Piezoelectric generator with nonlinear structure

Motion in nature is usually a low-frequency vibration such as walking, running, swinging arms, and so on, but traditional piezoelectric cantilever structures are inefficient at harvesting energy from low-frequency vibrations. T in the environment. To overcome this, a novel piezoelectric generator was designed. A cantilevered bimorph with a tip mass and a pair of preloading springs were fixed on its base to form a nonlinear piezoelectric generator. The energy transmission in the structure was analyzed. The harvester was modeled as a Euler–Bernoulli beam, and the piezoelectric material was assumed to be linear. The bending vibration was calculated using the Rayleigh–Ritz procedure, and the frequency characteristics of the output voltage were analyzed under different preloading distances. It was found that changing the preloading of the spring helped reduce the natural frequency of the cantilever, which facilitated conversion of ambient low-frequency vibrations into electrical energy. Then, the characteristics of low frequency energy harvesting were investigated experimentally. The theoretical results were consistent with the experimental data; moreover, the resonance frequency, which changes with the preloading distance, reduced from 43 to 35 Hz when the preloading distance was increased from 0 to 1 mm. In this paper, an effective structure to control the resonant frequency is proposed and its motion equation stated. The structure has potential for applications in predicting the effect of preloading distance on resonance frequency.

A New Algorithm for Solving Large-Scale Generalized Eigenvalue Problem Based on Projection Methods

In this paper, we consider four methods for determining certain eigenvalues and corresponding eigenvectors of large-scale generalized eigenvalue problems which are located in a certain region. In these methods, a small pencil that contains only the desired eigenvalue is derived using moments that have obtained via numerical integration. Our purpose is to improve the numerical stability of the moment-based method and compare its stability with three other methods. Numerical examples show that the block version of the moment-based (SS) method with the Rayleigh–Ritz procedure has higher numerical stability than respect to other methods.

Three-Dimensional Vibration Analysis of Laminated Composite Rectangular Plate with Cutouts

The main purpose of this paper is to establish an analysis model of laminated composite rectangular plate with/without cutouts on the basis of three-dimensional elasticity theory and provide the exact three-dimensional solution. In the present work, the effect of the cutout is considered by subtracting the energies of cutouts from the total energy of the entire plate. The standard three-dimensional trigonometric cosine Fourier series and auxiliary Fourier series are chosen as admissible functions, and the Hamilton’s principle and Rayleigh-Ritz procedure are used to obtain the exact solution. In order to verify the effectiveness and reliability of the proposed method, some numerical results are obtained, and the results are compared with the ones available in the literature or finite element analysis. Finally, the effects of some key parameters which will affect the vibration characteristics are analyzed, and the non-dimensional frequency parameters are obtained, which can serve as benchmark data for the future research.

A Benchmark Study on Eigenfrequencies of Fluid-Loaded Structures

In this paper, a coupled finite/infinite element method is applied for computing eigenfrequencies of structures in exterior acoustic domains. The underlying quadratic eigenvalue problem is addressed by a contour integral method based on resolvent moments. The numerical framework is applied to an academic example of a hollow sphere submerged in water. Comparisons of the computed eigenfrequencies to those obtained by boundary element discretizations as well as finite element discretizations in conjunction with perfectly matched layers verify the proposed numerical framework. Furthermore, extensive parameter studies are carried out illustrating the performance of the method with regard to both projection and discretization parameters. Finally, we point out that the proposed method achieves significantly smaller residuals of the computed eigenpairs than the Rayleigh Ritz procedure with second-order Krylov subspaces.

Polyvinylidene fluoride modal sensor design for elastically restrained beams resting on general non-uniform foundation

In this article, a unified solution of polyvinylidene fluoride modal sensor design for elastically restrained beams resting on general non-uniform foundation is proposed using an improved Fourier series method. Modal sensor shape is determined from the charge output equation of polyvinylidene fluoride film and the superposition of the second-order derivative of beam mode shape. With the aim to make the spatial differentials of various order sufficiently continuous in the interval [0, L], Fourier series with auxiliary boundary-smoothed terms are employed to construct the displacement expression. Energy formulation is utilized for system dynamic description, with all the unknown expansion coefficients solved in conjunction with Rayleigh–Ritz procedure. The proposed model is validated through the comparison of modal parameters of simply supported beam resting on elastic foundation with those available in literature. Correctness and effectiveness of the designed polyvinylidene fluoride modal sensor are verified by calculating the modal sensitivity coefficients and the charge output frequency response under external excitation. Based on the model established, the perturbation of practical boundary restraining stiffness on sensing accuracy of such polyvinylidene fluoride sensor is studied, and the influences of boundary condition on polyvinylidene fluoride modal sensor design are investigated for the beam structure resting on general non-uniform foundation.

Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.