ...