Linear static analysis and finite element modeling for laminated composite plates using third order shear deformation theory

In this paper, deformations of a laminated composite plate due to mechanical loads are presented. Third order shear deformation theory of plates, which is categorized in equivalent single layer theories, is used to derive linear dynamic equations of a rectangular multi-layered composite plate. Moreover, derivation of equations for FEM and numerical solutions for displacements and stress distributions of different points of the plate with a sinusoidal distributed mechanical load for Navier type boundary conditions are presented

On the solarity waves in arteries

Solitary waves are coincided with separatrices, which surround an equilibrium point with characteristics like a center, a sink, or a source. The existence of closed orbits in phase plane predicts the existence of such an equilibrium point. If there exists another saddle point near that equilibrium point, separatrix orbit appears. In order to prove the existence of solution for any kind of boundary value problem, we need to apply the fixed-point theorems. The Schauder's fixed-point theorem was used to show that there exists at least one nontrivial solution for equation of wave motion in arteries. The equation of wave motion in arteries has a nonlinear character, and the amplitude of the wave depends on the wave velocity. There is no general analytical or straightforward method for prediction of the amplitude of solitary waves. Therefore, the solution must be found by numerical or nonstraightforward methods. The methods of saddle point trajectory, escapetime, and escape-energy are introduced and shown that they are applicable methods with enough accuracy. Application of any of these approximate methods depends on the equation of motion, and the user preference. Applying a phase plane analysis, it was shown that the domain of periodic solution is surrounded by a separatrix. The separatrix is coincident with the desired solitary wave. The amplitude of the solitary wave is the most important characteristic of the wave, and will be predicted with each of the above methods

Distribution of sub and super harmonic solution of Mathieu equation within stable zone

The third stable region of the Mathieu stability chart, surrounded by one p-transition and one 27p-transition curve is investigated. It is known that the solution of Mathieu equation is either periodic or quasi-periodic when its parameters are within stable regions. Periodic responses occur when they are on a "splitting curve". Splitting curves are within stable regions and are corresponding to coexisting of periodic curves where an instability tongue closes. Distributions of sub and super-harmonics, as well as quasi-periodic solutions are analyzed using power spectral density method

Low velocity impact of sandwich composite plates

In this paper we investigate impact and compression after impact properties of plain weave carbon fiber sandwich composites. Impact tests were conducted on different sample types to obtain information about absorbed energy and maximum impact force. The different samples consisted of foam-filled and hollow honeycomb cores with four-layer carbon fiber facesheets on one or both sides. The impact and compression after impact data provided valuable information to allow for comparisons between the different sample types. Also, the compression after impact tests were conducted in order to determine the reduction in compressive strength when comparing impacted to non-impacted samples. In conclusion, a two-degrees-of-freedom spring/mass model was compared to experimental results. The comparison helped illustrate the limitations of current impact theory

Comparison of exact and approximate frequency response of a piecewise linear vibration isolator

In this paper an investigation is carried out to classify the steady state responses of asymmetric piecewise linear vibration isolators as double hitting, single hitting, and no hitting. In each class, the analysis has been carried out using a set of coupled nonlinear algebraic equations following Natsiavas and Gonzalez [1]. Applying perturbation technique, a closed form analytic expression of the frequency response is also derived for symmetric conditions. The exact frequency response is utilized to validate the analytic results obtained by perturbation techniques. Direct comparison indicates the results obtained by averaging method are mathematically and practically close to the exact solution

Time response dynamics of linear model of microcantilever

This paper presents analytic derivation of dynamic behavior of a liniearized micro-electro-mechanical resonator. The parametric oscillation results from a displacement-dependent electrostatic force generated by oscillation of a microbeam. The utilized device is a MEMS with a time-varying capacitor. The stability and steady state dynamic behavior of the MEMS has been analyzed without polarization voltage. The main characteristic of the no-polarization model is effects of parameters in stability of the system. A set of stability charts is provided for prediction of the boundary between the stable and unstable domains for the principal resonance. Applying perturbation method, analytical equations are derived to describe both the steady state and time response of the system

Frequency response of vibration isolators with saturation spring element

An investigation using averaging method is carried out to obtain the frequency response of a class of vibration isolators with saturation spring. The saturation characteristics are modeled using a hyperbolic-tangent function. The hyperbolic-tangent saturation function is compared with other popular saturation functions, using piecewise nonlinear approximation. A parameteric study indicates that piecewise linear approximation of saturating functions provide results that are close enough to the results of hyperbolic tangent approximation. A sensitivity analysis of frequency response of the system is also investigated based on the piecewise linear approximation

An investigation on the effect of high velocity impact on the kevlar/carbon sandwich composite plates

Not availabl

Mathematical modeling of thermal effects in steady state dynamics of microresonators using Lorentzian function: part I thermal damping

Mathematical modeling of thermal effects on steady state dynamics of microresonators, utilizing an analytical approach is studied. Thermal phenomena has two distinct effects, which in this report are called, thermal damping and temperature relaxation. In this part of a two-part report we investigate the thermal damping and its effects on microresonator dynamics. To do this, first the reduced order mathematical model of the system is introduced as a forced mass-spring-damper system, and then a linearized model of electric actuated microbeam resonator is employed. The effect of thermal damping is modeled as an increase in damping rate, utilizing a Lorentzian function of excitation frequency. The steady state frequency-amplitude dependency of the system will be derived utilizing averaging perturbation method. The developed analytic equation describing the frequency response of the system around resonance can be utilized to explain the dynamics of the system, as well as design of dynamic parameters. However, we have focused on exploration of thermal damping