This paper addresses the vibratory mechanics associated with frequency discrimination of basilar membrane within the cochlear of the inner ear. Periodic excitation is provided to the oval window, which results in generation of waves within the fluid-filled cochlear traveling towards the apex. These waves interact with the compliant basilar membrane structure causing its vibratory motion. Solution procedure of the fluid/structure model consists of a two-step process. First, a finite element calculation (ANSYS) solves for the membrane vibration with an initial harmonic pressure distribution. Second, a control volume analysis links the resultant vibratory motion with the fluid pressure acting on the basilar membrane, thus a pressure feedback loop is accomplished. Results show that dominant factors affecting vibratory characteristics of the basilar membrane are its structural geometry and attenuation of pressure wave as it travels away from the oval window. Calculations clearly capture the designed function of the basilar membrane, principally its frequency discrimination behavior.

Based upon our recent development of Stroh-like forma lism for symmetric/unsymmetric laminates, most of the relations for bending problems can be organized into the forms of Stroh formalism for two-dimensional problems. Through the use of Stroh-like formalism, the fundamental elasticity matrices Ni, S, H and L appear frequently in the real form solutions of plate bending problems. Therefore, the determination of these matrices becomes important in the analysis of plate bending problems. In this paper, by following the approach for two-dimensional problems, we obtain the explicit expressions of the fundamental elasticity matrices for symmetric and unsymmetric laminates, which are all expressed in terms of the extensional, bending and coupling stiffnesses of the composite laminates.

In this paper, we extended Blondeaux [1], Liu, et al. [2] and Mei and Yu's [3] theories to study the porous effect on instability of rippled bed under the partially standing surface waves. Comparisons are made with both Blondeaux and Mei & Yu's theoretical predictions and experimental data performed by many other authors. We found that based on the linear instability analysis and the parameter regimes we explored the percolation effect can change the threshold conditions by 10 ∼ 20 percent and the seepage force is negligible up to O(∈). Furthermore, the steady streamings with or without porous effect show the considerable difference in intensities at the same locations and it might change the sediment transport rate especially the suspended load.

Based on the frequency-shaping optimal control method, this paper proposes a time-domain robust disturbance rejection design approach for a class of uncertain flexible mechanical systems subject to persistent disturbances and time-varying parameter perturbations. In the approach, a frequency-shaping output filter is first employed to combine with the mechanical system and a Kalman filter to form an augmented system. Some eigenvalues of the frequency-shaping output filter coincide with the unstable poles of the disturbance dynamics to perform disturbance rejection. Then, for the designed closed-loop system to have asymptotic stability, a new robust stability condition is proposed. It is shown that, using the proposed stability condition, the resulting controller can suppress the persistent disturbance and keep the flexible mechanical system from the possibility of instability caused by spillover and time-varying parameter perturbations. Finally, two examples are given to demonstrate the use of the design approach.

An integrated optical method for measuring deformation of micro-mechanical systems with better than sub-micron resolutions is detailed. Both a confocal laser scanning microscope and a photon tunneling microscope were integrated into a single microscopy system due to their complimentary capabilities for examining sub-micrometer deformations. A halogen lamp and laser were adopted as the two light sources for the measurements. Since topographic information of samples up to a 15μm by 15μm area can be measured, a three-dimensional displacement field of the sample was extracted by comparing topographies of the same specimen area before and after deformation. The bending and twisting deformation of a micro-mirror driven by the electrostatic force was measured to demonstrate the capability of this newly developed instrument. The experimental data obtained agrees reasonably well with the theoretical results calculated by adopting an analytical solution and a finite element method. The small discrepancy in the result can be traced to the surface roughness effect, which is often non-negligible in micro-systems.

A new 3C duct design method is proposed for designing a high quality, energy-efficiency cost-effective air duct system. It not only considers the demand of volume flow rate, but also takes into consideration a number of issues including system pressure balance, noise, vibration, space limitation and total system cost. This new method comprises three major calculation procedures: initial computer-aided design (CAD), computer-aided simulation (CAS) and correction processes (CP). An example is presented in this study to understand the characteristics of 3C method. It shows that 3C duct design method provides a simple computation procedure for an optimum air duct system. It also shortens the design schedule, prevents human calculation errors, and reduces the dependence on designer experience. In addition to apply in a new duct system design, 3C duct design method is also a powerful design tool for the expansion of an existing duct system.

The thermally enhanced ball grid array (TEBGA) electronic packaging under thermal cycling and thermal loading was investigated numerically. Two-dimensional finite element analysis by ANSYS was used for calculating the temperature distribution and thermal stress on the symmetric and diagonal cross sections of TEBGA. The thermal failure based on the peel and shear stresses at interfaces of TEBGA took place at the interface between the heat sink and epoxy moulding compound. The Tasi-Hill failure criterion was modified to predict the failure at various interfaces in TEBGA package. The TEBGA geometric parameters, including the thickness of the heat sink, the thickness of the adhesive layer between the heat sink and the die, and the thickness of the reinforcing copper ring, were varied to assess their effects on the failure mode of TEBGA. The results showed that for a TEBGA under thermal cycling, the stress values were reduced for thicker adhesive layers and thinner heat sinks; for a TEBGA under thermal loading, the die-to-ambient thermal resistance of TEBGA decreased for thinner adhesive layers and thicker heat sinks. The slimmer heat sink of extruded plate type can dissipate more heat and can reduce the stress values. Proper choice of geometric parameters of TEBGA package can prevent its failure at interfaces and furthermore, improve the reliability of electronic packaging.

This paper develops an analytical model for the plastic collapse of a statically indeterminate rectangular beam containing a crack. Limit analysis, elastic-plastic fracture mechanics, compliance and J-integral concepts are used to study JIC and dJ/da that influence the crack propagation. The relations among the plastic hinge, applied load, linear displacement, rotational angle and crack growth leads to a better understanding of the problem as a consequence of this study. The conclusions are: (1) Unstable ductile fracture occurs at the crack propagates before plastic collapse or at dJ/da is smaller than the minimum critical value. (2) LBB (leak-before-break) characteristic of the statically indeterminate rectangular beam is valid if the crack propagates before plastic collapse.

In this paper, a modified numerical integration scheme is presented that improves the accuracy of the numerical integration of the Galerkin weak form, within the integration cells of the analyzed domain in the element-free methods. A geometrical interpretation of the Gaussian quadrature rule is introduced to map the effective weighting territory of each quadrature point in an integration cell. Then, the conventional quadrature rule is extended to cover the overlapping area between the weighting territory of each quadrature point and the physical domain. This modified numerical integration scheme can lessen the errors due to misalignment between the integration cell and the boundary or interface of the physical domain. Some numerical examples illustrate that this newly proposed integration scheme for element-free methods does effectively improve the accuracy when solving solid mechanics problems.

In this paper, based on a variational formalism which originally proposed by Mei [1] for infinite elastic medium and extended by Yeh, et al. [2,3] for elastic half-plane, a hybrid method which combines the finite element and series expansion method is implemented to solve the diffraction of plane waves by a cavity buried in an elastic half-plane. The finite domain which encloses all inhomogeneities including the cavity can be easily formulated by finite element methods. The unknown boundary data obtained by subtracting the known free fields from the total fields which include the boundary nodal displacements and tractions at the interface between the finite domain and the surrounding elastic half-plane are not independent of each other and can be correlated through a series representation. Due to the continuity condition at the interface, the same series representation is still valid for the exterior elastic half-plane to represents the scattered wave. The unknown coefficients of this series are treated as generalized coordinates and can be easily formulated by the same variational principle. The expansion function of the series is composed of basis function. Each basis function is constructed from the basis function for an infinite plane by superimposing an additional homogeneous reflective term to satisfy both traction free conditions at ground surface and radiation conditions at infinity. The numerical results are made against those obtained by boundary element methods, and good agreements are found.

A modified error indicator and an extended locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh are developed to study the supersonic flow over a backward-facing step. In the Cartesian coordinate system, the unsteady Euler equations are solved. The modified error indicator, in which the unified magnitude of density gradient and unified magnitude of gradient of vorticity magnitude are incorporated, is utilized to treat the new node spacing of mesh remeshing. To assess the accuracy of the extended locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh, two flow calculations which include the oblique-shock reflection at a wall and transonic flow around an NACA 0012 airfoil are performed. Based on the comparison with the related numerical and experimental data, the accuracy of the present approach is confirmed. According to the high-resolutional result on the adaptive mesh, the structure of backstep corner vortex, expansion wave and oblique shock wave is distinctly captured.

This paper investigates the compressive strength and workability of High-Performance Concrete (HPC) which yields a slump at 250 ± 20mm and a slump flow at 650 ± 50mm. From the complete stress-strain curve, it shows the peak strain will be higher while the strength increases. Two kinds of the post failure models can be distinguished. The first type (Type I) is called strain softening and the second type (Type II) is called strain snapping back. Also, it is found that the modulus of elasticity Ec decreases as the volume of cementitious paste Vp increases. On the other hand, Poisson's ratio ν increases as Vp increases.

This paper reports the development of a point-focused PVDF transducer with a large aperture surface and its application on measuring Lamb wave dispersion curves. The point-focused transducer is constructed by forcing a piezoelectric PVDF film into a concave spherical shape. The acoustic waves radiated from the PVDF film are then focused into a point without using any acoustic lens. Similar to its line-focused counterpart, the point-focused transducer is capable of measuring dispersion curves of lamb waves provided its aperture angle is large enough. To verify this, experimental testing is carried out on several thin metal plates and good measurement results are observed. Future improvements and applications on the transducer will be addressed.

This paper deals with non-linear behavior of an elastically restrained shallow spherical shell with imperfections and subjected to uniform normal load by the asymptotic iteration method. An asymptotic relation between the external load and central transverse displacement (deflection) of the structure incorporating the effects of the characteristic geometrical parameter, imperfection factor and edge-restraint coefficients is formulated. The corresponding solutions resulting from the use of the second and third iteration processes are compared with each other and available data. The numerical calculations show that the second iteration is adequate for the non-linear analysis of the structure. The effects of geometrical imperfections and boundary constraint coefficients on buckling of the structures are presented graphically.

The turbulence time and length scales representing the energy containing eddies are by Tt = CtT k/ε and ℓt = Ctℓ k32/ε, respectively, while the Kolmogorov time and length scales representing the energy dissipative eddies are expressed by Tk = CkT (ν/ε)1/2 and ℓk = Ckℓ (ν3/ε)1/4, respectively. The available DNS data for fully developed channel flows with and without wall injection / suction are used to determine the coefficients. It is found that, with the typical values of CtT = Ctℓ = 1 which are usually adopted in the turbulence study, ckT = 2 and Ckℓ = 3. However, this set of coefficients lead to underprediction of the thickness of viscous sublayer . By relaxing the usual assumption of CtT = Ctℓ= 1, a new set of coefficients: CtT = Ctℓ = 0.8, CkT = 4, and Ckℓ = 9 is suggested. The calculated with this set of coefficients becomes more physically reasonable.

In this paper, the FEM with the incremental endochronic cyclic plasticity (EndoFEM) and the rc controlled node-released strategy are employed to study the fatigue crack opened/closed load (Pop) of Al 2024-T3 CCT specimens provided by Mageed and Pandey under several crack lengths and the constant amplitude with various load ratio (R). After statisfactory results are achieved by comparisons of computed Pop values and cited experimental data, the simulations will be extended to the crack lengths with significant bending effect due to short ligaments or high peak (Pmax) or high positive or very low negative R cyclic loads. Through these simulations, the complete map of Pop/Pmax vs. Kmax and R can be constructed and thereafter its correspondant empirical formulae can be proposed. Using these formulae and selecting the traditional fatigue crack growth parameter ΔKeff, the Al 2024-T3 fatigue crack growth rate da/dN vs. ΔK and R data, provided by Hiroshi and Schijve, can be employed to proposed empirical formulae of da/dN vs. ΔKeff and R. After integration, fatigue-crack-growth length a vs. N curves computed by EndoFEM can be obtained. The results are agreed very well with the existing experimental curves.

According to the above procedures of simulation and steps of comparions with experiment, this paper may provides an integrate methodology of numerical simulation in the studies of fatigue crack growth for academic and industrial researches and design analysis.

This study elucidated the complicated phenomena of wave refraction and diffraction around a circular island due to random incident waves traveling with a current. Various combinations of random incident wave and current conditions were used to investigate the wave height distributions around a circular island numerically and experimentally. Numerical calculations were carried out based on the theory derived by Lin & Hsu [1]. According to the results, it shows that numerical calculations can predict experimental data quantitatively well.

Multilayer piezoelectric stack actuators are widely used in many industrial applications and the investigation on the dynamic behavior of this element is needed. In this study, two optical interferometric techniques called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV) are used to experimentally investigate the vibration characteristics of a single-layer piezoelectric disc and a multilayer piezoelectric stack actuator. These two techniques are full-field measurement for AF-ESPI and point-wise displacement measurement for LDV. Because the clear fringe patterns obtained by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and corresponding vibration mode shapes of the piezoelectric disc and the multilayer piezoelectric stack actuator are obtained simultaneously by the AF-ESPI method. Interferometric fringe patterns for both the in-plane and out-of-plane vibration mode shapes are demonstrated. In addition to the proposed two optical techniques, numerical computations based on a commercially available finite element package are presented for comparison with the experimental results. Good agreement between the measured data by experimental methods and the numerical results predicted by FEM is found in resonant frequencies and mode shapes for the single-layer piezoelectric disc. However, some discrepancies are observed for the results obtained by AF-ESPI and impedance analysis for the multilayer piezoelectric stack actuator. A detailed discussion is made to address important issues of this problem.

In this paper, the crack problem of a large beam-like strip weakened by a circular arc crack with in-plane bending moments applied at both ends is approximately solved using the complex variable technique. Complex stress functions corresponding to the applied bending moments are superposed with those due to the disturbance of the crack to satisfy the governing boundary equation. The conformal mapping function devised to transform the contour surface of a circular arc crack to a unit circle is then substituted in the boundary equation to facilitate the evaluation of Cauchy integrals. In this way, the complex stress functions due to the crack disturbance are determined and the stress intensity factors are calculated through a limiting process to give their explicit forms. Eventually, the geometric functions for the variation of the stress intensity factors on account of the crack shape are plotted as a function of the curvature of a circular-arc crack.

A general solution to the magnetoelastic problem with a rigid line inclusion is presented. Based upon the complex variable theory, the proposed analysis dealing with sectionally holomorphic functions can be reduced to find the solution of the Hilbert problem. It is indicated that the magnetoelastic stress fields near the inclusion tip possess a square root singularity just like that of the corresponding crack problem. The stress singularity coefficients which are defined in this study to characterize the near tip fields are similar to the stress intensity factors for crack problem. Numerical results of the stress distribution in the vicinity of inclusion tip are also displayed in graphic form to elucidate the effect of various parameters.