Journal of Aerospace Engineering

The dynamic flexibility (DF) and improved dynamic flexibility (IDF) methods can be applied to extract constrained structural modes from free-free modal test data. The residual flexibility method is also good for boundaries of constrained structure with rigid supports. Under elastic support boundary conditions both the DF and residual flexibility methods cannot produce accurate results. This paper expands the previously published IDF method to become a more general approach for structural design engineers. A new method called the general dynamic flexibility (GDF) method has been developed in this paper to extract constrained structural modes from free test data. The GDF method can always be applied as follows: (1) when the boundary support stiffness is very stiff, the GDF method can accurately obtain results from rigid support as by Liu et al. in 2001 and Zhang and Wei in 2003; (2) when the support stiffness is soft, the present method can produce results similar to those free-free modal parameters measured by hanging structures using rubber band; (3) when the support stiffness is zero, the method can reproduce true free-free modal parameters; and (4) when the support stiffness has any finite values, the GDF method can also achieve satisfactory results for engineering use. The algorithm included in the GDF method converges rapidly and is numerically stable in the analysis. This feature is very practical for many engineering applications for using the GDF method.

In this paper, a $\mu$ controller is designed for a satellite formation flying system around the Earth based on an uncertainty model derived from a nonlinear relative position equation. In this model, nonzero eccentricity and varying semimajor axis are included as parametric uncertainties. $J_2$ perturbation, atmospheric drag, and actuation and sensor noise are bounded by functional uncertainties. The $\mu$ controller design based on the nominal mission (an $800\mathrm{km}$ altitude circular reference orbit) is capable of achieving desired performance, is robust to uncertainties, and satisfies fuel consumption requirements even in a challenge nonnominal mission (a 0.1 eccentricity and $\mathrm{7,978}\mathrm{km}$ semimajor axis elliptic reference orbit) with the same control gain. In this nonnominal mission, the designed $\mu$ controller is able to keep formation with almost the same level of the $\mathrm{\Delta }V$ budget $(43.86\mathrm{m}∕\mathrm{s}∕\mathrm{year})$ as used in the nominal mission $(39.65\mathrm{m}∕\mathrm{s}∕\mathrm{year})$ . For comparison, linear quadratic regulator (LQR) and sliding mode controllers (SMC) are developed and extensively tuned to get the same $\mathrm{\Delta }V$ consumption as that of the designed $\mu$ controller for the nominal mission. However, as shown in the simulation, the designed linear robust controller (LQR) and nonlinear robust controller (SMC) have a serious $\mathrm{\Delta }V$ consumption penalty ( $1.72\mathrm{km}∕\mathrm{s}∕\mathrm{year}$ for SMC) or are unstable (for LQR) in the nonnominal mission.

Existing notions of stress in a quantum mechanical framework are reviewed and discussed in a semitutorial manner suitable for a mechanics audience. Notwithstanding early fundamental work in this area since the 1930s, the increasing availability of computational tools to perform ab initio quantum mechanical calculations with high accuracy and efficacy has renewed interest in this field especially in the context of computational mechanics and materials science. Although some unresolved issues remain, the subject has evolved considerably in the past two decades with various authors offering their own unique viewpoint. In the present paper, we summarize the debate over the “definition” of stress in a quantum mechanical setting and discuss some controversial issues such as the uniqueness of the stress.

Thin films bonded to compliant substrates often develop wrinkles when subjected to an applied or inherent compressive stress. This paper presents a bilayer model to account for surface effects on the wrinkling of ultrathin solid films. Assuming a surface layer of finite thickness, effects of surface properties on the critical strain, the equilibrium wavelength, and the wrinkle amplitude are discussed in comparison with conventional analysis. We apply this model to explain experimental observations of wrinkling in thin polymer films. The measured wrinkle wavelengths and amplitudes deviate from conventional analysis for ultrathin films with thickness less than $30\mathrm{nm}$ . The bilayer model provides a consistent understanding of the observed deviations, based on which a set of material properties for the surface and the bulk of the polymer films are deduced from the experimental data.

In this paper, the nonlinear static and free vibration analyses of doubly curved cross-ply laminated panels subjected to thermomechanical loading are examined. The shell theory adopted in the present case is an extension of Reissner’s shallow shell simplifications that accounts for parabolic distribution of the transverse shear strains through thickness of the shell and tangential stress-free boundary conditions. A multiterm Galerkin’s method is adopted to solve the governing nonlinear partial differential equations. The static equilibrium paths are traced using the Newton-Raphson method in conjunction with the Riks approach to overcome the limit points. The free vibration frequencies about a static equilibrium state of a deformed panel are reported by solving the linear eigenvalue problem. Analytical results are presented for symmetric [0/90/0] and antisymmetric [0/90] cross-ply laminated doubly curved panels that illustrate the influence of geometric properties, in-plane edge boundary conditions, lateral distributed load and temperature field on the nonlinear behavior and natural frequencies.

Piezoceramic transducers (PZTs) are extensively used in vibration and noise control, and damage detection of various engineering structures. In the last decade, its application has been extended to include their interactions with the host structure in electromechanical impedance models. The interaction between the host structure and PZT is governed by both the extensional and longitudinal vibrations of the transducer. However, the interaction models developed in the last decade consider only the one-dimension or two-dimension extensional actuations, ignoring the longitudinal actuations. This study examines the three-dimensional (3D) interaction of a transducer with the host structure, considering both the extensional and the longitudinal actuations of the transducer. It does not impose any restriction on the shape, size, and electrical properties of the PZT and thus contains additional features over the existing PZT-structure interaction models. This paper is Part I of a two-part paper, which presents a new “directional sum” numerical–analytical admittance formulation with experimental verification. Part II of this paper will elaborate on the damage analysis and characterization of PZT properties for the new 3D model.

Piezoceramic transducers (PZTs) are extensively used in the nondestructive evaluation of damages in various engineering structures. This paper, the second of a two-part paper, focuses on the application of a PZT using three-dimensional (3D) directional sum impedance (DSI). The semianalytical 3D admittance has been formulated and experimentally validated in the first paper. This part deals with the application of the 3D DSI model in damage analysis where by damages were numerically simulated for various types of specimens and the DSI admittance signatures were predicted and compared. The deviations of the signature from that of the undamaged state provide an indicator for the health of the structure. This technique is nondestructive in nature, and the damages were quantified using root-mean-square deviation in signatures with respect to the undamaged state signature. In Part I, the properties of the PZT and their influences on admittance signatures were briefly presented. In this part, a thorough investigation was made and the importance of all the PZT properties in damage analysis was presented.

The purpose of this work is to study the nonlinear vibrations induced due to wheel contact. The contact force is nonlinear and is considered to be caused due to a nonpolynomial $3∕2$ type of spring (Hertzian) as is commonly assumed to model wheel contact. Approximate periodic free vibration solutions are derived using an analytical technique based on the averaging method and is compared numerically. The case of the nonlinear wheel with nonlinear damping (van der Pol) is also studied and the possibility of the existence of a limit cycle is explored. The existence of initial condition dependent free periodic vibrations or a limit cycle under certain circumstances may be important for passenger comfort and noise generation or for vehicle safety as it may cause wear and tear of the mechanical components of the vehicle.