geometrically nonlinear governing equations for a plate with linear viscoelastic material are derived. the material model is of boltzmann superposi¬tion principle type. a third-order displacement field is used to model the shear deformation effects. for the solution of the nonlinear governing equations the dynamic relaxation (dr) iterative method together with the finite difference discretizati...

A prismatic beam made of a behaviorally nonlinear material is analyzed under aharmonic load moving with a known velocity. The vibration equation of motion is derived usingHamilton principle and Euler-Lagrange Equation. The amplitude of vibration, circular frequency,bending moment, stress and deflection of the beam can be calculated by the presented solution.Considering the response of the beam,...

Abstract: It is assumed that a beam made of material has a physical nonlinear behavior. This beam is analyzed under the moving concentrated and distributed continuous loads. The vibration equations of motion are derived from the Hamilton's Principle and Euler–Lagrange Equation. In this study, the amplitude of vibration, circular frequency, bending moment, stress and deflection of the beam has b...

  ABSTRACT: A prismatic beam made of a behaviorally nonlinear material situated on nonlinear elastic foundation is analyzed under a moving harmonic load moving with a known velocity. The vibration equation of motion    is derived using Hamilton principle and Euler Lagrange equation. The amplitude of vibration, circular frequency, bending moment, stress and deflection of the beam can be calculat...

Important: Review Appendix A of [3] and make sure you understand it. The text below hits a few important topics from that material and adds a few more relevant items. Some of it will be covered in class but it is up to you to fill in the rest. Many of the things discussed here will be referred to during the semester.

Manuscript received November 20, 2014. Of course, things can get complicated in nonlinear problems with large deformations (and rotations) because the final deformed area may be different from the initial area, among other things [1]. Stress is in fact a tensor [1]. It can be written in any of several forms as follows [1]. (Cauchy stress tensor shown in Fig. 2) In 3-D it can be written as, σ = ...

Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use instead phase-field-type theories where conventional linear elastic strain is quadratically coupled to an additional field that describes the evolution of the refe...

Batisite was reported to be a nonlinear optical material showing second harmonic generation. Using dielectric spectroscopy and polarization measurements, we provide a thorough investigation of the dielectric and charge-transport properties of this material. Batisite shows the typical characteristics of a linear lossy dielectric. No evidence for ferro- or antiferroelectric polarization is found....