M. Mahinfalah

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.

Photoelastic determination of mixed mode stress intensity factors for sharp reentrant corners

Abstract This paper uses photoelasticity and digital image analysis to develope an algorithm for determining stress intensity factors (SIFs) in 90° reentrant corners. To utilize the advantage of “whole-field” photoelasticity and to minimize the random experimental errors, the overdeterministic least squares method of Sanford combined with Newton-Raphson method is used to obtain SIFs. The algorithm is used to determine SIFs in plates with 90° reentrant corner(s) and the obtained SIFs agree well with the available numerical and theoretical values.

The effects of hail damage on the fatigue strength of a graphite/epoxy composite laminate

Abstract An investigation was undertaken to determine the effects of hail damage on the fatigue strength of a graphite/epoxy composite laminate. Skteen-ply coupons were subjected to simulated hail impact by iceballs of 25.4 or 38.1 mm in diameter. Upon impact, the 25.4 mm diameter iceball possessed 7.1 J of kinetic energy, while the 38.1 mm diameter iceball possessed a kinetic energy of 27.4 J. For further comparison, additional coupons were impacted with a 12.7 mm diameter aluminum sphere with either 7.1 or 27.4 J of kinetic energy. Inspection revealed that neither iceball impact event caused any internal damage, while each aluminum sphere impact caused delaminations within each coupon. After being impacted and inspected, each coupon was subjected to constant amplitude tension-tension fatigue. It was determined that neither the 25.4 mm diameter iceball impact nor the 38.1 mm diameter iceball impact affected the fatigue performance of this particular laminate. The 7.1 J aluminum sphere impact also did not affect this laminate, while the 27.4 J aluminum impact did adversely affect the fatigue performance of this material.

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.

MATHEMATICAL MODELING OF THERMAL EFFECTS IN STEADY STATE DYNAMICS OF MICRORESONATORS USING LORENTZIAN FUNCTION: PART 2 - TEMPERATURE RELAXATION

Thermal phenomena have two distinct effects, which are called, in this report, “thermal damping” and “temperature relaxation”. In this second part of a two-part report we (only) model and investigate the temperature relaxation and its effects on microresonator dynamics. A reduced order mathematical model of the system is introduced as a mass-spring-damper system actuated by a linearized electrostatic force. Temperature relaxation is the thermal stiffness softening and is modeled as a decrease in stiffness rate, utilizing a Lorentzian function of excitation frequency. The steady state frequency-amplitude dependency of the system will be derived utilizing averaging perturbation method. Analytic equation describing the frequency response of the system near resonance which can be utilized to explain the dynamics of the system, as well as design of involved dynamic parameters is developed.Copyright

Mathematical Modeling of Thermal Effects in Steady State Dynamics of Microresonators Using Lorentzian Function: Part 1 — 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.Copyright

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.Copyright

Frequency Response of Vibration Isolators With Saturating Spring Elements

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.Copyright

Periodic Behavior of a Nonlinear Third Order Vibrating System

In modeling of dynamical systems, differential equations, either ordinary or partial, are a common outcome of the modeling process. The basic problem becomes the existence of solution of these deferential equations. In the early days of the solution of deferential equations at the beginning of the eighteenth century the methods for determining the existence of nontrivial solution were so limited and developed very much on an ad hoc basis. Most of the efforts on dynamical system are related to the second order systems, derived by applying Newton equation of motion to dynamical systems. But, behavior of some dynamical systems is governed by equations falling down in the general nonlinear third order differential equation x″′+f(t,x,x′,x″)=0, sometimes as a result of combination of a first and a second order system. It is shown in this paper that these equations could have nontrivial solutions, if x, x′, x″, and f(t,x,x′,x″) are bounded. Furthermore, it is shown that the third order differential equation has a τ-periodic solution if f(t,x,x′,x″) is an even function with respect to x′. For this purpose, the concept of Green’s function and the Schauder’s fixed-point theorem has been used.Copyright

Time Response Dynamics of Linear Model of Microcantilever-MEMS

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.Copyright