Simulation of non-selfadjoint control of thin elastic plates in the presence of conservative in-plane forces

Based on the analysis presented in [1], a closed-form solution for the response of a controlled plate to a transversely applied dynamic loading is presented. Both the applied loading and the control are considered to be continuously distributed. The results and the corresponding parametric study are presented for two common boundary conditions of SSSS and SFSF in the plates

Analysis of non-selfadjoint control of thin elastic plates in the presence of conservative in-plane forces

This work deals with the theoretical developments required for the analysis of non-selfadjoint control of linearly elastic homogeneous thin plates in the presence of conventional in-plane loads. To represent the actual physical problem, the system is modelled as a distributed bi-parameter system with distributed rather than lumped masses. Using the Green function approach, the controlled response of the system is obtained as an integral solution with an unsymmetric kernel that is derived from an 'auxiliary' system rather than the 'fundamental' eigenvalue-generating-system. The theoretical treatment of the problem is discussed in this manuscript, while the corresponding simulations and parametric study will be presented in a forthcoming paper

Vibration of rods with a concentrated mass in the presence of non-conservative forces

Separable and non-selfadjoint boundary-value problems representing the vibration of linearly elastic unidimensional systems are considered. The elastic system is modelled as a continuous distributed-parameter system where singularities in the mass distribution function can be neatly taken into account. Specifically, extending Green's function approach, the free vibration, stability and forced vibration of fixed-free rods with a tip mass and under the action of uniformly distributed non-conservative loads have been investigated analytically

Long-time dynamic response of linearly elastic non-self-adjoint and non-separable systems: A green function approach

The solution of non-self-adjoint and non-separable initial-boundary-value problems is treated by using a Green function approach. Specifically, the analysis of the long-time response of a finite, isotropic, homogeneous, linearly elastic cantilever plate, in a state of plane strain to an antisymmetric and dynamically applied distributed surface load, has been shown to constitute such a non-self-adjoint and non-separable problem. The Green function of the problem is determined, based on the method given by J. Miklowitz for solving non-separable waveguide problems, by using a double Laplace transform and an entirety condition on the solution. The Green functions for two near-field and far-field domains are obtained. Hence, the response of the plate to any antisymmetric dynamically applied distributed surface load is determined in the form of an integral equation for the two domains, with the respective Green functions as the kernels of integration. It is concluded that the "elementary" theories and the "engineering methods" in which a "dynamic load factor" is applied to the static solution tend to underestimate the maximum values of the plate deflections in the vicinity of the free end of the cantilever plate

Random response and energy dissipation of a hysteretic structure subjected to white noise excitation

A non-Gaussian closure approach is applied to random response of a hysteretic structure subjected to Gaussian white noise excitation. The non-stationary response mean squares and stationary power spectral densities of the displacement, velocity and hysteretic component of the restoring force are predicted. In addition, due to their importance in characterizing hysteretic structures, the mean value and root-mean-square (RMS) of energy dissipation rate which are the second and fourth-order response statistics, respectively, are also computed. It is shown that the mean value of the stationary energy dissipation rate depends only on the amplitude of external excitation. Various structural parameters which determine different elastoplastic behaviours of the response are considered in the study. The convergence of the method is demonstrated by increasing the number of high-order moments in the analysis. Favourable comparisons with numerical simulation and other techniques are observed. This approach has the advantage of numerically generating equations of high-order moments which are used in estimating non-Gaussian responses. The non-Gaussian random response of complex nonlinear behaviour of structures such as hysteresis can be estimated satisfactorily

Actuation of slender thin-wall anisotropic open cross-section beams based on asymptotically-correct Vlasov theory

An asymptotically-correct analysis of passive anisotropic thin-wall open cross-section beam-like structures using the Variational Asymptotic Method (VAM) is extended to include embedded Active Fibre Composites (AFCs). Application of the VAM splits the problem into nonlinear one-dimensional (1D) theory along the selected beam reference line and linear 2D generalized 5×5 Vlasov theory augmented by a 5×1 actuation vector over the cross-section. The linear 2D cross-sectional theory is verified against the University of Michigan/Variational Beam Sectional Analysis (UM/VABS) software and applied to examples of the aforementioned structures with practical cross-sectional geometry and material anisotropy under DC actuating voltage. The theory is shown to be easily implemented and efficient, yet reliable enough to perform interdisciplinary studies and analysis of various engineering applications of such structures