Base Acceleration Excitations Research Articles

Stationary Stochastic Response Analysis of the FG-GPLRC Irregular Quadrilateral Plate Based on the Chebyshev–Ritz Method

The stationary random response characteristics of irregular quadrilateral plates under the base acceleration excitation are investigated in this paper. The computational model chosen in this paper is functionally graded graphene platelet reinforced composites (FG-GPLRC). Simultaneously, the material parameters are calculated employing the modified Halpin–Tsai model. A unified dynamic model based on the first-order shear deformation theory (FSDT) is proposed for FG-GPLRC irregular plates, where the displacement variables are considered as the first kind Chebyshev polynomials combined with coordinate transformation. The Chebyshev–Ritz method is utilized to derive the kinetic equations of irregular quadrilateral plates, and then the pseudo-excitation method (PEM) is employed to solve the stationary stochastic response of the system under the base acceleration excitation. The free vibration and stationary stochastic response of the plates under various boundaries are validated by a sufficient number of numerical studies, and the computational results display a favorable match with the published literature and finite element method (FEM), which verifies the correctness and reliability of the present method. Finally, a detailed parametric analysis of the stationary stochastic response characteristics of FG-GPLRC irregular quadrilateral plates is presented. The effects of various mass fractions, number of layers, geometric dimensions of GPL, and boundary constraints on the stationary stochastic vibration behaviors of FG-GPLRC irregular quadrilateral plates are considered.

A grounded inerter-based oscillating TMD for suppressing harmonic and random vibrations

Inspired by the lightweight passive vibration control technology, in this work a new anti-vibration device is proposed to significatively improve the protection for stationary mechanical structures subjected to different kinds of vibratory loads. Such a device is herein termed as the grounded inerter-based two-degree-of-freedom tuned mass damper (GI-TDOF-TMD) composed by a grounded inerter and TDOF-TMD with rotational and translational motions, which controls the primary structure's dominant modal shape by using the synergistic dynamic effects of both devices. In order to fairly evaluate the GI-TDOF-TMD's vibration mitigation effectiveness with respect to other devices, the damped and undamped primary structure's nondimensional compliance and mobility transfer functions are firstly computed from a generalized mathematical model that considers four types of random and harmonic excitation inputs which are the following: force general case, base acceleration excitation, base displacement input and inertial force generated by the unbalance in rotary machinery. For harmonically excited mechanical systems, the H∞ performance measure is applied to minimize the maximum resonant peaks of the displacement and velocity dimensionless frequency response functions (FRFs). As the Extended Fixed-Points Technique (EFPT) is analogous to the H∞ criterion, quasi-optimal solutions are firstly computed to perfectly calibrate the FRF's invariant points. After performing this, the evolution of the FRF's control invariant frequencies revealed that GI-TDOF-TMD performs well at low inertance values. Therefore, the GI-TDOF-TMD's maximum control performance is obtained when the inerter's inertial force is the same as that yielded by the TMD's physical mass. In view of such a dynamic behavior, the GI-TDOF-TMD approximately provides 40% and 17% improvements when compared with respect to the classic dynamic vibration absorber (DVA) and TMD-inerter (TMDI), respectively. Then, the GI-TDOF-TMD's power dissipation capability is demonstrated by applying the H2 norm approach to the randomly excited damped mechanical structures. Additionally, it is also revealed through the stochastic energy balance that the GI-TDOF-TMD's internal power dissipation effectiveness is directly reflected on the minimization of the primary structure's kinetic energy. Moreover, for random inputs, the proposed device can broaden the effective operating bandwidth in approximately 45% and 19% when compared to the classic DVA and TMDI, respectively. Therefore, the GI-TDOF-TMD works better than the TMDI in terms of structural displacement and velocity response mitigation, which can be useful in civil engineering applications.

A VAM-based equivalent model for random vibration of composite sandwich plate with arrowhead-on cores

The composite sandwich plate with an arrowhead-on core (arrowhead-on CSP) is a new type of composite structure that has the advantages of a low weight, high specific strength, high specific stiffness, and negative Poisson’s ratio. In this study, the equivalent plate properties were obtained using the variational asymptotic method (VAM) to asymptotically analyze the energy functional stored in the unit cell. On this basis, a two-dimensional virtual equivalent model was constructed for random vibration analysis using the pseudo excitation method. To verify the accuracy and effectiveness of the equivalent model, the dynamic behaviors (free and random vibrations) of arrowhead-on CSPs under different conditions were analyzed. The power spectral density (PSD), the root mean square (RMS) values of the lateral displacement, velocity, and acceleration responses under a base acceleration excitation, and the modal effective mass fraction under vibrations were also investigated. Finally, the effects of the layup configuration of the composite facesheets and the geometric parameters of the arrowhead-on core on the dynamic characteristics of the equivalent plate were studied. The study revealed that the equivalent model was very efficient and accurate in free and random vibration analysis, which provided a reference for the dynamic characteristic optimization of arrowhead-on CSPs.

Statistical linearization for random vibration energy harvesting with piezoelectric material nonlinearity

Due to piezoelectric softening and dissipative nonlinearities, the piezoelectric cantilever energy harvester exhibits nonlinear hysteresis when subjected to large excitation. These nonlinearities have brought significant challenges to the modeling and response prediction of randomly excited piezoelectric energy harvesting systems. In this study, the voltage responses of the nonlinear piezoelectric cantilever energy harvester under random excitation are initially assumed to follow the Gaussian distribution which is experimentally validated later. The equivalent linear transfer function are derived from the approximate linearization of the stiffness and damping using the statistical linearization (SL) technique. The mathematical expectations of the voltage responses are calculated from the multivariate normal distributions. Frequency sweep experiments are conducted to a cantilever energy harvester to identify the nonlinear piezoelectric material properties. The statistically linearized model was experimentally validated under random base acceleration excitation by comparing the probability density function of the predicted voltage responses and average power against the experimental measurements. The advantage of the SL technique lies in allowing one to use an iterative procedure to estimate the equivalent linear terms while the analytical expressions are unattainable because of the complex nonlinearity in the governing equations. The results show that the prediction of the SL model to the random base acceleration excitation agrees with experimental measurements with a broadband frequency range, although only the fundamental mode of the beam is considered.

The efficiency of linear electromagnetic vibration-based energy harvester at resistive, capacitive and inductive loads

Abstract Energy harvesters and almost all energy generation devices receive the motivation for design from their efficiency and efficiency play an important role in the feasibility and practicability of the design. In this paper, we investigate the efficiency of electromagnetic vibration-based energy harvesters at various electrical loads. In our problem the efficiency depends on excitation frequency, coil and load parameters as well as electromagnetic coupling coefficient. The author first proves that the input power that the harvester receives from its environment at constant base acceleration and constant excitation frequency is always equal to the power that consumes in electrical and mechanical dampers, then the author defines the resonance frequency and plot three efficiency diagrams i.e. plot of efficiency versus (excitation) frequency, plot of maximum efficiency at a constant frequency versus load and in the end plot of the efficiency versus output power at varying load capacitance and resistance. The author observes that maximum efficiency not only does not occur at resonance (i.e. at maximum power) but also is very low (less than 1e−10%) for typical parameters at resonance. Also the maximum efficiency for typical optimum parameters is around 17.45%.

Random vibration study of functionally graded porous curved beams with elastically restrained ends

Firstly, the random vibration characteristics of functionally graded porous (FGP) curved beams with elastically restrained ends are studied. An efficient model is presented by the Timoshenko beam theory and spectral-Chebyshev method. In this paper, three different types of porous distribution are considered, and the relationship between porosity coefficient and material parameters is determined according to the typical mechanical properties of open cell foam metal. Four types of curved beams with different curvatures are selected for the study, which are elliptical beam, parabolic beam, hyperbolic beam and circular beam. The one-dimensional admissible displacement functions of the FGP curved beam are constructed by Chebyshev polynomials of the first kind with Gauss-Lobatto sampling points discretization. Three artificial boundary springs are used to impose elastic boundary constraints at the ends of the curved beam. The pseudo excitation method is used to apply stationary and non-stationary random excitations, including point excitation and base acceleration excitation. The stationary random vibration responses of the FGP curved beam with different boundary conditions, involving the power spectral density (PSD) and root mean square (RMS) values of displacement, velocity and acceleration, are calculated and agreed well with the finite element method (FEM). At last, the RMS values of the non-stationary random vibration response of the FGP curved beam are given.

Analytical stochastic responses of thin cylindrical shells under various stationary excitations

This study proposed an efficient analytical framework to achieve exact stochastic responses of circular cylindrical shells under various stationary excitations. By introducing the exact modal shapes of closed and open cylindrical shells based on the Flügge theory, the analytical power spectral densities of responses for the two shells were derived via the pseudo excitation method (PEM), where the calculus operation in the spatial domain and the integral in frequency domain were involved. To take full advantage of PEM for matrix operation and improve computational efficiency, the discrete analytical method (DAM), implementing analytically the calculus operation in the spatial domain and discretizing the frequency domain, was proposed. Furthermore, the exact stationary stochastic responses of three shell examples under point, surface, base acceleration and spacecraft specification spectrum excitations were achieved. By comparing the root mean squares of responses, especially twisting moment and membrane shear force with those by finite element analysis software, the high accuracy and efficiency of DAM were demonstrated. The remarkable effect of frequency bandwidth of excitation on stochastic responses was also revealed. The exact stochastic responses calculated by DAM can be taken as benchmark solutions to verify the numerical methods for the high-frequency wideband random vibration problem.

Tuning of a wide range of low resonance frequencies by a novel multi-resonant piezoelectric energy harvester

The power generation from environment vibrations through piezoelectric energy harvesting devices gained a huge research attention because of its ability to provide consistent power source to the wireless sensor networks. In recent years, researchers are attracted towards multi-resonant piezoelectric energy harvesters because of their wide operating bandwidth. This paper introducing a novel multi-resonant piezoelectric energy harvester that consisting two L-shaped and one straight branched beam along with proof masses on their free ends. The proposed device is capable to provide maximum peak of its output response at three close resonant frequencies. The main emphasis of the present paper is towards analyzing the geometry of L-shaped branched beams in view of tune up the three fundamental resonant frequencies within 10 Hz along with achieving first and third higher mode frequencies below 100 Hz. This study has been carried out by eigen frequency analysis using COMSOL multiphysics software under 0.2 g base acceleration excitation. It has been optimized from the study that the three close resonant frequencies have been reduced down within 10 Hz range by increasing the width of vertical part of L-shaped branched beams.

Energy harvesting from unimorph piezoelectric circular plates under random acoustic and base acceleration excitations

Abstract Piezoelectric materials have been extensively employed in small scale energy harvesting devices. Commonly, the ambient excitation in these energy harvesting systems is considered to be harmonic. While in practical cases, these excitations are random in nature. The objective of the current paper is to use random vibration theory to investigate energy harvesting from a clamped circular plate interconnected to a circular piezoelectric layer. The excitations are assumed to be a random uniform pressure applied to the plate resulted from an acoustic wave and a random base acceleration of the system. Lagrange equations are utilized to derive the coupled equations describing the dynamic behavior of the plate and the circuit voltage. The random inputs are assumed to be band-limited uncorrelated white noises. Using the random vibration theory, the statistical parameters describing the plate’s dynamic and the harvested voltage are derived in terms of random characteristics of the inputs. A parametric study is carried out to investigate the effect of different design parameters on the harvested power. Also, an optimization problem is solved for maximizing the power density in the system. Using the results of the optimization problem, the power density can be significantly improved up to 3.2 mW/m2. The quantitative and qualitative results obtained in this paper can be effectively used for the optimal design of other piezoelectric energy harvesters under stochastic excitations.

Structural topology optimization under stationary random base acceleration excitations

Structural topology optimization subjected to stationary random base acceleration excitations is investigated in this paper. In the random response analysis, the Large Mass Method (LMM) which attributes artificial large mass values at each driven nodal Degree Of Freedom (DOF) to transforming the base acceleration excitations into force excitations is proposed. The Complete Quadratic Combination (CQC) which is commonly used to calculate the random responses in previous optimization has been proven to be computationally expensive especially for large-scale problems. In order to conquer this difficulty, the Pseudo Excitation Method (PEM) and the combined method of PEM and Mode Acceleration Method (MAM) are adopted into the dynamic topology optimization, and random responses are calculated using these two methods to ascertain a high efficiency over the CQC. A density-based topology optimization method minimizing dynamic responses is then formulated based on the integration of LMM and PEM or the combined method of PEM and MAM. Numerical examples are presented to verify the accuracy of the proposed schemes in dynamic response analysis and the quality of the optimized design in improving dynamic performance.

Integrated layout and topology optimization design of multi-component systems under harmonic base acceleration excitations

The integrated optimization of component layout and structural topology is studied in this paper to improve the dynamic performance of the multi-component structure systems under harmonic base acceleration excitations. Considering linear systems, including multi-point constraints interconnecting the components and structures as an integrity, the dynamic responses and the corresponding design sensitivities are analytically derived based on the mode acceleration method. To obtain precise dynamic response, structural real damping characteristics are measured using vibration experiments, which are relevant to the structural dynamic response, especially when the excitation frequencies fall into the resonant frequency band. Further verifications are done by the comparison of Rayleigh damping, constant damping ratio, and hysteretic damping model with experimental results of structures achieved by resin-based additive manufacturing. In this way, structural real damping characteristics are taken into account in the integrated optimization. Numerical examples and vibration testing results are presented to show the validity of the optimization procedure and its potential application in engineering.

Optimum design of linear multiple tuned mass dampers subjected to white-noise base acceleration considering practical configurations

This study investigates the application of multiple tuned mass dampers (MTMDs) for situations wherein multiple small-sized tuned mass dampers (TMDs) are required to be installed owing to practical reasons such as a space limitation, for transportation, and for ease of handling. This paper presents an optimum design and analysis of linear MTMDs with various practical configurations on a single-degree-of-freedom (SDOF) primary structure subjected to a zero-mean white-noise base-acceleration excitation. Six practical configurations are developed and comparatively analyzed, each of which is constrained with linearly distributed frequency ratios, uniformly distributed damping coefficients, linearly distributed mass ratios, and combinations thereof. Two different optimization techniques were adopted in this study. The first minimizes the nominal performance objective function while the second minimizes the mean value of the objective function while assuming that the associated structural parameters are perturbative. All the optimized parameters and plots are presented in a non-dimensional form in order to provide results that are useful for practical design. Among the six cases investigated, a three-parameter optimum solution based on frequency and damping ratios showed sufficiently satisfactory control performance and is recommended for practical design. Furthermore, this study provides the contour maps that enable designers to accommodate the moving TMD units within a permissible stroke limit.

An E-shape broadband piezoelectric energy harvester induced by magnets

We describe in this work a broadband magnetic E-shape piezoelectric energy harvester with wide frequency bandwidth. We develop first a nonlinear electromechanical model of the harvester based on the Hamilton variation principle that simulates the effect of the nonlinear magnetic restoring force at different spacing distances. The model is used to identify the distances existing between two different magnets that enable the system to perform with a specific nonlinearity. The performance of the E-shape piezoelectric energy harvester is also investigated through experiments, with E-shape energy harvesters at different spacing distances tested under several base acceleration excitations. We observe that the frequency domain output voltage of the system shows a general excellent controllable performance, with a widening of the frequency bandwidth. The half-power bandwidth of the linear energy harvester for a distance of 25 mm is 0.8 Hz only, which can be expanded to 2.67 Hz for the larger distance of 11 mm between magnets. The energy harvester presented in this work shows promising performances for broad-spectrum vibration excitations compared to conventional cantilever piezoelectric energy harvester systems with a tip mass.

Shock isolation performance of a geometric anti-spring isolator

In this paper, shock isolation performance of a geometric anti-spring (GAS) isolator is investigated. The static and dynamic stiffness property of GAS isolator is discussed. The mathematical simulation is used to explore the effect of several parameters on shock isolation performance of GAS isolator under a modified half-sine pulse acceleration excitation. Shock isolation experiments of GAS isolator under base acceleration excitation with different excitation amplitudes and payloads are carried out. The results show that the dynamic stiffness characteristic of GAS isolator determines its shock isolation performance. When shock acceleration amplitude is not too large, GAS isolator shows better shock acceleration and absolute displacement isolation performance than the equivalent linear system. The effects of shock acceleration amplitude, payload, and damping on the shock isolation performance of GAS isolator are discussed, which provide guidelines for its further practical application.

Benchmark solutions of stationary random vibration for rectangular thin plate based on discrete analytical method

This paper aims to accurately and efficiently achieve the benchmark solutions of stationary stochastic responses for rectangular thin plate. Firstly, the exact solutions of free vibration for thin plate with SSSS, SSSC, SCSC, SFSF, SSSF and SCSF boundary conditions are introduced to random vibration analysis. Based on pseudo excitation method (PEM), the analytical power spectral density (PSD) functions of the transverse deflection, velocity, acceleration and stress responses for thin plate under random base acceleration excitation are derived. Subsequently, to enhance computational efficiency, the discrete analytical method (DAM) that realizes the discretization for the modal coordinates and frequency domain is proposed. Finally, the efficiency of DAM and the accuracy of benchmark solutions are scrutinized by comparison with the analytical solutions and finite element solutions.

Structural topology optimization under harmonic base acceleration excitations

This work is focused on the structural topology optimization methods related to dynamic responses under harmonic base acceleration excitations. The uniform acceleration input model is chosen to be the input form of base excitations. In the dynamic response analysis, we propose using the large mass method (LMM) in which artificial large mass values are attributed to each driven nodal degree of freedom (DOF), which can thus transform the base acceleration excitations into force excitations. Mode displacement method (MDM) and mode acceleration method (MAM) are then used to calculate the harmonic responses and the design sensitivities due to their balances between computing efficiency and accuracy especially when frequency bands are taken into account. A density based topology optimization method of minimizing dynamic responses is then formulated based on the integration of LMM and MDM or MAM. Moreover, some particular appearances such as the precision of response analysis using MDM or MAM, and the duplicated frequencies are briefly discussed. Numerical examples are finally tested to verify the accuracy of the proposed schemes in dynamic response analysis and the quality of the optimized design in improving dynamic performances.

A micromachined low-frequency piezoelectric harvester for vibration and wind energy scavenging

To efficiently scavenge ambient vibration energy and wind energy at the same time, a low-frequency piezoelectric harvester was designed, fabricated and tested. A lumped-parameter model of the cantilevered piezoelectric energy harvester with a proof mass was established and the closed-form expressions of voltage and power on a resistance load under base acceleration excitation were derived. After effects of the lengths of the proof mass and electrodes on output power were analyzed, a MEMS harvester was optimally designed. By using aluminum nitride as piezoelectric layer, a MEMS energy harvester was fabricated with bulk micromachining process. Experimental results show that the open-circuit frequency of the MEMS harvester is about 134.8 Hz and the matched resistance is about 410 kΩ. Under the harmonic acceleration excitation of ±0.1 g, the maximum output power is about 1.85 µW, with the normalized power density of about 6.3 mW cm−3 g−2. The critical wind speed of the device is between 12.7 and 13.2 m s−1 when the wind direction is from the proof mass to the fixed end of the cantilever. The maximum output power under 16.3 m s−1 wind is about 2.27 µW.

Research on Influence of Valley Width on the Acceleration Distribution of the Central Points of Concrete-Faced Rockfill Dam

3-D dynamical response analysis of concrete-faced rockfill dam is presented. Using equivalent-linear model, based on different dam heights and different shapes of river valley, the responses of dam subjected to different seismic intensity inputs have been studied. Especially the systematic analysis about the influence of the valley width on the distribution of the acceleration at the central points the bank slope is conducted. The results show that, the distribution of the horizontal acceleration along the dam heights at the central points on the central section of concrete-faced rockfill dam performs that the acceleration magnification which increases remarkably over 0.8H is a little smaller during 0~0.8H. For high concrete-faced rockfill dam, with the base acceleration excitations unchanged and the bank slope becoming steep (a gradient of 0.4), the valley width has a great impact on the magnification of the horizontal acceleration. The narrower the river valley is, the bigger the acceleration magnification is. With the slowing of the valley slope, the distribution of the acceleration magnification remains unchanged but the maximum reduces a little.

Research on Influence of the Bank Slope on the Acceleration Distribution of the Central Points of Concrete-Faced Rockfill Dam

3-D dynamical response analysis of concrete-faced rockfill dam is presented. Using equivalent-linear model, based on different dam heights and different shapes of river valley, the responses of dam subjected to different seismic intensity inputs have been studied. Especially the systematic analysis about the influence of the bank slope on the distribution of the acceleration at the central points the bank slope is conducted. The results show that, the distribution of the horizontal acceleration along the dam heights at the central points on the central section of concrete-faced rockfill dam performs that the acceleration magnification which increases remarkably over 0.8H is a little smaller during 0~0.8H. For high concrete-faced rockfill dam, with the base acceleration excitations unchanged and the bank slope becoming gentle, the maximum acceleration on the top of the dam reduces. Under various seismic intensities, for non-high dams in the broad river valley the slope has almost no impact on the magnification of the horizontal acceleration.

Empirical Formula for Calculating Maximum Acceleration of Concrete-Faced Rockfill Dam

On the condition of different dam heights and different shapes of river valley, 3-D dynamical responses of concrete-faced rockfill dams subjected to different seismic intensity input are analyzed based on equivalent-linear model in this paper. The results show that on the condition of the same dam height and the base acceleration excitations unchanged, the position of the maximum acceleration on the axis of the top moves from the middle to the riversides symmetrically with the increase of the river valley width. For the narrow river valley, the position of the maximum acceleration which occurs near the riversides to the wide valley is on the middle of the axis at the top. The result negates the application of 2-D dynamical computation for wide valleys, and shows that for the seismic response of high concrete-faced rockfill dams, the seismic amplification factor along the axis should be given, except for that along the dam heights. Statistical analysis is also made to the seismic coefficient, and an empirical equation for calculating the maximum acceleration of the dam is provided, which provide an reference for the seismic stability analysis of rockfill dams using pseudo-static method.