Angelo Luongo

Bio: Angelo Luongo is an academic researcher from University of L'Aquila. The author has contributed to research in topics: Nonlinear system & Equations of motion. The author has an hindex of 40, co-authored 169 publications receiving 3949 citations. Previous affiliations of Angelo Luongo include Sapienza University of Rome.

Planar non-linear free vibrations of an elastic cable

Abstract: Continuum non-linear equations of free motion of a heavy elastic cable about a deformed initial configuration are developed. Referring to an assumed mode technique one ordinary equation for the cable planar motion is obtained via a Galerkin procedure, an approximate solution of which is pursued through a perturbation method. Suitable nondimensional results are presented for the vibrations in the first symmetric mode with different values of the cable properties. Which procedure is the proper one to account consistently for the non-linear kinematical relations of the cable in one ordinary equation of motion is discussed.

Stability, Bifurcation and Postcritical Behaviour of Elastic Structures

Abstract: 1. The Liapunov Theory of Equilibrium Stability (M. Pignataro). Differential equations. Simple types of equilibrium points. Equilibrium points of non-linear systems. Stability of equilibrium according to Liapunov. Theorems on the stability of equilibrium. Analysis of the stability of equilibrium by linear approximation. Criterion of negative real parts of all the roots of a polynomial. 2. The Stability of Equilibrium and Post-Buckling Behaviour of Discrete Mechanical Systems (M. Pignataro). Lagrange and Hamilton equations of motion. Stability of equilibrium according to Liapunov. Lagrange-Dirichlet theorem. Theorems of Liapunov and Chetayev. Analysis of the stability of linear systems. Criterion of stability of discrete systems. A system of one degree of freedom with: Stable symmetrical post-critical behaviour Unstable symmetrical post-critical behaviour Asymmetrical post-critical behaviour Non-linear pre-critical behaviour. A system of two degrees of freedom. 3. Analysis of Bifurcation for Discrete Systems. Characterisation of the Points of an Equilibrium Path from Examination of Local Properties (N. Rizzi). Local analysis of the properties of points belonging to an equilibrium path. Perturbation method in the asymptotic determination of regular equilibrium paths through a point Q. Search for critical points along a known equilibrium path and local analysis of the bifurcated path in the vicinity of the bifurcation point. Analysis of bifurcation for a system of two degrees of freedom. Outlines of the analysis of bifurcation starting from an approximate equilibrium path. 4. Stability of Equilibrium and Post-Critical Behaviour of Continuous Systems (M. Pignataro). Theorems of stability and instability. Critical condition of equilibrium. Criterion of stability of continuous systems. Construction of equilibrium paths by means of perturbation analysis. 5. Analysis of Beams and Plane Frames (N. Rizzi, M. Pignataro). Beam models. Critical load and post-critical behaviour of beams loaded axially at one end. Particular problems. Simply supported beam axially loaded at mid-span. Stability of beams. Symmetric, simply supported, two bar frame. Hinged symmetrical portal frame. Application of the method of finite elements to problems of bifurcation in plane frames. 6. Thin-Walled Beams with Open Cross-Section (A. Luongo). Hypotheses on the mechanical behaviour of thin-walled beams. Kinematics of the beam. Formulation of the linearised problem of stability. Thin-walled beams subjected to: Uniform compression Eccentric axial loads Under pure bending. Flexural-torsional stability of beams subjected to lateral loads. Methods of discretisation. Outline of the post-critical behaviour of thin-walled beams. 7. Analysis of Plates and Shells (A. Luongo, M. Pignataro). Some basic results of the theory of surfaces and shells. Kinematics of shells. Elastic strain energy. Stability of plates. Critical load of: Rectangular plates Stiffened plates.

A comprehensive review on vibration energy harvesting: Modelling and realization

Abstract: This paper presents a state-of-the-art review on a hot topic in the literature, i.e., vibration based energy harvesting techniques, including theory, modelling methods and the realizations of the piezoelectric, electromagnetic and electrostatic approaches. To minimize the requirement of external power source and maintenance for electric devices such as wireless sensor networks, the energy harvesting technique based on vibrations has been a dynamic field of studying interest over past years. One important limitation of existing energy harvesting techniques is that the power output performance is seriously subject to the resonant frequencies of ambient vibrations, which are often random and broadband. To solve this problem, researchers have concentrated on developing efficient energy harvesters by adopting new materials and optimising the harvesting devices. Particularly, among these approaches, different types of energy harvesters have been designed with consideration of nonlinear characteristics so that the frequency bandwidth for effective energy harvesting of energy harvesters can be broadened. This paper reviews three main and important vibration-to-electricity conversion mechanisms, their design theory or methods and potential applications in the literature. As one of important factors to estimate the power output performance, the energy conversion efficiency of different conversion mechanisms is also summarised. Finally, the challenging issues based on the existing methods and future requirement of energy harvesting are discussed.

Linear Differential Operators. By C. Lanczos. Pp. 580. 80s. 1961. (Van Nostrand, London)

Abstract: Preface Bibliography 1. Interpolation. Introduction The Taylor expansion The finite Taylor series with the remainder term Interpolation by polynomials The remainder of Lagrangian interpolation formula Equidistant interpolation Local and global interpolation Interpolation by central differences Interpolation around the midpoint of the range The Laguerre polynomials Binomial expansions The decisive integral transform Binomial expansions of the hypergeometric type Recurrence relations The Laplace transform The Stirling expansion Operations with the Stirling functions An integral transform of the Fourier type Recurrence relations associated with the Stirling series Interpolation of the Fourier transform The general integral transform associated with the Stirling series Interpolation of the Bessel functions 2. Harmonic Analysis. Introduction The Fourier series for differentiable functions The remainder of the finite Fourier expansion Functions of higher differentiability An alternative method of estimation The Gibbs oscillations of the finite Fourier series The method of the Green's function Non-differentiable functions Dirac's delta function Smoothing of the Gibbs oscillations by Fejer's method The remainder of the arithmetic mean method Differentiation of the Fourier series The method of the sigma factors Local smoothing by integration Smoothing of the Gibbs oscillations by the sigma method Expansion of the delta function The triangular pulse Extension of the class of expandable functions Asymptotic relations for the sigma factors The method of trigonometric interpolation Error bounds for the trigonometric interpolation method Relation between equidistant trigonometric and polynomial interpolations The Fourier series in the curve fitting 3. Matrix Calculus. Introduction Rectangular matrices The basic rules of matrix calculus Principal axis transformation of a symmetric matrix Decomposition of a symmetric matrix Self-adjoint systems Arbitrary n x m systems Solvability of the general n x m system The fundamental decomposition theorem The natural inverse of a matrix General analysis of linear systems Error analysis of linear systems Classification of linear systems Solution of incomplete systems Over-determined systems The method of orthogonalisation The use of over-determined systems The method of successive orthogonalisation The bilinear identity Minimum property of the smallest eigenvalue 4. The Function Space. Introduction The viewpoint of pure and applied mathematics The language of geometry Metrical spaces of infinitely many dimensions The function as a vector The differential operator as a matrix The length of a vector The scalar product of two vectors The closeness of the algebraic approximation The adjoint operator The bilinear identity The extended Green's identity The adjoint boundary conditions Incomplete systems Over-determined systems Compatibility under inhomogeneous boundary conditions Green's identity in the realm of partial differential operators The fundamental field operations of vector analysis Solution of incomplete systems 5. The Green's Function. Introduction The role of the adjoint equation The role of Green's identity The delta function -- The existence of the Green's function Inhomogeneous boundary conditions The Green's vector Self-adjoint systems The calculus of variations The canonical equations of Hamilton The Hamiltonisation of partial operators The reciprocity theorem Self-adjoint problems Symmetry of the Green's function Reciprocity of the Green's vector The superposition principle of linear operators The Green's function in the realm of ordinary differential operators The change of boundary conditions The remainder of the Taylor series The remainder of the Lagrangian interpolation formula