Showing papers on "Natural frequency published in 2018"

Nonlinear damping in nonlinear vibrations of rectangular plates: Derivation from viscoelasticity and experimental validation

Abstract: Even if still little known, the most significant nonlinear effect during nonlinear vibrations of continuous systems is the increase of damping with the vibration amplitude. The literature on nonlinear vibrations of beams, shells and plates is huge, but almost entirely dedicated to model the nonlinear stiffness and completely neglecting any damping nonlinearity. Experiments presented in this study show a damping increase of six times with the vibration amplitude. Based on this evidence, the nonlinear damanaping of rectangular plates is derived assuming the material to be viscoelastic, and the constitutive relationship to be governed by the standard linear solid model. The material model is then introduced into a geometrically nonlinear plate theory, carefully considering that the retardation time is a function of the vibration mode shape, exactly as its natural frequency. Then, the equations of motion describing the nonlinear vibrations of rectangular plates are derived by Lagrange equations. Numerical results, obtained by continuation and collocation method, are very successfully compared to experimental results on nonlinear vibrations of a rectangular stainless steel plate, validating the proposed approach. Geometric imperfections, in-plane inertia and multi-harmonic vibration response are included in the plate model.

Surface energy effect on free vibration of nano-sized piezoelectric double-shell structures

Abstract: Combining Goldenveizer-Novozhilov shell theory, thin plate theory and electro-elastic surface theory, the size-dependent vibration of nano-sized piezoelectric double-shell structures under simply supported boundary condition is presented, and the surface energy effect on the natural frequencies is discussed. The displacement components of the cylindrical nano-shells and annular nano-plates are expanded as the superposition of standard Fourier series based on Hamilton's principle. The total stresses with consideration of surface energy effect are derived, and the total energy function is obtained by using Rayleigh-Ritz energy method. The free vibration equation is solved, and the natural frequency is analyzed. In numerical examples, it is found that the surface elastic constant, piezoelectric constant and surface residual stress show different effects on the natural frequencies. The effect of surface piezoelectric constant is the maximum. The effect of dimensions of the double-shell under different surface material properties is also examined.

Natural Frequency Optimization of Variable-Density Additive Manufactured Lattice Structure: Theory and Experimental Validation

Abstract: Additive manufacturing (AM) is now capable of fabricating geometrically complex geometries such as a variable-density lattice structure. This ability to handle geometric complexity provides the designer an opportunity to rethink the design method. In this work, a novel topology optimization algorithm is proposed to design variable-density lattice infill to maximize the first eigenfrequency of the structure. To make the method efficient, the lattice infill is treated as a continuum material with equivalent elastic properties obtained from asymptotic homogenization (AH), and the topology optimization is employed to find the optimum density distribution of the lattice structure. Specifically, the AH method is employed to calculate the effective mechanical properties of a predefined lattice structure as a function of its relative densities. Once the optimal density distribution is obtained, a continuous mapping technique is used to convert the optimal density distribution into variable-density lattice structured design. Two three-dimensional (3D) examples are used to validate the proposed method, where the designs are printed by the EOS direct metal laser sintering (DMLS) process in Ti6Al4V. Experimental results obtained from dynamical testing of the printed samples and detailed simulation results are in good agreement with the homogenized model results, which demonstrates the accuracy and efficiency of the proposed method.

Parameters Design and Optimization for LC-Type Off-Grid Inverters With Inductor-Current Feedback Active Damping

Abstract: In this paper, the stability of LC -type voltage source inverter is investigated, with the emphasis focused on the LC resonance. It has been found that the traditional capacitor-voltage inductor-current dual-loop control is unstable when the resonance frequency is higher than one-sixth of the sampling frequency. In addition, due to the coupling between current inner loop and voltage outer loop, it is difficult to design control parameters to ensure the system stability in traditional dual-loop control. In order to develop a systemic design principle, the capacitor-voltage control with inductor-current feedback active damping evolved from traditional dual-loop control is analyzed in detail. The mathematic model is established to reveal the reason of instability, and the stable regions are identified. Moreover, the optimal damping coefficient is also derived to enhance the system damping performance. Finally, the experimental results are provided to verify the effectiveness of the proposed method.

Nonlinear free and forced vibration analyses of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section

Abstract: Nonlinear free and forced vibrations of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section are investigated. The beam has immovable, namely clamped-clamped and pinned-pinned boundary conditions, which leads to midplane stretching in the course of vibrations. Nonlinearities occur in the system due to this stretching. Damping and forcing terms are included after nondimensionalization. The equations are solved approximately using perturbation method and mode shapes by differential quadrature method. In the linear order natural frequencies and mode shapes are computed. In the nonlinear order, some corrections arise to the linear problem; the effect of these nonlinear correction terms on natural frequency is examined and frequency –response curves are drawn to show the unstable regions. In order to confirm the validity, our results are compared with others available in literature.

Vibration of mechanically-assembled 3D microstructures formed by compressive buckling

Abstract: Micro-electromechanical systems (MEMS) that rely on structural vibrations have many important applications, ranging from oscillators and actuators, to energy harvesters and vehicles for measurement of mechanical properties. Conventional MEMS, however, mostly utilize two-dimensional (2D) vibrational modes, thereby imposing certain limitations that are not present in 3D designs (e.g., multi-directional energy harvesting). 3D vibrational micro-platforms assembled through the techniques of controlled compressive buckling are promising because of their complex 3D architectures and the ability to tune their vibrational behavior (e.g., natural frequencies and modes) by reversibly changing their dimensions by deforming their soft, elastomeric substrates. A clear understanding of such strain-dependent vibration behavior is essential for their practical applications. Here, we present a study on the linear and nonlinear vibration of such 3D mesostructures through analytical modeling, finite element analysis (FEA) and experiment. An analytical solution is obtained for the vibration mode and linear natural frequency of a buckled ribbon, indicating a mode change as the static deflection amplitude increases. The model also yields a scaling law for linear natural frequency that can be extended to general, complex 3D geometries, as validated by FEA and experiment. In the regime of nonlinear vibration, FEA suggests that an increase of amplitude of external loading represents an effective means to enhance the bandwidth. The results also uncover a reduced nonlinearity of vibration as the static deflection amplitude of the 3D structures increases. The developed analytical model can be used in the development of new 3D vibrational micro-platforms, for example, to enable simultaneous measurement of diverse mechanical properties (density, modulus, viscosity etc.) of thin films and biomaterials.

Fast Computation of Radial Vibration in Switched Reluctance Motors

Abstract: This paper proposes a new method for fast radial vibration computation in switched reluctance motors. Only a piecewise first-order linear function is used to calculate the total peak acceleration, which is rather fast. The overall radial vibration is the superposition of natural oscillation of each mode. Before that, several critical parameters need to be calculated or measured in advance, including weight factor, natural frequency and damping ratio of each mode, in order to obtain the respective analytical expression of natural oscillation of each mode. First, the total peak acceleration concerning the multiple of current and its slope is derived analytically from the perspective of abrupt change of radial force. Then, a simple method for calculating weight factors is presented for the distribution of peak acceleration of each mode from the total peak acceleration. Natural frequencies are measured and compared by three methods, including finite-element analysis, hammer impulse test, and dc pulse excitation. The calculation of damping ratio is improved since the traditional damping ratio calculation method cannot be used in a multiple degree-of-freedom system. Finally, both simulation and experiments are conducted to verify the effectiveness and accuracy of the proposed method.

Exact natural frequencies and buckling load of functionally graded material tapered beam-columns considering semi-rigid connections:

Abstract: An exact free vibration and buckling analysis of a tapered beam-column with general connections is calculated. All structural elements are made of functionally graded material. In this study, a pow...

Wideband auto-tunable vibration energy harvester using change in centre of gravity

Abstract: Energy harvesters are preferred for enhancing the life of IoT nodes. In this paper, a vibration energy harvester with wideband auto-tunable resonant frequency for increased output is designed. With a variation in frequency of vibrating source, harvested energy reduces to zero value. To harvest the energy on regular basis from the vibrating source, tuning is required. This problem is resolved with the proposed design, which works on the principle of change in centre of gravity (CoG) of proof mass that leads to change the natural frequency of the device. The design is simulated and the static change in frequency with a change in CoG is analytically calculated. The simulated results are verified with fabricated device and similar outcome with boosted bandwidth is obtained. Frequency range is obtained between 22–35 Hz for fabricated device with $$\approx$$ 6.0 V $$_{pp}$$ voltage output for different positions of cylinders.

Modeling and dynamic analysis of bolted joined cylindrical shell

Abstract: Based on Sanders shell theory, modeling and dynamic analysis of bolted joined cylindrical shell were studied in this paper. When subjected to external excitations, contact state such as stick, slip and separation may occur at those locations of bolts. Considering these three contact states, an analytical model of cylindrical shell with a piecewise-linear boundary was established for the bolted joined cylindrical shell. First, the model was verified by the simplified line system, and the effects of stiffness in connecting interface and the number of bolts on natural frequency and mode shape were investigated. Then, through the response under instantaneous excitation, damping characteristic of the system was proved which is caused by the friction model. Last, the effects of external load frequency, response location, excitation amplitude and connecting parameters including stiffness and preload were numerically investigated and fully explained by 3-D frequency spectrum. The results indicated that periodic motion, times periodic motion and even chaotic motion were observed based on different parameters.

Finite element dynamic analysis of beams on nonlinear elastic foundations under a moving oscillator

Abstract: This paper presents a study on the dynamic response of beams on elastic foundations, subjected to a uniformly moving oscillator. Using a finite element model programmed within a MATLAB environment the response of the system is studied for three different types of mechanical behaviour of the foundation: (a) linear elastic (classical Winkler model), (b) nonlinear elastic (in which the foundation reaction displays a cubic dependence on the beam displacement) and (c) bilinear elastic (with different compressive and tensile stiffnesses). The effects of the oscillator's natural frequency and velocity and of the foundation's stiffness and damping are investigated. In particular, critical velocities of the oscillator and ranges of velocities for which the system is dynamically unstable are numerically determined for the first time in the above mentioned nonlinear cases.