Most composites exhibit a damping figure of merit, a crucial index of a material's dynamic behavior, lower than the value predicted by the Hashin–Shtrikman bound. This work found that the biomimetic hierarchical staggered composites inspired by bone structure can have a damping figure of merit tens of times higher than the Hashin–Shtrikman composite. The optimum state is achieved when the hard and soft phases contribute equally to the overall stiffness of the composite in the direction parallel to the platelets. At this optimal point, the model predicts that the overall stiffness is half the Voigt bound while the damping loss factor is half that of the soft phase. This behavior stems from a deformation mechanism transition from soft-phase-dominant to hard-phase-dominant as the platelet's aspect ratio increases. The findings from this study may have important implications in the future design of composites to mitigate vibration and absorb shock in load-bearing structures.

It is proposed to investigate in this paper the damped vibrations of an incompressible liquid contained in a deformable tank. A linearized formulation describing the small movements of the system is presented. At first, a diagonal damping is introduced in the reduced equations of the hydroelastic sloshing problem. We obtain a nonclassically damped coupled system with a damping matrix that is not symmetric. Then, by projecting the system onto its complex modes, the frequency and time responses for different type of loads are built. A numerical application is illustrated on a test case.

An investigation into the passive vibration reduction of the nonlinear spring pendulum system, simulating the ship roll motion is presented. This leads to a four-degree-of-freedom (4-DOF) system subjected to multiparametric excitation forces. The two absorbers in the longitudinal and transverse directions are usually designed to control the vibration near the simultaneous subharmonic and internal resonance where system damage is probable. The theoretical results are obtained by applying the multiple scale perturbation technique (MSPT). The stability of the obtained nonlinear solution is studied and solved numerically. The obtained results from the frequency response curves confirmed the numerical results which were obtained using time history. For validity, the numerical solution is compared with the analytical solution. Effectiveness of the absorbers ( E a ) are about 13 000 for the first mode ( x ) and 10 000 for the second mode ( ϕ ). A threshold value of linear damping coefficient can be used directly for vibration suppression of both vibration modes. Comparison with the available published work is reported.

The frequency response of a flat plate in a viscous fluid is a problem with applications in microsystems, including gyroscopes, accelerometers, viscometers, and biological sensing. To find the frequency response away from the resonant frequency, the equations of motion are combined with the solution to Stokes’ second problem to produce an analytic solution for the motion of the plate in response to a sinusoidal driving force. These results are used to determine the gain, phase lag, and dynamic stability of the system. The behavior of the system depends on an effective damping ratio ζ eff , which depends on the resonator dimensions, and is proportional to the square root of the viscosity times the fluid density.

This paper describes a technique for determining the dynamic aerodynamic yaw moment derivative based on the time response data using an oscillating model rig. The aerodynamic yaw moment derivatives are initially estimated using oscillation frequency and amplitude decay. The results from the dynamic measurement are compared with conventional static test and presented in the form of aerodynamic magnification. The yaw moment derivative exceeds that determined statically across reduced frequency range measured. The yaw damping derivative was found to be a function of freestream speed; at low velocities it is negative but progressively increases to a positive value. With further increases in speed, a self-sustained oscillation is observed with almost constant frequency and amplitude. This result is attributed to coupling between the model wake and the model stability; however, the exact behavior of the interaction is not fully understood; this phenomenon is under further investigation.

A one dimensional analytical model is developed for the steady state, axisymmetric flow of damp powder within a rotating impervious cone. The powder spins with the cone but migrates up the wall of the cone (along a generator) under centrifugal force. The powder is treated as incompressible and Newtonian viscous, while the shear traction at the interface is taken to be both velocity and pressure dependent. A nonlinear second order ordinary differential equation is established for the mean through-thickness velocity as a function of radius in a spherical coordinate system, and the dominant nondimensional groups are identified. For a wide range of geometries, material parameters, and operating conditions, a midzone exists wherein the flow is insensitive to the choice of inlet and outlet boundary conditions. Within this central zone, the governing differential equation reduces to an algebraic equation with an explicit analytical solution. Furthermore, the bulk viscosity of the damp powder does not enter this solution. Consequently, it is suggested that the rotating impervious cone is a useful geometry to measure the interfacial friction law for the flow of a damp powder past an impervious wall.

A stochastic averaging method for predicting the response of multi-degree-of-freedom quasi-nonintegrable-Hamiltonian systems (nonintegrable-Hamiltonian systems with lightly linear and (or) nonlinear dampings subject to weakly external and (or) parametric excitations of Poisson white noises) is proposed. A one-dimensional averaged generalized Fokker–Planck–Kolmogorov equation for the transition probability density of the Hamiltonian is derived and the probability density of the stationary response of the system is obtained by using the perturbation method. Two examples, two linearly and nonlinearly coupled van der Pol oscillators and two-degree-of-freedom vibro-impact system, are given to illustrate the application and validity of the proposed method.

The half power method is a technique commonly used for calculating the system damping using frequency response curves. Past derivations typically assume a small damping ratio but do not keep track of the order of magnitude when simplifying results and focus mainly on displacement frequency response curves. This paper provides two separate and rigorous derivations of the half power bandwidth for displacement and acceleration frequency response functions. The exact expressions are simplified systematically using binomial expansions to include third order effects. The third order and classical approximations are compared with the exact expressions, and the truncation errors are presented for both displacement and acceleration cases. The high order effects are more apparent and the truncation errors are greater for the acceleration case. The classical method is sufficiently accurate for many practical cases where the damping ratio is less than 0.1 but higher order corrections may be used to reduce truncation error for systems where the damping ratio is higher.

This paper discusses a theoretical approach to investigate the dependency relationship between the stiffness matrix and the complex eigenvectors in the identification of structural systems for the case of insufficient instrumentation setup. The main result of the study consists of proving, in the case of classical damping, the independency of the stiffness subpartition corresponding to the measured degrees-of-freedom from the unmeasured ones. The same result is shown to be valid in the case of nonclassical damping but only for tridiagonal sparse stiffness matrix systems. A numerical procedure proves the above results and also shows the dependency relationship for the general nonclassical damping cases.

This paper proposes a new approach for the reduction in the model-order of linear multiple-degree-of-freedom viscoelastic systems via equivalent second-order systems. The assumed viscoelastic forces depend on the past history of motion via convolution integrals over kernel functions. Current methods to solve this type of problem normally use the state-space approach involving additional internal variables. Such approaches often increase the order of the eigenvalue problem to be solved and can become computationally expensive for large systems. Here, an approximate reduced second-order approach is proposed for this type of problems. The proposed approximation utilizes the idea of generalized proportional damping and expressions of approximate eigenvalues of the system. A closed-form expression of the equivalent second-order system has been derived. The new expression is obtained by elementary operations involving the mass, stiffness, and the kernel function matrix only. This enables one to approximately calculate the dynamical response of complex viscoelastic systems using the standard tools for conventional second-order systems. Representative numerical examples are given to verify the accuracy of the derived expressions.

Several magnetic force models were developed to interpret various phenomena of a soft ferromagnetic beam plate subjected to a uniform external magnetic field with different incident angles. In this paper, a new transverse magnetic force model for the interface between a ferromagnetic material and the air is derived with the continuation of magnetoelastic stress across the material boundary. It is noted that both the normal and the tangential components of magnetic field on the material boundary are considered in this model. By applying such a transverse magnetic force and the effect of magnetic viscous damping, a new theoretical model is constructed in this study to predict the natural frequency of a soft ferromagnetic beam plate placed in an in-plane magnetic field. The numerical results of the present study are displayed graphically and compared with the experimental data, which appeared in literature to assure the exactness of the present work.

This paper deals with the flexural instability of flexible spinning cylinders partially filled with viscous fluid. Using the linearized Navier–Stokes equations for the incompressible flow, a two-dimensional model is developed for fluid motion. The resultant force exerted on the flexible cylinder wall as the result of the fluid motion is calculated as a function of lateral acceleration of the cylinder axis in the Laplace domain. Applying the Hamilton principle, the governing equations of flexural motion of the rotary flexible cylinder mounted on general viscoelastic supports are derived. Then combining the equations describing the fluid force on the flexible cylinder with the structural dynamics equations, the coupled-field governing equations of the system are obtained. A numerical technique is devised with the obtained model for stability analysis of the flexible cylinder and some examples are presented. The effect of material viscoelasticity and structural damping on the stability margins of the flexible cylinder is examined, and some parameter studies on the governing parameters of the critical spinning speed are carried out.

Ceramic materials applied by air plasma spray are used as components of thermal barrier coatings. As it has been found that such coatings also dissipate significant amounts of energy during vibration, they can also contribute to reducing the amplitude of resonant vibrations. In order to select a coating material for this purpose, or to adjust application parameters for increased dissipation, it is important that the specific mechanism, by which such dissipation occurs, be known and understood. It has been suggested that the dissipative mechanism in air plasma sprayed coatings is friction, along interfaces arising from defects between and within the “splats” created during application. An analysis, similar to that for the dissipation in a lap joint, is developed for an idealized microstructure characteristic of such coatings. A measure of damping (loss modulus) is extracted, and the amplitude dependence is found to be similar to that observed with actual coating materials. A critical combination of parameters is identified, and variations within the microstructure are accounted for by representing values through a distribution. The effective or average value of the storage (Young’s) modulus is also developed, and expressed in terms of the parameters of the microstructure. The model appears to provide a satisfactory analytical representation of the damping and stiffness of these materials.

Elastoplastic deformation occurs widely in engineering impact. Although many empirical solutions of elastoplastic impact between two spheres have been obtained, the analytical solution, verified by means of other methods, to the impact model has not been put forward. This paper proposes a dynamic pattern of elastoplastic impact for two spheres with low relative velocity, in which three stages are introduced and elastic and plastic regions are both considered. Finite element analyses with various parameters are carried out to validate the above model. The numerical results prove to agree with the theoretical predictions very well. Based on this model, the dissipation nature of elastoplastic impact are then analyzed, and the conclusion can be drawn that materials with lower yield strength, higher elastic modulus, and higher mass density have better attenuation and dissipation effects. The study provides a basis to predict the particle impact damping containing plastic deformation and to model the impact damped vibration system enrolling microparticles as a damping agent.

Micro-electro-mechanical systems (MEMS) often use beam or plate shaped conductors that are very thin with h / L ≈ O ( 10 − 2 – 10 − 3 ) (in terms of the thickness h and length L of a beam or side of a square plate). A companion paper ( Ghosh and Mukherjee, 2009, “Fully Lagrangian Modeling of Dynamics of MEMS With Thin Beams—Part I: Undamped Vibrations,” ASME J. Appl. Mech., 76, p. 051007 ) addresses the coupled electromechanical problem of MEMS devices composed of thin beams. A new boundary element method (BEM) is coupled with the finite element method (FEM) by Ghosh and Mukherjee, and undamped vibrations are addressed there. The effect of damping due to the surrounding fluid modeled as Stokes flow is included in the present paper. Here, the elastic field modeled by the FEM is coupled with the applied electric field and the fluid field, both modeled by the BEM. As for the electric field, the BEM is adapted to efficiently handle narrow gaps between thin beams for the Stokes flow problem. The coupling of the various fields is carried out using a Newton scheme based on a Lagrangian description of the various domains. Numerical results are presented for damped vibrations of MEMS beams.

The dynamic stability of a two degrees-of-freedom system under bounded noise excitation with a narrowband characteristic is studied through the determination of moment Lyapunov exponents. The partial differential eigenvalue problem governing the moment Lyapunov exponent is established. For weak noise excitations, a singular perturbation method is employed to obtain second-order expansions of the moment Lyapunov exponents and Lyapunov exponents, which are shown to be in good agreement with those obtained using Monte Carlo simulation. The different cases when the system is in subharmonic resonance, combination additive resonance, and combined resonance in the absence of noise, respectively, are considered. The effects of noise and frequency detuning on the parametric resonance are investigated.

In this paper, a methodology is presented for the identification of the complete mass, damping, and stiffness matrices of a dynamical system using a limited number of time histories of the input excitation and of the response output. Usually, in this type of inverse problems, the common assumption is that the excitation and the response are recorded at a sufficiently large number of locations so that the full-order mass, damping, and stiffness matrices can be estimated. However, in most applications, an incomplete set of recorded time histories is available and this impairs the possibility of a complete identification of a second-order model. In this proposed approach, all the complex eigenvectors are correctly identified at the instrumented locations (either at a sensor or at an actuator location). The remaining eigenvector components are instead obtained through a nonlinear least-squares optimization process that minimizes the output error between the measured and predicted responses at the instrumented locations. The effectiveness of this approach is shown through numerical examples and issues related to its robustness to noise polluted measurements and to uniqueness of the solution are addressed.

This paper studies the influence of road camber on the stability of single-track road vehicles. Road camber changes the magnitude and direction of the tire force and moment vectors relative to the wheels, as well as the combined-force limit one might obtain from the road tires. Camber-induced changes in the tire force and moment systems have knock-on consequences for the vehicle’s stability. The study makes use of computer simulations that exploit a high-fidelity motorcycle model whose parameter set is based on a Suzuki GSX-R1000 sports machine. In order to study camber-induced stability trends for a range of machine speeds and roll angles, we study the machine dynamics as the vehicle travels over the surface of a right circular cone. Conical road surfaces allow the machine to operate at a constant steady-state speed, a constant roll angle, and a constant road camber angle. The local road-tire contact behavior is analyzed by approximating the cone surface by moving tangent planes located under the road wheels. There is novelty in the way in which adaptive controllers are used to center the vehicle’s trajectory on a cone, which has its apex at the origin of the inertial reference frame. The results show that at low speed both the weave- and wobble-mode stabilities are at a maximum when the machine is perpendicular to the road surface. This trend is reversed at high speed, since the weave- and wobble-mode dampings are minimized by running conditions in which the wheels are orthogonal to the road. As a result, positive camber, which is often introduced by road builders to aid drainage and enhance the friction limit of four-wheeled vehicle tires, might be detrimental to the stability of two-wheeled machines.

Rayleigh quotients in the context of linear, nonconservative vibrating systems with viscous and nonviscous dissipative forces are studied in this paper. Of particular interest is the stationarity property of Rayleigh-like quotients for dissipative systems. Stationarity properties are examined based on the perturbation theory. It is shown that Rayleigh quotients with stationary properties exist for systems with proportional viscous and nonviscous damping forces. It is also shown that the stationarity property of Rayleigh quotients in the case of nonproportional damping (viscous and nonviscous) is conditional upon the diagonal dominance of the modal damping matrix.

In general, it is not possible to obtain total motion absorption of a certain degree of freedom in a harmonically excited damped system by passive control. This paper presents a method of obtaining total absorption in viscously damped system by active control, including time delay, which is unavoidable in digital controlled system. The control is applied on one degree of freedom and the absorption is achieved at another point. This study is carried out by both complex and real analyses. The necessary and sufficient condition for obtaining total absorption is given. Examples demonstrate the various results.