Numerical and experimental investigations are carried out to study the combined effect of rotation and support nonuniformity on the modal characteristics of circular thick disks. The laboratory experiments on stationary and rotating circular disks are conducted to investigate the effects of partial support conditions on the in-plane and out-of-plane vibration responses of annular disks with different radius ratios. Numerical results suggested that the nonuniformity of the support along the circumferential directions of the boundaries affects the modal characteristics of the disk along the in-plane and out-of-plane directions, while introducing additional coupling between the modes. Specifically, some of the frequency peaks in the frequency spectrum obtained under uniform boundary conditions split into two distinct peaks in the presence of a point support. The results show that the in-plane modes of vibration are comparable with those associated with out-of-plane modes and are contributing to the total noise radiation. The coupling between in-plane and out-of-plane modes is found to be quite significant due to the nonuniformity of the boundary conditions. The experimental study confirms the split in natural frequencies of the disk that is observed in the numerical results due to both rotation and support nonuniformity. The applicability and accuracy of the formulations is further examined through analysis of modal characteristics of a railway wheel in contact with the rail.

The present paper develops a nonlinear stiffness sensor for measuring cubic nonlinear elasticity. The measurement system consists of a vibrator with a control circuit. We apply linear-plus-nonlinear feedback to actuate the vibrator attached to a measurement object for inducing van der Pol type self-excited oscillation so that the response amplitude of the oscillation can be set arbitrarily by changing the nonlinear feedback gain. We focus on the fact that the nonlinear elasticity of the measurement object causes a natural frequency shift related to the magnitude of vibration amplitude of the vibrator. We can set the response amplitude to various values by changing the nonlinear feedback gain and measuring the shift of the response frequency depending on the magnitude of the response amplitude. As a result, based on the bend of the experimentally obtained backbone curve, the nonlinear elasticity of the measurement object is identified.

This paper presents four alternate models of varying complexity to examine mechanical snubbing in elastomeric isolators. Although the modeling, analysis, and experimentation presented is limited to snubbing of elastomeric isolators, the models are generic and can be adapted to other snubbing mechanisms as well, such as friction snubbing. Two of the four models presented in this paper use the Bouc–Wen model in order to capture hysteresis and gradual stiffening behavior, which is generally exhibited by elastomeric snubbing systems. The other two models are relatively simplistic and do not account for a time-varying parameter to model significant hysteresis. However, these two models can still be useful for applications with a small range of excitation frequencies and for applications where the snubbing design needs to incorporate an abrupt transition in stiffness. A parameter identification technique is used to determine the variables associated with each model. The parameter identification technique is based on the use of an optimization algorithm associated with the force–displacement characterization. All four models presented in this paper capture the coupled dynamics of the isolation system and the snubbing system and are, therefore, a significant improvement upon the currently used models. The models presented are expected to facilitate the design and analysis of a passive isolation system in conjunction with the design of the snubbing system and the base frame supporting the snubbing system.

Active sandwich panels are an example of smart noise attenuators and a realization of hybrid active-passive approach for the problem of broadband noise reduction. The panels are composed of thin elastic faceplates linked by the core of a lightweight absorbent material of high porosity. Moreover, they are active, so piezoelectric actuators in the form of thin patches are fixed to their faceplates. Therefore, the passive absorbent properties of porous core, effective at high and medium frequencies, can be combined with the active vibroacoustic reduction necessary in a low frequency range. Important convergence issues for fully coupled finite-element modeling of such panels are investigated on a model of a disk-shaped panel under a uniform acoustic load by plane harmonic waves, with respect to the important parameter of the total reduction of acoustic transmission. Various physical phenomena are considered, namely, the wave propagation in a porous medium, the vibrations of elastic plate and the piezoelectric behavior of actuators, the acoustics-structure interaction and the wave propagation in a fluid. The modeling of porous core requires the usage of the advanced biphasic model of poroelasticity, because the vibrations of the skeleton of porous core cannot be neglected; they are in fact induced by the vibrations of the faceplates. Finally, optimal voltage amplitudes for the electric signals used in active reduction, with respect to the relative size of the piezoelectric actuator, are computed in some lower-to-medium frequency range.

This paper investigates passive and semi-active vibration control using fluidic flexible matrix composites ( F 2 MC ) . F 2 MC tubes filled with fluid and connected to an accumulator through a fixed orifice can provide damping forces in response to axial strain. If the orifice is actively controlled, the stiffness of F 2 MC tubes can be dynamically switched from soft to stiff by opening and closing an on/off valve. Fiber reinforcement of the F 2 MC tube kinematically relates the internal volume to axial strain. With an open valve, the fluid in the tube is free to move in or out of the tube, so the stiffness is low. With a closed valve, however, the high bulk modulus fluid resists volume change and produces high axial stiffness. The equations of motion of an F 2 MC -mass system are derived using a 3D elasticity model and the energy method. The stability of the unforced dynamic system is proven using a Lyapunov approach. A reduced-order model for operation with either a fully open or fully closed valve motivates the development of a zero vibration (ZV) controller that suppresses vibration in finite time. Coupling of a fluid-filled F 2 MC tube to a pressurized accumulator through a fixed orifice is shown to provide significant passive damping. The open-valve orifice size is optimized for optimal passive, skyhook, and ZV controllers by minimizing the integral time absolute error cost function. Simulation results show that the optimal open valve orifice provides a damping ratio of 0.35 compared with no damping in closed-valve case. The optimal ZV controller outperforms optimal passive and skyhook controllers by 32.9% and 34.2% for impulse and 34.7% and 60% for step response, respectively. Theoretical results are confirmed by experiments that demonstrate the improved damping provided by optimal passive control F 2 MC and fast transient response provided by semi-active ZV control.

In this paper, the parametric stability of axially accelerating viscoelastic beams is revisited. The effects of the longitudinally varying tension due to the axial acceleration are highlighted, while the tension was approximately assumed to be longitudinally uniform in previous studies. The dependence of the tension on the finite support rigidity is also considered. The generalized Hamilton principle and the Kelvin viscoelastic constitutive relation are applied to establish the governing equations and the associated boundary conditions for coupled planar motion of the beam. The governing equations are linearized into the governing equation in the transverse direction and the expression of the longitudinally varying tension. The method of multiple scales is employed to analyze the parametric stability of transverse motion. The stability boundaries are derived from the solvability conditions and the Routh-Hurwitz criterion for principal and sum resonances. In terms of stability boundaries, the governing equations with or without the longitudinal variance of tension are compared and the effects of the finite support rigidity are also examined. Some numerical examples are presented to demonstrate the effects of the stiffness, the viscosity, and the mean axial speed on the stability boundaries. The differential quadrature scheme is developed to numerically solve the governing equation, and the computational results confirm the outcomes of the method of multiple scales.

In this paper, the coupling effects among three elastic wave modes, flexural, tangential, and radial shear, on the dynamics of a planar curved beam are assessed. Two sets of equations of motion governing the in-plane motion of a curved beam are derived, in a consistent manner, based on the theory of elasticity and Hamilton’s principle. The first set of equations retains all resulting linear coupling terms that includes both static and dynamic coupling among the three wave modes. In the derivation of the second set of equations, the effects of Coriolis acceleration and high-order elastic coupling terms are neglected, which leads to a set of equations without dynamic coupling terms between the tangential and shear wave modes. This second set of equations of motion is the one most commonly used in studies on thick curved beams that include the effects of centerline extensibility, rotary inertia, and shear deformation. The assessment is carried out by comparing the dynamic behavior predicted by each curved beam model in terms of the dispersion relations, frequency spectra, cutoff frequencies, natural frequencies and mode shapes, and frequency responses. In order to ensure the comparison is based on accurate results, the wave propagation technique is applied to obtain exact wave solutions. The results suggest that the contributions of the dynamic and high-order elastic coupling terms to the response of a thick curved beam are quite significant and that these coupling terms should not be neglected for an accurate analysis of a thick curved beam with a large curvature parameter.

A straight, slender beam with elastically restrained boundaries is investigated for optimal design of an intermediate elastic support with the minimum stiffness for the purpose of raising the fundamental frequency of the beam to a given value or to its upper bound. Based on the optimality criterion of the support design, the characteristic frequency equation can readily be formulated. Then, a closed-form solution is presented for estimating the minimum stiffness and optimum position of the intermediate support such that the analysis of the various classical boundary conditions is only a degenerate case of the present problem. With the procedure developed, the effects of the general cases of the beam restraint boundaries on the optimal design of the intermediate support are studied in detail. Numerical results show that the optimum position will move gradually apart from the end with the degree increment of the boundary restraints. Moreover, it is also observed that the rotational restraint affects the optimal design of the support more remarkably than the translational one at the lower values of the restraint constants, but becomes less effective at the higher constants.

A reduction procedure for joint models that was developed in earlier work is extended to allow for relative motion between surfaces, and the effect of this procedure on timestep issues is considered. A general one-dimensional structure containing a frictional interface is considered. Coulomb friction is approximated with nonlinear springs of large but finite stiffness. The system of equations describing this structure is reduced in a procedure similar to Guyan reduction by assuming that the system deforms only in the shapes that it takes when the interface is massless. The result of this procedure is that the dynamics associated with the interface region are removed from the analysis. Following the development of the reduction procedure, the reduced formulation is specialized to the case of a simple lap joint. A numerical example problem is considered in which both the full and reduced equations of motion are integrated over time. It is seen that, for the example problem considered, the reduction procedure results in tremendous computational savings with little loss of accuracy. Based on the results of the simple example problem, it appears that the proposed reduction procedure has potential to be an accurate and effective method of alleviating the timestep difficulties associated with direct finite element analysis of joints in structural dynamics applications.

In the second paper of the two part study of membrane microair vehicles, computations are performed for a plunging membrane airfoil. The computational model uses a sixth-order finite difference solution of the Navier–Stokes equations coupled to a finite element solution of a set of nonlinear string equations. The effect, on the structural and fluid response, of plunging Strouhal number, reduced frequency, and static angle of attack is examined. Qualitatively, the flow field is found to be very complex with interactions of vortices shed from various locations along the chord of the airfoil. At a low angle of attack and a low Strouhal number, increasing reduced frequency results in a decrease and an increase in the mean sectional lift and drag coefficients, respectively. Also, at a low angle of attack, increasing the Strouhal number has minimal effect at high and low values of reduced frequencies, but a significant effect is found at an intermediate value of reduced frequency. When the effect of angle of attack is studied for fixed values of Strouhal number and reduced frequency, it is found that the act of plunging gives improved mean sectional lift when compared with the case of a fixed flexible airfoil. The improvement does not increase monotonically with the angle of attack but instead is maximum at an intermediate value. Finally, increasing the value of the membrane prestrain, which stiffens the airfoil, results in a reduced value of the sectional lift coefficient for a given Strouhal number, reduced frequency, and angle of attack.

This is the first of two papers concerning the fluid and structural dynamic characteristics of membrane wing microair vehicles. In this paper, a (three) batten-reinforced fixed-wing membrane microair vehicle is used to determine the effect of membrane prestrain on flutter and limit cycle behavior of fixed-wing membrane microair vehicles. For each configuration tested, flutter and subsequent limit cycle oscillations are measured in wind tunnel tests and predicted using an aeroelastic computational model consisting of a nonlinear finite element model coupled to a vortex lattice solution of the Laplace equation and boundary conditions. Agreement between the predicted and measured onset of limit cycle oscillation is good as is the prediction of the amplitude of the limit cycle at the trailing edge of the lower membrane. A direct correlation between levels of strain and the phase of the membranes during the limit cycle is found in the computation and thought to also occur in the experiment.

The dynamic responses of a pile group embedded in a layered poroelastic half-space subjected to axial harmonic loads is investigated in this study. Based on Biot’s theory, the frequency domain fundamental solution for a vertical circular patch load applied in the layered poroelastic half-space is derived via the transmission and reflection matrix (TRM) method. Utilizing Muki’s method, the second kind of Fredholm integral equations describing the dynamic interaction between the layered half-space and the pile group is constructed. The proposed methodology was validated by comparing the results of this paper with a known result. Numerical results show that in a two-layered half-space, for the closely populated pile group with a rigid cap, the upper softer layer thickness has different influences on the central pile and the corner piles, while for the sparse pile group, it has almost the same influence on all the piles. For a three-layer half-space, the presence of a stiffer middle layer in the layered half-space will enhance the impedance of the pile group significantly, while a softer middle layer will reduce the impedance of the pile group.

This paper reports an extension of the space-time conservation element and solution element (CESE) method to simulate stress waves in elastic solids of hexagonal symmetry. The governing equations include the equation of motion and the constitutive equation of elasticity. With velocity and stress components as the unknowns, the governing equations are a set of 9, first-order, hyperbolic partial differential equations. To assess numerical accuracy of the results, the characteristic form of the equations is derived. Moreover, without using the assumed plane wave solution, the one-dimensional equations are shown to be equivalent to the Christoffel equations. The CESE method is employed to solve an integral form of the governing equations. Space-time flux conservation over conservation elements (CEs) is imposed. The integration is aided by the prescribed discretization of the unknowns in each solution element (SE), which in general does not coincide with a CE. To demonstrate this approach, numerical results in the present paper include one-dimensional expansion waves in a suddenly stopped rod, two-dimensional wave expansion from a point in a plane, and waves interacting with interfaces separating hexagonal solids with different orientations. All results show salient features of wave propagation in hexagonal solids and the results compared well with the available analytical solutions.

This paper proposes a novel piezoelectric energy harvesting device driven by aeroelastic flutter vibrations of a simple pin connected flap and beam. The system is subject to a modal convergence flutter response above a critical wind speed and then oscillates in a limit cycle at higher wind speeds. A linearized analytical model of the device is derived to include the effects of the three-way coupling between the structural, unsteady aerodynamic, and electrical aspects of the system. A stability analysis of this model is presented to determine the frequency and wind speed at the onset of the flutter instability, which dictates the cut-in conditions for energy harvesting. In order to estimate the electrical output of the energy harvester, the amplitude and frequency of the flutter limit cycle are also investigated. The limit cycle behavior is simulated in the time domain with a semi-empirical nonlinear model that accounts for the effects of the dynamic stall over the flap at large deflections. Wind tunnel test results are presented to determine the empirical aerodynamic model coefficients and to characterize the power output and flutter frequency of the energy harvester as functions of incident wind speed.

Multifunctional structures are pointed out as an important technology for the design of aircraft with volume, mass, and energy source limitations such as unmanned air vehicles (UAVs) and micro air vehicles (MAVs). In addition to its primary function of bearing aerodynamic loads, the wing/spar structure of an UAV or a MAV with embedded piezoceramics can provide an extra electrical energy source based on the concept of vibration energy harvesting to power small and wireless electronic components. Aeroelastic vibrations of a lifting surface can be converted into electricity using piezoelectric transduction. In this paper, frequency-domain piezoaeroelastic modeling and analysis of a cantilevered platelike wing with embedded piezoceramics is presented for energy harvesting. The electromechanical finite-element plate model is based on the thin-plate (Kirchhoff) assumptions while the unsteady aerodynamic model uses the doublet-lattice method. The electromechanical and aerodynamic models are combined to obtain the piezoaeroelastic equations, which are solved using a p-k scheme that accounts for the electromechanical coupling. The evolution of the aerodynamic damping and the frequency of each mode are obtained with changing airflow speed for a given electrical circuit. Expressions for piezoaeroelastically coupled frequency response functions (voltage, current, and electrical power as well the vibratory motion) are also defined by combining flow excitation with harmonic base excitation. Hence, piezoaeroelastic evolution can be investigated in frequency domain for different airflow speeds and electrical boundary conditions.

In this study, a modeling approach has been developed to take multiphysical effects into account in the prediction of the rotordynamic behavior of high speed minirotating machinery with a moderate flow confinement. The temperature increase in the confinement and the flow induced forces resulting from the surrounding fluid have been studied and these models are combined with the structural finite element models for determining the rotordynamic behavior. The structure has been analyzed via finite elements based on Timoshenko beam theory. Flow induced forces are implemented to the structure as added mass-stiffness-damping at each node representing the structure in the fluid confinement. A thermal model based on thermal networks in steady-state has been developed. This model is used to calculate the heat dissipation resulting from air friction and temperature increase in the air gap as a function of rotation speed. At each rotation speed, the temperature in the air gap between the rotor and stationary casing is calculated and air properties, which are used for the calculation of flow induced forces are updated. In this way, thermal and fluid effects in medium gap confinements are coupled with the rotordynamic model and their effects on stability, critical speeds, and vibration response are investigated. The experimental results are reported and compared with the theoretical results in an accompanying paper (Part II).

In comparison with the transverse vibrations of rectangular plates, far less attention has been paid to the in-plane vibrations even though they may play an equally important role in affecting the vibrations and power flows in a built-up structure. In this paper, a generalized Fourier method is presented for the in-plane vibration analysis of rectangular plates with any number of elastic point supports along the edges. Displacement constraints or rigid point supports can be considered as the special case when the stiffnesses of the supporting springs tend to infinity. In the current solution, each of the in-plane displacement components is expressed as a 2D Fourier series plus four auxiliary functions in the form of the product of a polynomial times a Fourier cosine series. These auxiliary functions are introduced to ensure and improve the convergence of the Fourier series solution by eliminating all the discontinuities potentially associated with the original displacements and their partial derivatives along the edges when they are periodically extended onto the entire x - y plane as mathematically implied by the Fourier series representation. This analytical solution is exact in the sense that it explicitly satisfies, to any specified accuracy, both the governing equations and the boundary conditions. Numerical examples are given about the in-plane modes of rectangular plates with different edge supports. It appears that these modal data are presented for the first time in literature, and may be used as a benchmark to evaluate other solution methodologies. Some subtleties are discussed about corner support arrangements.

In this article, the performance of a two degree-of-freedom dynamic vibration absorber (DVA) with very large or very small moment of inertia is studied. Although it has been shown previously that an optimally tuned DVA with a negligibly small moment of inertia marginally outperforms the optimally tuned DVA with a very large moment of inertia, the physical reasons for this have not been made clear. Using a simplified model of the stiffness elements of the DVA, it is shown that the two sets of parallel combinations of stiffness and damping elements of the DVA with negligibly small moments of inertia effectively act in series, rather than in parallel as in the other case. Furthermore, it is shown that the stiffness and damping elements can be represented as a single stiffness and a single damping element whose properties are frequency dependent. This frequency dependency means that there is additional freedom in choosing the optimum stiffness and damping of the DVA, which results in better performance.

A method for measuring the impedance matrix and the dynamic properties of a liquid-filled flexible hose is described in this paper. Dynamic hose properties are presented for a wide range of hose types. Nylon-reinforced hoses are shown to have considerably lower bulk moduli and stiffnesses than steel-reinforced hoses. The dynamic bulk moduli and stiffnesses are shown to be significantly and consistently higher than the static values. These results may be used to give an estimate of representative properties for a hose, based on its maximum pressure rating and its type of reinforcement.

A numerical approach is presented for linear and geometrically nonlinear forced vibrations of laminated composite plates with piezoelectric materials. The displacement fields are defined generally by high degree polynomials and the convergence of the results is achieved by increasing the degrees of polynomials. The nonlinearity is retained with the in-plane strain components only and the transverse shear strains are kept linear. The electric potential is approximated layerwise along the thickness direction of the piezoelectric layers. In-plane electric fields at the top and bottom surfaces of each piezoelectric sublayer are defined by the same shape functions as those used for displacement fields. The equation of motion is obtained by the Hamilton’s principle and solved by the Newmark’s method along with the Newton–Raphson iterative technique. Numerical procedure presented herein is validated by successfully comparing the present results with the data published in the literature. Additional numerical examples are presented for forced vibration of piezoelectric sandwich simply supported plates with either a homogeneous material or laminated composite as core. Both linear and nonlinear responses are examined for mechanical load only, electrical load only, and the combined mechanical and electrical loads. Displacement time histories with uniformly distributed load on the plate surface, electric volts applied on the top and bottom surfaces of the piezoelectric plates, and mechanical and electrical loads applied together are presented in this paper. The nonlinearity due to large deformations is seen to produce stiffening effects, which reduces the amplitude of vibrations and increases the frequency. On the contrary, antisymmetric electric loading on the nonlinear response of piezoelectric sandwich plates shows increased amplitude of vibrations.