Excitation Frequency Ratio Research Articles

A Complex Mode Superposition Method Based on Hysteretic Damping Model for Mode Static Correction

Due to modal truncation, the dynamic responses calculated by the mode superposition method have some errors. In this paper, the source of truncation error of the complex mode superposition method for hysteretic damped systems with non-proportional characteristics is analyzed. It includes truncation errors of external excitation load and Hilbert transform term. With the increase of mode order, the ratio of excitation frequency to natural frequency gradually approaches zero. Combined with the expression of structural modal response caused by harmonic wave, the corresponding approximate expression of high-order modal response is obtained. Through quasi-static analysis, a complex mode superposition method of non-proportionally damped systems for mode static correction is proposed. Numerical examples show that when the ratios of the domain frequencies of the external excitation to the natural frequency of some high-order modes are small, the complex mode superposition method for mode static correction has a good effect.

Vibrational energy transfer in coupled mechanical systems with nonlinear joints

This study investigates vibrational transfer and energy flow in nonlinearly coupled systems, each subjected to a harmonic force with different excitation frequency. A nonlinear joint having either smooth or non-smooth stiffness characteristics at the coupling interface is considered. The steady-state dynamic responses are obtained by a method of harmonic balance with alternating frequency and time and by a direct numerical integration. The time-averaged transmitted power is used to assess the direction of energy flow and the power transfer between the systems. It is shown that as the excitation frequency ratio increases, the point of zero net power transfer between subsystems moves to lower frequencies. The cubic stiffness nonlinearity mainly affects the power transfer in the vicinity of the second resonance frequencies. It is also shown that the second resonance frequencies of both subsystems and the point of zero net power transfer shift to higher frequencies when the bilinear stiffness ratio increases. For the power transfer curves, the bilinear stiffness ratio controls the location of the second resonance frequencies. Findings from this study can provide insights to aid design of interfacial joints with regards to vibration transfer in coupled systems under multi-frequency excitations. The study reveals energy flow mechanisms through joint structures, which should benefit their dynamic designs aiming at an enhanced vibration suppression performance.

Transient dynamics of 2D-FG porous microplates under moving loads using higher order finite element model

This study presents the higher order finite element model to explore the transient vibration of two-dimensional functionally graded (2D-FG) porous microplate under harmonic moving loads, that can be helped in design of nanoplate devices such as NEMS, nanofilters, nanoresonators, and nanoswitches. A normal and shear deformable plate theory with five unknowns is exploited with the modified couple stress theory to portray the kinematic relations, constitutive stress–strain equations, and size-dependence effect. This complicated problem is investigated for the first time based on Newmark’s method to obtain time history analysis of 2D-FG porous microplates having in-plane inhomogeneity. In-plane displacements and stretching component of the transverse displacement are interpolated by using Bogner-Fox-Schmit rectangular element with four degrees of freedom (DOF) for each node satisfying the C1 continuity requirement. In addition, bending and shear components of the transverse displacement are presented by a nonconforming rectangular element with six DOF for each node satisfying the C2 continuity requirement. Various boundary conditions are considered to evaluate the influences of the thickness to material length parameter, aspect ratio, gradient index in two directions, material loss due to porosity in two directions, load velocity parameter and load excitation frequency ratio. It is revealed based on the results that dynamic deflections of 2D-FG porous microplates are significantly affected by the variation of the analysis parameters mentioned above.

A lumped-parameter coupled electro-piezo-aeroelastic model for flapping wings

Induced-strain actuated flapping wings and fins, achieved by surface-mounted piezoelectric actuators, do not need conventional motors and mechanisms, potentially reducing system weight, energy consumption, and mechanical complexity compared to conventional systems. A piezocomposite flapping wing or an underwater oscillating fin with induced-strain actuation can interact with the ambient fluid to yield flow vectoring, control, and lift or thrust generation. In this article, an electro-piezo-aeroelastic coupled lumped-parameter model is developed to predict the dynamic behavior of strain actuated flapping wings, and obtain insight into coupling mechanisms such as bend-twist coupling, fluid-structure interaction, and electro-piezo coupling. The piezoelectric wing is modeled as a laminated orthotropic plate. Using the Rayleigh-Ritz method, the distributed wing motion can be represented by lumped wing heave, chordwise curvature, and pitch displacements by assuming prescribed deformation shapes. The assumed shapes are compatible with the fluid effects interpreted as translational and torsional added mass and damping to the structure. The aeroelastic model is then coupled to the circuit model via electro-piezo coupling. The mechanical model is validated using the finite element method. It is found that four wing tip parameters, including first and second order heave motion, pitch, and chordwise curvature are sufficient to represent the wing motion. The lumped parameter wing model is then used to investigate the system optimal parameters for maximizing desired aero- and/or hydro-dynamic responses. System properties such as structural parameters, excitation frequency ratio, etc., are under investigation. The lumped parameter model is computationally efficient, and suitable for trade studies and multi-disciplinary design optimization. Also, the lumped parameter model serves as a foundation for flapping flight analysis, e.g., analyzing lift force, leading-edge vortex stabilization, and tip vortex shedding.

A reduced-order multi-body model with electromechanical-aeroelastic coupling for mechanism-free ornithopters

Piezoelectric material-actuated so-called solid-state (i.e., mechanism-free) ornithopters do not need conventional motors and mechanisms, potentially saving weight and energy consumption, reducing mechanical complexity, and improving wing flexibility. In solid-state ornithopters, wing flapping can be achieved by surface-mounted piezoelectric actuators. The design of a solid-state ornithopter is a complex multi-disciplinary task, and optimization of wing topology, actuator placement, and excitation parameters requires a computationally efficient model to predict its dynamic response and performance metrics. In this paper, effectively, a novel flight simulation model is presented based on a reduced-order lumped parameter multi-body model coupled with a vortex lattice program. The proposed lumped parameter model can be represented by an equivalent multi-body mechanical model or a circuit model. The coupling considered in the lumped parameter model includes: (1) the body-wing momentum interaction, (2) bend–twist​ coupling of the piezocomposite wings, (3) fluid–structure interactions between the flapping wings, oscillating body, and the ambient fluid, and (4) electromechanical coupling between a resistive–inductive–capacitive driving circuit and the piezocomposite wings. The wing motion is described using the Rayleigh–Ritz method, in which the representative wing modes are identified as spanwise plunge, chordwise curvature, and twist. The body-wing interaction is modeled using Hamilton’s principle. The fluid-induced effects on the wings have three contributions: added mass and damping, quasi-steady aerodynamic forces obtained using the vortex lattice program, and unsteady aerodynamic forces calculated using the Theodorsen formulation, which is integrated into the wing heave and pitch degrees of freedom in the lumped parameter model. The proposed reduced-order model proposed is computationally efficient, suitable for trade studies and multi-disciplinary design optimization, and can be easily converted to state representation for controller development purposes. The capabilities of this model are demonstrated through tethered and gliding flight simulations. System properties such as circuit parameters, structural parameters, excitation frequency ratio, etc., are investigated. Phugoid and short period modes are observed in gliding flight simulations. The contribution of active flapping is found by the comparison of flight simulations with and without active flapping. A net thrust contributed by unsteady lift is demonstrated even though the thrust-lift ratio is low. The proposed model serves as an extensible framework for modeling and design optimization of ornithopters.

A hybrid artificial intelligence control of a turbulent jet: Reynolds number effect and scaling

This work aims to investigate experimentally the effect of the Reynolds numberRe,based on the nozzle diameterD, on jet mixing manipulation using an unsteady radial minijet. A novel artificial intelligence (AI) control system has been developed to manipulate the jet overRe = 5800–40 000. The system may optimize simultaneously the control law and a time-independent parameter, which dictate the actuation ON/OFF states and amplitude, respectively. The control parameters include the mass flow rate, excitation frequency and diameter ratios (Cm,fe/f0andd/D) of the minijet to the main jet as well as the duty cycle (α) of minijet injection. Jet mixing is quantified usingKeandK0, whereKis the decay rate of the jet centreline mean velocity, and subscriptseand 0 denote the manipulated and unforced jets, respectively. It has been found that the maximumKeachievable does not vary withRe.Scaling analysis of the huge volume of experimental data obtained from the AI system reveals that the relationshipKe = g1(Cm,fe/f0,α,d/D, Re, K0) may be reduced toKe/K0 = g2$(\zeta )$, whereg1andg2are different functions and the scaling factor$\zeta = ({C_m}/\alpha ){(D/d)^{1 - n}}(1/Re){({f_e}/{f_{e,opt}})^m}$,mand 1 − nare the power indices, and subscriptoptdenotes the value at whichKeis maximum. The scaling law is discussed in detail, along with the physical meanings of the dimensionless parametersKe/K0,ζ,$({C_m}/\alpha ){(D/d)^{1 - n}}(1/Re)$and${({f_e}/{f_{e,opt}})^m}$.

Effects of pendulum tuned mass dampers on the dynamic response of jacket platforms

We investigate effects of pendulum tuned mass damper (PTMD) configuration as well as structural excitation frequency by ocean waves on the dynamic response of a jacket platform. To do this, an offshore jacket platform equipped with a PTMD with different values of frequency ratio (β), damping ratio (ξd) and mass ratio (m‾) is numerically simulated in ANSYS software under the action of irregular waves with different values of structural excitation frequency ratio (α). The results of the numerical simulations are validated against the experimental and numerical data available in the literature. The validations were in complete agreement with the benchmarking data. The results suggest that with a constant β, an increase in ξd of about 20 times reduces the standard deviation of the deck displacements (σ) tblf about 7.41%. Further, with an increase in β, σ increases when β>1 and decreases when β≤1. Regarding the pendulum mass ratio, an increase in m‾ of about 14 times results in a 12.91% reduction in σ within the range of ξd≤0.15. Out of the latter range (i.e. for ξd>0.15), σ is not significantly affected by m‾. Considering σ as the fitness function, the most optimal configuration for the PTMD system is achieved for α=1.2, β=1 and ξd=0.2.

Dynamic model of vibrating plate coupled with a granule bed

A dynamic model is proposed to study the nonlinear behavior of a granule-bed–vibrating-plate coupling system based on the theory of a completely inelastic bouncing ball. The process of interactions between the ball and plate is divided into three stages: synchronized motion, separation, and impact. The discrete-element method is used to obtain the form of the impact function inspired by the bird impact model, and the analytical solutions of the overall process are derived. Furthermore, parametric research is performed to demonstrate the influence on the motion of the plate of system parameters including the amplitude of the excitation force, particle mass, and damping. The calculation results indicate that the model can be used to analyze the coupling dynamic behaviors of particles and plates, and abundant nonlinear phenomena, such as period-doubling bifurcations, can be observed. The motion of the plate always shows chaos in particular frequency bands (the ratio of external excitation frequency to natural frequency was between 0.63 and 0.75 for the conditions in this study).

Effect of Flexibly Attached Secondary Systems on Dynamic Behavior of Light Structures

This paper investigates the effect of flexibly attached secondary systems (FSS) on the dynamic behavior of primary structures (PS) under harmonic and seismic ground excitations. An FSS affects the main structure during ground excitation differently than a secondary system that is rigidly attached to it. Small displacements in the FSS are used to derive the equations of motion that define the behavior of the PS and FSS. The analytical formulation presented is validated by a finite element (FE) study conducted in SAP2000. The influence of mass ratio, tuning frequency ratio, and excitation frequency ratio on the dynamic behavior of the PS is investigated. The results show that the combined system (PS+FSS) behaves as a modified single degree of freedom (SDOF) structure at higher tuning frequency ratios. The dynamic response of the structure is independent of the mass ratio at low tuning frequency ratio of FSS. Under seismic excitations, the flexible structure’s response reduces considerably as the mass ratio increases, compared to a stiff structure at a higher tuning frequency ratio. When the tuning frequency ratio is equal to one, smaller mass ratios of FSS increase the seismic performance of the stiff structure. A design methodology is proposed to measure the spectral acceleration of the primary structure by incorporating the effect of FSS in the design response spectrum. An analysis of the tuning frequency ratio and mass ratio on the modified design spectrum is also presented. Finally, the proposed design methodology is validated with an existing study.

Transmission rules of ultrasonic at the contact interface between soil medium in farmland and ultrasonic excitation transducer

To analyze the phenomenon of distortion and frequency dispersion in the ultrasonic pressure curve at the excitation transducer-soil contact interface (incident interface), a new method to study the ultrasonic propagation in farmland soil media based on DEM (discrete element method) was proposed in this paper. And its feasibility was verified through simulation and actual measurement equivalent experiments. The excitation amplitude, excitation frequency and soil compression ratio were used as influencing factors to carry out single-factor experiments. The analysis was carried out from three aspects: the time domain and the frequency domain curve of the ultrasonic, and the microscopic characteristics of the soil particles near the interface. The experimental results show that the reduction of soil compression ratio, the increase of excitation frequency and amplitude can trigger the non-linear response of the soil, which will lead to the distortion of the ultrasonic waveform. Among them, the compression rate has the most significant influence on the distortion of the sound wave. When the compression ratio is 0%, the trough and the second peak disappear. When the compression ratio reaches 12%, the amplitude of the trough and the second peak are 424% and 749% of the compression ratio of 6%, which is far greater than the influence of other factors. As the excitation frequency increases from 20 kHz to 60 kHz, the ultrasonic frequency domain range increases from 0 to 40 kHz to 0–150 kHz, the dispersion phenomenon is enhanced, which leads to a more serious waveform distortion, while other factors have less influence on the dispersion phenomenon. Under the ultrasound, it is found that the soil particles have a hysteresis phenomenon, that is, the direction of the force and the velocity of the soil particles is inconsistent. And as the soil compression ratio decreases, the excitation frequency increases, the greater the excitation amplitude, the more serious the hysteresis phenomenon, and then causes more serious ultrasonic distortion. The research of ultrasonic waves at the transducer-soil interface is helpful to reveal the propagation law of ultrasonic waves in soil, which provides a theoretical reference for the improvement of the accuracy of ultrasonic testing instruments.

Nonlinear vibration analysis of CFRP spherical shell panel under hygrothermal effects

Based on the nonlinear static stability analysis, this paper establishes the governing equations of the nonlinear dynamic stability of a spherical shell panel of carbon fiber-reinforced polymer (CFRP) under the hygrothermal effects; the Galerkin method is used to solve the governing equations. Then, for the free vibration of CFRP spherical shell panel, the analytical expression of the ratio of nonlinear vibration frequency to natural frequency is obtained by employing the multiscale method; for forced vibration, the analytical expression of the ratio of excitation frequency to natural frequency is obtained by considering the harmonic excitation load. Finally, the effects of geometric parameters, boundary conditions, loads, and the hygrothermal effects on the amplitude-frequency response curves of the CFRP spherical shell panel are discussed.

Axisymmetric jet manipulation using multiple unsteady minijets

A turbulent round jet with a Reynolds number of 8000 based on the minijet exit diameter is experimentally manipulated using 1–6 unsteady radial minijets. Five control parameters are investigated, including the minijet number or configuration (N), the duty cycle (α) of minijet injection, and the mass flow rate, excitation frequency, and diameter ratio (Cm,N, fe/f0, and d/D) of an individual minijet to a main jet. The decay rate (Ke) of the jet-centerline mean velocity under manipulation strongly depends on these five parameters. The typical flow structures or conceptual flow models are proposed for each minijet configuration based on extensive measurements. Three distinct mechanisms behind the highly effective manipulation are identified and discussed from the flow structures. It has been found that the optimal fe/f0 and α, i.e., (fe/f0)opt and αopt at which the maximum Ke or Ke,max occurs, do not vary with N, though optimal Cm,N or (Cm,N)opt does. Empirical scaling analysis performed under (fe/f0)opt reveals that the relationship Ke = g1 (N, Cm,N, α, d/D) may be reduced to Ke/Ke,max = g2 ζ, where g1 and g2 are different functions, and the scaling factor ζ = Cm,N/(Cm,N)opt, representing physically the minijet penetration depth. Both Ke,max and (Cm,N)opt are found to depend on N, α, and d/D. Discussion conducted based on Ke/Ke,max = g2 ζ provides important insight into the jet control physics. It is also discussed how fe/f0 and α are connected to the vortex interaction and, hence, Ke.

Optimal design of brace-viscous damper and pendulum tuned mass damper using Particle Swarm Optimization

We implemented Particle Swarm Optimization (PSO) to determine the most optimal properties of the brace-viscous damper system (BVDS), pendulum tuned mass damper (PTMD), and combined BVDS-PTMD system in mitigation of dynamic response of a jacket platform. To do this, a scaled prototype of an offshore jacket is numerically simulated in ANSYS subjected to ocean waves. Concerning BVDS, at each story, the variables being optimized are (1) BVDS configuration such as chevron, toggle, diagonal; (2) damping coefficient, and (3) brace area. The properties of PTMD being optimized are the damping ratio (ξd), frequency ratio (β), structural excitation frequency ratio (α), and mass ratio (m¯). To do the optimization, the results of ANSYS are exploited to calculate the PSO cost function (standard deviation of deck displacements (σsd)). Regarding the deck displacement and base shear force, the optimization results proved that the optimal BVDS-PTMD combined system outperforms the optimal BVDS and the optimal BVDS performance is better than that of the PTMD system. Both in the optimal BVDS and integrated BVDS-PTMD, the chevron configuration for the top floor and toggle configuration for the first to third floors are evaluated as the optimum arrangement by the optimization algorithm.

Numerical study on two-degree-of-freedom vortex induced vibrations suppression of a circular cylinder via synthetic jets at different excitation frequencies

In this work, a pair of synthetic jets are investigated for control of vortex induced vibration (VIV) of a circular cylinder in uniform flow in the low Reynolds number regime. In particular, the study focuses on three representative phase differences (0, π/2, and π) between the pair of synthetic jets to study the influence of synthetic jet excitation frequency ratio fsj* (fsj* = fsj/fn,water) on 2DOF VIVs control by two-dimensional numerical simulation. The Reynolds number is fixed at 150, the mass ratio m* (m* = mosc/md) of the circular cylinder is 2.0, and the natural oscillation frequencies in the in-flow and cross-flow directions are equal. The amplitude response, frequency response, hydrodynamic forces, and wake patterns are analyzed. The results show that both in-flow and cross-flow oscillations of the circular cylinder can be significantly suppressed by synthetic jets with various phase differences, and the wake becomes symmetric when fsj* ≥ 4.0. When fsj* < 4.0, many fluctuations can be observed from the changing curves of in-flow and cross-flow oscillation amplitudes, and the oscillation may be enhanced by the occurrence of lock-in between the oscillation frequencies and the synthetic jet excitation frequencies. Besides, vortex shedding modes of the controlled cases are significantly different in blowing and suction phases of the synthetic jet, when the excitation frequency is very low, such as fsj* = 0.2.

Nonlocal Ionization Theory and Secondary Electron Emission Coefficient: Application in Helium and Neon DC Microdischarge at High Pressure

In this article, we are interested in giving a detailed study of the nonlocal ionization theory (NIT) and their secondary electron emission coefficient (SEEC). As for expelling, we present the spatial distributions of both Coulomb logarithm of electron–electron and electron-ion collisions, ionization and excitation frequency ratios, and source term of particle charged, as well as ion temperature in helium and neon dc microdischarge at high pressure. The pressure range is from 40 to 70 torr, and the applied potential is from 200 to 230 V. In the framework, we have developed an empirical expression of the secondary electron emission corresponding to the helium and neon discharge. The current–voltage results are in good agreement with the experimental data. We have computed the real ion temperature using the generalized Einstein’s relation, and in my knowledge, this is for the first time in the literature. As a result, the helium ion temperature reached 34 times the gas temperature at the cathode and reached 56 times the gas temperature in neon.

Parametric analysis on hydroelastic behaviors of hydrofoils and propellers using a strongly coupled finite element/panel method

This paper analyzed the hydroelastic behaviors of hydrofoils and marine propellers immersed in incompressible, inviscid and irrotational fluids. Strongly coupled fluid–structure interaction analyses were performed using a three-dimensional (3-D) potential-based panel method in conjunction with a 3-D finite element method. The present method is developed for hydroelastic analyses of geometrically complex-shaped propeller blades, and the application of the method to the hydroelastic problems of hydrofoils is straightforward. The parameters dominating the added-mass and -damping matrices of the hydrofoils and propellers are examined. The effects of the translational motion of the hydrofoil and the rotational motion of the propeller on the added-mass and -damping matrices are compared based on different non-penetration boundary conditions and distributions of the inflow velocity. It is found that for hydroelastic analyses of propellers, the reduced frequency, i.e., the ratio of excitation frequency to rotational frequency, is a key parameter for determining the added-mass and -damping matrices of the propellers. The effect of the advance ratio on the added-mass and -damping matrices of the propeller blade depends upon the ratio of excitation frequency to rotational frequency. For hydrofoils, the added-damping matrix is significantly affected by the ratio of the excitation frequency multiplied by chord length and divided by axial inflow velocity.

Parametric study and scaling of jet manipulation using an unsteady minijet

A parametric study is conducted for the control of a turbulent jet using a single unsteady minijet. A number of control parameters that influence the decay rate $K$ of the jet centreline mean velocity are investigated, including the mass flow rate ratio $C_{m}$, excitation frequency ratio $f_{e}/f_{0}$ and exit diameter ratio $d/D$ of the minijet to main jet, along with the duty cycle ($\unicode[STIX]{x1D6FC}$) of the minijet injection. Extensive hot-wire, particle image velocimetry and flow visualization measurements were performed in the manipulated jet. Various flow structures have been identified, such as the flapping flow, non-flapping flow and that showing a manipulable thrust vector, depending on $C_{m}$, $f_{e}/f_{0}$ and $\unicode[STIX]{x1D6FC}$. Empirical scaling analysis unveils that, prior to the minijet impingement upon the wall of the nozzle and the generation of turbulence, the relationship $K=g_{1}$ ($C_{m}$, $f_{e}/f_{0}$, $d/D$, $\unicode[STIX]{x1D6FC}$) may be reduced to $K=g_{2}$ ($\unicode[STIX]{x1D709}$), where $g_{1}$ and $g_{2}$ are different functions and the scaling factor $\unicode[STIX]{x1D709}=(\sqrt{MR}/\unicode[STIX]{x1D6FC})(d/D)^{n}$ ($\sqrt{MR}\equiv C_{m}(D/d)$ is the momentum ratio and $n$ is a constant that depends on $\unicode[STIX]{x1D6FC}$) is physically the effective momentum ratio per pulse or effective penetration depth. Discussion is conducted based on $K=g_{2}$ ($\unicode[STIX]{x1D709}$), which provides important insight into the jet control physics.

POD ANALYSIS OF A BLOOMING JET AT A MODERATE REYNOLDS NUMBER

Jet flow in general has a wide range of applications, from propulsion of large aircraft to cooling of electronic circuit. Jet is also a source of noise which is needed to be controlled suitably and since large scales of fluid motion play a primary role in transport phenomena, selective manipulation of these structures is needed to achieve efficient control. The snapshot method of proper orthogonal decomposition (POD) has been utilized to analyze the fluctuating velocity vector for a blooming jet at the Reynolds number Re = 4300 and excitation frequency ratio Rf = 2.4. The baseline data is developed with the help of large eddy simulation (LES). Higher-order spatial and temporal discretizations are used to solve the governing equations. For Re = 4300, at least 96 snapshots are required for good spectral resolution. For capturing 90% of the total energy of the unsteady flow field, at least 40 modes are required. The eigenvalue/singular distributions for the forced jet show the formation of odd-even pairs of modes. The first pair itself contains the details of branching. In addition, higher-order modes capture the inherent jet instability mechanisms and related flow structures.

Nonlinear high-order dynamic stability of AL-foam flexible cored sandwich beam with variable mechanical properties and carbon nanotubes-reinforced composite face sheets in thermal environment

In this paper, the nonlinear dynamic stability analysis of sandwich beam including AL-foam flexible core and carbon nanotubes-reinforced composite face sheets subjected to axial periodic load are investigated by using generalized differential quadrature method. The flexible core of sandwich beam is made of Aluminum alloy foam with variable mechanical properties in the thickness direction. With considering the high-order geometrical nonlinearity in the core and face sheets, the high-order sandwich panel theory and modified couple stress theory are employed for AL-foam flexible core and face sheets, respectively. The governing nonlinear partial differential equations of dynamic stability are derived from the Hamilton’s principle and then discretized by using generalized differential quadrature method to convert them into a linear system of Mathieu–Hill equations. These formulations lead to nine partial differential equations which are coupled in axial and transverse deformations. The boundaries of the instability region are achieved by Bolotin’s method and are illustrated in the dimensionless nonlinear excitation frequency (Ω NL) and excitation frequency ratio (Ω NL/Ω L) to load amplitude plane. A parametric study is carried out to investigate the influence of some important parameters such as slenderness ratio, face sheet thickness, temperature rise, carbon nanotube volume fraction, static load factor, coefficients of Pasternak foundation, and end supports on the nonlinear dynamic instability characteristics of AL-foam core sandwich beam. The numerical results show that with temperature increasing, the nonlinear excitation frequency (Ω NL) and width of corresponding unstable zone decrease, but dynamic frequency ratio (Ω NL/Ω L) and associated unstable region increase. With an increase in the application of sandwich structures for compressible core in advanced industries such as spacecraft, high-speed aircraft, naval vessels, transportation, and automobiles, a further interest in the problem-involving dynamic instability of structures has resulted. Because of their applications, sandwich structures are frequently exposed to periodic axial compressive forces and so the dynamic instability has been a very important topic in structural dynamics and is of practical importance in different engineering industries.

On optimization of energy harvesting from base-excited vibration

This paper re-examines and clarifies the long-believed optimization conditions of electromagnetic and piezoelectric energy harvesting from base-excited vibration. In terms of electromagnetic energy harvesting, it is typically believed that the maximum power is achieved when the excitation frequency and electrical damping equal the natural frequency and mechanical damping of the mechanical system respectively. We will show that this optimization condition is only valid when the acceleration amplitude of base excitation is constant and an approximation for small mechanical damping when the excitation displacement amplitude is constant. To this end, a two-variable optimization analysis, involving the normalized excitation frequency and electrical damping ratio, is performed to derive the exact optimization condition of each case. When the excitation displacement amplitude is constant, we analytically show that, in contrast to the long-believed optimization condition, the optimal excitation frequency and electrical damping are always larger than the natural frequency and mechanical damping ratio respectively. In particular, when the mechanical damping ratio exceeds a critical value, the optimization condition is no longer valid. Instead, the average power generally increases as the excitation frequency and electrical damping ratio increase. Furthermore, the optimization analysis is extended to consider parasitic electrical losses, which also shows different results when compared with existing literature. When the excitation acceleration amplitude is constant, on the other hand, the exact optimization condition is identical to the long-believed one. In terms of piezoelectric energy harvesting, it is commonly believed that the optimal power efficiency is achieved when the excitation and the short or open circuit frequency of the harvester are equal. Via a similar two-variable optimization analysis, we analytically show that the optimal excitation frequency depends on the mechanical damping ratio and does not equal the short or open circuit frequency. Finally, the optimal excitation frequencies and resistive loads are derived in closed-form.