We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...

Linear multistep methods using higher derivatives are discussed. The order of damping at infinity which measures the stability behavior of a fc-step method for large h is introduced. ,4-stable methods with positive damping order are most suitable for stiff problems. A method for computing the damping order is given. Necessary and sufficient conditions for A -stability, A (a) -stability and stif...

This research quantitatively investigates fluid damping of MEMS and NEMS flexural resonators such as scanning probe and carbon nano-tube resonators, aiming to improve the quality factor prediction and therefore the resonator design. Fluid damping in beam-type resonators is most affected by resonant frequency, device dimensions and cross-sectional shape which are systematically examined within. ...

Résumé: Le but de ce projet est une investigation des techniques d’amortissement pour l’équation d’onde. Cette étude est intéressante tant du point de vue de la physique et que de l’analyse numérique. En effet l’amortissement apparâıt fréquemment dans les systèmes avec friction. Du point de vue mathématique, l’amortissement donne une meilleure régularité de l’équation élastique qui est importan...

The dynamical core of an atmospheric general circulation model is engineered to satisfy a delicate balance between numerical stability, computational cost, and an accurate representation of the equations of motion. It generally contains either explicitly added or inherent numerical diffusion mechanisms to control the buildup of energy or enstrophy at the smallest scales. The diffusion fosters c...

We consider squeeze film gas damping during microbeam motion away and toward a substrate as occurs during opening and closing of RF switches and other MEMS devices. The numerical solution of the gas damping problem in two-dimensional geometries is obtained based on the Boltzmann-ESBGK equation. The difference in damping force between downward and upward moving beams is shown to vary from as lit...

This paper studies the interaction between non-viscous damping and nonlinearities for nonlinear oscillators with reflection symmetry. The non-viscous damping function is an exponential damping model which adds a decaying memory property to the damping term of the oscillator. We consider the case of softening and hardening behaviour in the frequency response of the system. Numerical simulations ...

1. Abstract An efficient damping layout optimization method of structural-acoustic systems is proposed to minimize acoustic responses using a gradient-based optimization algorithm. To analyze vibro-acoustic systems, a hybrid model that uses finite elements for the structures and boundary element for the cavity is developed. The four-parameter fractional derivative model is used to represent the...

We present a model reduction Lanczos method for the computation of frequency response functions of Rayleigh damping problems. The connection with modal extraction and modal superposition is made. The usual model reduction methods require complex arithmetic. With the proposed method, complex arithmetic is only used for the reduced problem. A numerical example from structural damping is given.

Our primary energy consumption is supported in 81% by the combustion of fossil energy commodities (IEA, 2010). The demand on energy will grow by about 60% in the near future (Shell, 2008). The efficiency of the combustion processes is crucial for the environment and for the use of the remaining resources. At the Karlsruhe Institute of Technology the longterm project Collaborative Research Centr...