G. Nakhaie Jazar

Root mean square optimization criterion for vibration behaviour of linear quarter car using analytical methods

In this paper, a linear two-degree-of-freedom quarter car model is used to derive a number of analytical formulae describing the dynamic behaviour of passively suspended vehicles running on a harmonically bumped road. The linearity of the system allows us to analytically investigate the steady-state response characteristics. We derive analytical expressions for the root mean square (RMS) of the sprung mass absolute acceleration and relative displacement. This paper demonstrates the shortcomings of existing classical optimization methods. Hence we introduce a new optimization method based on minimizing the absolute acceleration RMS with respect to the relative displacement RMS. The RMS optimization method is applied for the symbolic derivation of analytical formulae featuring the best compromise among conflicting performance indices pertaining to the vehicle suspension system, i.e., sprung mass acceleration and working space. The proposed optimization technique is utilized to find the optimal damping and stiffness curves for the main suspension. The RMS optimal values are used to create design charts for suspension parameters, which are very useful particularly in the presence of physical constraints such as a limit on relative displacement. We introduce a numerical example to illustrate the optimality of the obtained solutions.

Practical Frequency and Time Optimal Design of Passive Linear Vibration Isolation Mounts

Summary In this paper we examine a linear one-degree of freedom vibration isolator mount. The linearity of the system allows us to analyze its frequency and time response characteristics analytically. Optimal damping and stiffness values for the isolator are obtained by minimizing certain cost functions, which are the Root Mean Square (RMS) of the absolute acceleration and the relative displacement. These RMS cost functions are used to create a design chart for the isolator parameters. This is very useful particularly in the presence of physical constraints such as a limit in relative displacement. The time response of the system for a unit step input is also considered to gain an insight into the transient characteristics of the system. We obtain an optimal value for the damping ratio of the system in order to minimize the transmitted acceleration. Combining the frequency and time response analyses leads to an optimal value for the mount natural frequency and damping ratio satisfying both time and frequency domains. The results are verified numerically using measured acceleration as input.

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.

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.

Nonlinear Modeling and Simulation of Thermal Effects in Microcantilever Resonators Dynamic

Thermal dependency of material characteristics in micro electromechanical systems strongly affects their performance, design, and control. Hence, it is essential to understand and model that in MEMS devices to optimize their designs. A thermal phenomenon introduces two main effects: damping due to internal friction, and softening due to Young modulus temperature relation. Based on some reported theoretical and experimental results, we model the thermal phenomena and use two Lorentzian functions to describe the restoring and damping forces caused by thermal phenomena. In order to emphasize the thermal effects, a nonlinear model of the MEMS, by considering capacitor nonlinearity, have been used. The response of the system is developed by employing multiple time scales perturbation method on nondimensionalized form of equations. Frequency response, resonant frequency and peak amplitude are examined for variation of dynamic parameters involved.

Nonlinear Dynamics of MicroResonators

The variation of effective parameters in Micro Electro Mechanical Systems strongly affects their performance, design, and control. Hence, it is essential to understand and model the effective parameters in MEMS devices to optimize their designs. Typical MEMS (Microresonator) employ a parallel-plate capacitor, in which one plate is actuated electrically and its motion is detected by capacitive changes. In this paper we investigate nonlinear modelling of microresonators. The nonlinearities from capacitor (quadratic) and midplane stretch were considered for this purpose. The achieved microbeams equations are nondimensionalized and by using the multiple scales method received to the equations which identified the relations between system dynamics and effective parameters of system. In other part of this paper we expand the Fuzzy Generalized Cell Mapping (FGCM) for multiparameter systems then apply FGCM to the microresonator and see how the uncertainties can affect the working domain of dynamical systems. It can be seen FGCM is so useful method for detecting the working region with variation of parameters.

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

Stability Analysis of a piecewise nonlinear vibration isolator

Many vibration isolators can be modeled with a discontinuity in the stiffness and damping coefficients. The sudden change in the values of the coefficients can be represented as a piecewise linear or nonlinear function. Soft suspensions are best for isolation; however, a nonlinear hardening suspension is required to minimize relative displacement at high amplitudes. Often, the physical design limits the relative displacement. Taking advantage of nonlinearity in the suspension is not enough in limiting the relative displacement at very high amplitude. Therefore, a secondary suspension must be involved to limit very high relative displacements. In this investigation, the averaging method was applied to the differential equation generated from the model to find the frequency response. A sensitivity analysis was performed to find regions of instability in the frequency responseCopyright

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

Jump Avoidance Conditions for Piecewise Linear Vibration Isolator

Piecewise linear systems being highly non-linear, standard perturbation methods cannot produce an analytical expression for the frequency response. Hence, an adapted averaging method is employed to obtain an implicit function for frequency response of a bilinear system under steady state. This function is examined for jump-avoidance and a condition is derived which when met ensures that the undesirable phenomenon of ‘Jump’ does not occur and the system response is functional and unique.Copyright