Dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads

Piccardo, Giuseppe,Tubino, Federica Techno-Press 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.44 No.5

The dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads is analysed. The non-dimensional form of the motion equation of a beam crossed by a moving harmonic load is solved through a perturbation technique based on a two-scale temporal expansion, which permits a straightforward interpretation of the analytical solution. The dynamic response is expressed through a harmonic function slowly modulated in time, and the maximum dynamic response is identified with the maximum of the slow-varying amplitude. In case of ideal Euler-Bernoulli beams with elastic rotational springs at the support points, starting from analytical expressions for eigenfunctions, closed form solutions for the time-history of the dynamic response and for its maximum value are provided. Two dynamic factors are discussed: the Dynamic Amplification Factor, function of the non-dimensional speed parameter and of the structural damping ratio, and the Transition Deamplification Factor, function of the sole ratio between the two non-dimensional parameters. The influence of the involved parameters on the dynamic amplification is discussed within a general framework. The proposed procedure appears effective also in assessing the maximum response of real bridges characterized by numerically-estimated mode shapes, without requiring burdensome step-by-step dynamic analyses.

Dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads

Giuseppe Piccardo,Federica Tubino 국제구조공학회 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.44 No.5

The dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads is analysed. The non-dimensional form of the motion equation of a beam crossed by a moving harmonic load is solved through a perturbation technique based on a two-scale temporal expansion, which permits a straightforward interpretation of the analytical solution. The dynamic response is expressed through a harmonic function slowly modulated in time, and the maximum dynamic response is identified with the maximum of the slow-varying amplitude. In case of ideal Euler-Bernoulli beams with elastic rotational springs at the support points, starting from analytical expressions for eigenfunctions, closed form solutions for the time-history of the dynamic response and for its maximum value are provided. Two dynamic factors are discussed: the Dynamic Amplification Factor, function of the non-dimensional speed parameter and of the structural damping ratio, and the Transition Deamplification Factor, function of the sole ratio between the two non-dimensional parameters. The influence of the involved parameters on the dynamic amplification is discussed within a general framework. The proposed procedure appears effective also in assessing the maximum response of real bridges characterized by numerically-estimated mode shapes, without requiring burdensome step-by-step dynamic analyses.

Proper orthogonal decomposition in wind engineering - Part 1: A state-of-the-art and some prospects

Solari, Giovanni,Carassale, Luigi,Tubino, Federica Techno-Press 2007 Wind and Structures, An International Journal (WAS Vol.10 No.2

The Proper Orthogonal Decomposition (POD) is a statistical method particularly suitable and versatile for dealing with many problems concerning wind engineering and several other scientific and humanist fields. POD represents a random process as a linear combination of deterministic functions, the POD modes, modulated by uncorrelated random coefficients, the principal components. It owes its popularity to the property that only few terms of the series are usually needed to capture the most energetic coherent structures of the process, and a link often exists between each dominant mode and the main mechanisms of the phenomenon. For this reason, POD modes are normally used to identify low-dimensional subspaces appropriate for the construction of reduced models. This paper provides a state-of-the-art and some prospects on POD, with special regard to its framework and applications in wind engineering. A wide bibliography is also reported.

Proper orthogonal decomposition in wind engineering. Part 1: A state-of-the-art and some prospects

Giovanni Solari,Luigi Carassale,Federica Tubino 한국풍공학회 2007 Wind and Structures, An International Journal (WAS Vol.10 No.2

The Proper Orthogonal Decomposition (POD) is a statistical method particularly suitable and versatile for dealing with many problems concerning wind engineering and several other scientific and humanist fields. POD represents a random process as a linear combination of deterministic functions, the POD modes, modulated by uncorrelated random coefficients, the principal components. It owes its popularity to the property that only few terms of the series are usually needed to capture the most energetic coherent structures of the process, and a link often exists between each dominant mode and the main mechanisms of the phenomenon. For this reason, POD modes are normally used to identify low-dimensional subspaces appropriate for the construction of reduced models. This paper provides a state-of-the-art and some prospects on POD, with special regard to its framework and applications in wind engineering. A wide bibliography is also reported.

Proper orthogonal decomposition in wind engineering. Part 2: Theoretical aspects and some applications

Luigi Carassale,Giovanni Solari,Federica Tubino 한국풍공학회 2007 Wind and Structures, An International Journal (WAS Vol.10 No.2

Few mathematical methods attracted theoretical and applied researches, both in the scientific and humanist fields, as the Proper Orthogonal Decomposition (POD) made throughout the last century. However, most of these fields often developed POD in autonomous ways and with different names, discovering more and more times what other scholars already knew in different sectors. This situation originated a broad band of methods and applications, whose collation requires working out a comprehensive viewpoint on the representation problem for random quantities. Based on these premises, this paper provides and discusses the theoretical foundations of POD in a homogeneous framework, emphasising the link between its general position and formulation and its prevalent use in wind engineering. Referring to this framework, some applications recently developed at the University of Genoa are shown and revised. General remarks and some prospects are finally drawn.

Proper orthogonal decomposition in wind engineering - Part 2: Theoretical aspects and some applications

Carassale, Luigi,Solari, Giovanni,Tubino, Federica Techno-Press 2007 Wind and Structures, An International Journal (WAS Vol.10 No.2

Few mathematical methods attracted theoretical and applied researches, both in the scientific and humanist fields, as the Proper Orthogonal Decomposition (POD) made throughout the last century. However, most of these fields often developed POD in autonomous ways and with different names, discovering more and more times what other scholars already knew in different sectors. This situation originated a broad band of methods and applications, whose collation requires working out a comprehensive viewpoint on the representation problem for random quantities. Based on these premises, this paper provides and discusses the theoretical foundations of POD in a homogeneous framework, emphasising the link between its general position and formulation and its prevalent use in wind engineering. Referring to this framework, some applications recently developed at the University of Genoa are shown and revised. General remarks and some prospects are finally drawn.

Experimental investigation of the aeroelastic behavior of a complex prismatic element

Nguyen, Cung Huy,Freda, Andrea,Solari, Giovanni,Tubino, Federica Techno-Press 2015 Wind and Structures, An International Journal (WAS Vol.20 No.5

Lighting poles and antenna masts are typically high, slender and light structures. Moreover, they are often characterized by distributed eccentricities that make very complex their shape. Experience teaches that this structural type frequently suffers severe damage and even collapses due to wind actions. To understand and interpret the aerodynamic and aeroelastic behavior of lighting poles and antenna masts, this paper presents the results of static and aeroelastic wind tunnel tests carried out on a complex prismatic element representing a segment of the shaft of such structures. Static tests are aimed at determining the aerodynamic coefficients and the Strouhal number of the test element cross-section; the former are used to evaluate the critical conditions for galloping occurrence based on quasi-steady theory; the latter provides the critical conditions for vortex-induced vibrations. Aeroelastic tests are aimed at reproducing the real behavior of the test element and at verifying the validity and reliability of quasi-steady theory. The galloping hysteresis phenomenon is identified through aeroelastic experiments conducted on increasing and decreasing the mean wind velocity.

Experimental investigation of the aeroelastic behavior of a complex prismatic element

Cung Huy Nguyen,Andrea Freda,Giovanni Solari,Federica Tubino 한국풍공학회 2015 Wind and Structures, An International Journal (WAS Vol.20 No.5

Lighting poles and antenna masts are typically high, slender and light structures. Moreover, they are often characterized by distributed eccentricities that make very complex their shape. Experience teaches that this structural type frequently suffers severe damage and even collapses due to wind actions. To understand and interpret the aerodynamic and aeroelastic behavior of lighting poles and antenna masts, this paper presents the results of static and aeroelastic wind tunnel tests carried out on a complex prismatic element representing a segment of the shaft of such structures. Static tests are aimed at determining the aerodynamic coefficients and the Strouhal number of the test element cross-section; the former are used to evaluate the critical conditions for galloping occurrence based on quasi-steady theory; the latter provides the critical conditions for vortex-induced vibrations. Aeroelastic tests are aimed at reproducing the real behavior of the test element and at verifying the validity and reliability of quasi-steady theory. The galloping hysteresis phenomenon is identified through aeroelastic experiments conducted on increasing and decreasing the mean wind velocity.