Nonstationary Transient Vibroacoustic Response of a Beam Structure

This study consists of an investigation into the nonstationary transient response of the Verification Test Article (VETA) when subjected to random acoustic excitation. The goal is to assess excitation models that can be used in the design of structures and equipment when knowledge of the structure and the excitation is limited. The VETA is an instrumented cantilever beam that was exposed to acoustic loading during five Space Shuttle launches. The VETA analytical structural model response is estimated using the direct averaged power spectral density and the normalized pressure spectra methods. The estimated responses are compared to the measured response of the VETA. These comparisons are discussed with a focus on prediction conservatism and current design practice

Custom-designed orthopedic implants evaluated using finite element analysis of patient-specific computed tomography data: femoral-component case study

<p>Abstract</p> <p>Background</p> <p>Conventional knee and hip implant systems have been in use for many years with good success. However, the custom design of implant components based on patient-specific anatomy has been attempted to overcome existing shortcomings of current designs. The longevity of cementless implant components is highly dependent on the initial fit between the bone surface and the implant. The bone-implant interface design has historically been limited by the surgical tools and cutting guides available; and the cost of fabricating custom-designed implant components has been prohibitive.</p> <p>Methods</p> <p>This paper describes an approach where the custom design is based on a Computed Tomography scan of the patient's joint. The proposed design will customize both the articulating surface and the bone-implant interface to address the most common problems found with conventional knee-implant components. Finite Element Analysis is used to evaluate and compare the proposed design of a custom femoral component with a conventional design.</p> <p>Results</p> <p>The proposed design shows a more even stress distribution on the bone-implant interface surface, which will reduce the uneven bone remodeling that can lead to premature loosening.</p> <p>Conclusion</p> <p>The proposed custom femoral component design has the following advantages compared with a conventional femoral component. (i) Since the articulating surface closely mimics the shape of the distal femur, there is no need for resurfacing of the patella or gait change. (ii) Owing to the resulting stress distribution, bone remodeling is even and the risk of premature loosening might be reduced. (iii) Because the bone-implant interface can accommodate anatomical abnormalities at the distal femur, the need for surgical interventions and fitting of filler components is reduced. (iv) Given that the bone-implant interface is customized, about 40% less bone must be removed. The primary disadvantages are the time and cost required for the design and the possible need for a surgical robot to perform the bone resection. Some of these disadvantages may be eliminated by the use of rapid prototyping technologies, especially the use of Electron Beam Melting technology for quick and economical fabrication of custom implant components.</p

Modal Interaction In The Response Of Laminates

A higher-order shear-deformation theory is used to analyze the interaction of two modes in the response of thick laminated rectangular plates to transverse harmonic loads. The case of a two-to-one autoparametric resonance is considered. Four first-order ordinary differential equations describing the modulation of the amplitudes and phases of the internally resonant modes are derived using the averaged Lagrangian when the higher mode is excited by a primary resonance. It is shown that besides the single-mode solution, two-mode solutions exist for a certain range of parameters. It is further shown that, in the multi-mode case, the lower mode, which is indirectly excited through the internal resonance may dominate the response

Analysis Of The Nonlinearity Associated With The Free Vibration Of An Orthotropic Shell

The symbolic manipulator Mathematica is used to analyze the nonlinearity associated with the free vibration of a simply-supported orthotropic shell. This expands upon earlier analyses conducted by Rivieccio and Nayfeh (1995) on the nonlinear free vibration of an orthotropic shell. The nonlinear equation of motion is derived using the time-averaged Lagrangian analysis technique. The effects of various initial amplitudes on the nonlinear natural frequencies are evaluated. The effects of the different shell geometries on the nonlinearity are investigated. The nonlinearity is found to decrease with increasing radius of curvature, opening angle, and length

Nonlinear Vibration Of Composite Shell Subjected To Resonant Excitations

Analysis of the vibration of a shallow, simply supported, nonsymmetric unbalanced cross-ply laminated, circular cylindrical composite shell is presented. The subject is particularly relevant, considering the widespread use of cylindrical shell structures in engineering applications. This research applies the discretized Lagrangian/method of multiple scales solution technique. The Donnell shallow shell strain-displacement relations and the single-mode displacement field from the linear eigenvalue problem are applied. The system Lagrangian is developed and integrated over the spatial domain and then substituted into Lagrange\u27s equation. The resulting equation of motion is a second-order temporally nonlinear ordinary differential equation in the form of the Duffing oscillator. The natural frequency, the coefficient of the cubic nonlinearity, and the strength of the nonlinearity are investigated. The method of multiple scales is applied to the nonlinear equation of motion in order to analyze the frequency response. Primary resonance, subharmonic resonance, and superharmonic resonance are analyzed

Thermally Induced Displacement In Simply-Supported Laminates

Thermally-induced transverse displacement of unidirectional ply, cross-ply and anti-symmetric angle-ply composite plate is investigated. The laminates are assumed to be simply supported along the four edges. The dynamic flexural response due to sudden surface heating is examined, with emphasis on the effects of plate thickness and stacking sequence on the maximum plate deflection of a graphite-epoxy composite. The total displacement is obtained by superposition of the first mode quasi-static and dynamic solutions. The quasi-static displacement is derived using a Levy-type solution while the dynamic displacement is formulated by utilizing the Classical Lamination Theory (CLT), Galerkin\u27s Method and the Laplace Transform. The results show that thermally-induced displacements in unidirectional and cross-ply laminates for the same thickness are far less than those in angle-ply laminates. © World Scientific Publishing Company

Analysis of the free vibration of an orthotropic shell

The symbolic manipulator Mathematica is used to analyze the nonlinearity associated with the free vibration of a simply-supported orthotropic shell. This expands upon earlier analyses conducted by Rivieccio and Nayfeh (1995) on the nonlinear free vibration of an orthotropic shell. The nonlinear equation of motion is derived using the time-averaged Lagrangian analysis technique. The effects of various initial amplitudes on the nonlinear natural frequencies are evaluated. The effects of the different shell geometries on the nonlinearity are investigated. The nonlinearity is found to decrease with increasing radius of curvature, opening angle, and length

Analysis Of The Nonlinearity Associated With The Free Vibration Of An Orthotropic Shell

The symbolic manipulator Mathematica is used to analyze the nonlinearity associated with the free vibration of a simply-supported orthotropic shell. This expands upon earlier analyses conducted by Rivieccio and Nayfeh on the nonlinear free vibration of an orthotropic shell. The nonlinear equation of motion is derived using the time-averaged Lagrangian analysis technique. The effects of various initial amplitudes on the nonlinear natural frequencies are evaluated. The effects of the different shell geometries on the nonlinearity are investigated. The nonlinearity is found to decrease with increasing radius of curvature, opening angle, and length. © 1996 American Society of Civil Engineers

Nonlinear Dynamics Of Polar-Orthotropic Circular Plates

The dynamics of nonlinear polar orthotropic circular plates with simply supported boundary condition are investigated. Kirchhoff strain displacement relations for thin plates plus next higher-order nonlinear terms (von Karman type geometric nonlinearity) are considered. Lagrangian density function and Hamilton\u27s principle are utilized to derive Lagrange\u27s equations, from which the equations of motion and associated boundary conditions are derived. Analytical solution is obtained by the perturbation techniques and numerical solution by the Runge-Kutta method. Phase diagrams, discrete Fast Fourier Transform (FFT diagrams) and time history responses are presented for studying the forced vibration behavior. The sub-harmonic and primary resonances are studied as well as the effect of adding damping foil layers. The quadratic term in the governing equation plays a softening role on the overall behavior of the plate due to its relatively large coefficient. The increase of damping tends to smooth out the unstable region (i.e. jump phenomenon) in the system. © World Scientific Publishing Company