Το θέμα της διδακτορικής διατριβής αφορά στην ανάπτυξη προτύπων μηχανικής και πεπερασμένων στοιχείων για τον υπολογισμό της δυναμικής απόσβεσης σε πολύστρωτες κατασκευές από σύνθετα υλικά, εύκαμπτες στρώσεις και πιεζοηλεκτρικά στοιχεία. Ο όρος «εύκαμπτες» προσδιορίζει υλικά με χαμηλό μέτρο ελαστικότητας σε σχέση με τα μεταλλικά και τα σύνθετα υλικά, όπως ιξωδοελαστικά προσθέματα και αφρώδη υλικά. Αναπτύσσεται κώδικας πεπερασμένων στοιχείων για την πρόβλεψη δυναμικής απόσβεσης και γίνονται συγκρίσεις με μετρήσεις της. Η δυναμική απόσβεση μελετάται σε: 1. Λεπτές δοκούς, πλάκες, ανοιχτά και κλειστά λεπτότοιχα κελύφη (Κεφ. 3). 2. Λεπτές δοκούς και πλάκες με πιεζοηλεκτρικά στοιχεία συνδεδεμένα με ηλεκτρικές αντιστάσεις (Κεφ. 4). 3. Δοκούς μεγάλου πάχους με εύκαμπτες στρώσεις (Κεφ. 5). 4. Δοκούς μεγάλου πάχους με εύκαμπτες στρώσεις και πιεζοηλεκτρικά στοιχεία (Κεφ. 6). 5. Πλάκες μεγάλου πάχους (Κεφ. 7). Τα πεπερασμένα στοιχεία που αναπτύσσονται έχουν επιπλέον τών μητρώων μάζας και δυσκαμψίας, μητρώο απόσβεσης, το οποίο περιέχει πληροφορία από τα επίπεδα του σύνθετου υλικού και της πολύστρωτης δομής, ενώ οι συντελεστές απόσβεσης στρώσης σύνθετου υλικού προσδιορίζονται μέσω πειραμάτων μορφικής ανάλυσης. Tα πεπερασμένα στοιχεία που αναπτύσσονται στα Κεφάλαια 5, 6 και 7 βασίζονται σε πρωτότυπες ανώτερης τάξης θεωρίες διακριτών στρώσεων και μπορούν να προβλέψουν με ακρίβεια τη στατική και δυναμική απόκριση σύνθετων πολύστρωτων κατασκευών μεγάλου πάχους και έντονης δομικής ανομοιογένειας, ιδιαίτερα τις κατά το πάχος κατανομές των εκτός επιπέδου παραμορφώσεων και τάσεων, με ελάχιστο αριθμό διακριτών στρώσεων και κομβικών βαθμών ελευθερίας. Επιπλέον, προβλέπουν εκτός επιπέδου διατμητικές τάσεις στη διεπιφάνεια μεταξύ διακριτών στρώσεων. Μελετάται η επίδραση δομικών παραμέτρων στη δυναμική απόσβεση της κατασκευής. Οι βασικότερες παράμετροι που εξετάζονται είναι η γωνία στρώσης, η διαδοχή της δομής, το πάχος της κατασκευής, η καμπυλότητα σε κελύφη και το πάχος του δομικού αφρού σε δοκούς τύπου sandwich. Μελετάται επίσης η αλληλεπίδραση των δύο μηχανισμών απόσβεσης που συνυπάρχουν σε σύνθετες κατασκευές με πιεζοηλεκτρικά στοιχεία συνδεδεμένα με ηλεκτρικές αντιστάσεις. Η παρεμβολή εύκαμπτων στρώσεων στη δομή αυξάνει τη μορφική απόσβεση χωρίς να επηρεάζει ιδιαίτερα τις φυσικές συχνότητες, ενώ τα πιεζοηλεκτρικά στοιχεία μπορούν να την αυξήσουν περαιτέρω, είτε με παθητικό τρόπο, συνδεόμενα με ηλεκτρικές αντιστάσεις, είτε με ενεργητικό τρόπο, ενισχύοντας την εκτός επιπέδου διάτμηση. / Integrated mechanics and a finite element method are developed for predicting the viscoelastic damped free-vibration response of laminated composite structures with interlaminar compliant layers and piezoelectric components. The theoretical framework is incorporated into a finite element computer code, which predicts the damping of a range of composite structures, such as: 1. Thin beams, plates, doubly curved open and closed shallow shells (Chapter 3). 2. Thin multi-damped beams and plates with shunted piezoelectric layers (Chapter 4). 3. Thick composite beams with interlaminar damping layers and thick sandwich beams (Chapter 5). 4. Thick composite and sandwich beams with piezoelectric layers (Chapter 6). 5. Thick composite plates (Chapter 7). The models developed include damping from ply to structural level and are experimentally validated. The finite elements have a damping matrix, in addition to stiffness and mass matrices, hence the damped dynamic structural response can be predicted by determining the composite ply damping coefficients by means of modal testing experiments. In Chapters 5, 6 and 7, a novel high-order layerwise theory developed enables effective modeling of interlaminar shear effects on the damping of thick piezoelectric composite structures strongly anisotropic through-thickness. The high-order finite element method yields robust predictions of the local through-thickness response, including electric potential and shear stresses that appear to exhibit complex parabolic profiles, using a minimum number of discrete layers and nodal degrees of freedom. Moreover, it enables prediction of interlaminar shear stresses at ply interfaces and, most importantly, at the actuator interfaces where shear stresses were found to reach steep peak values. Thus, the present theory appears capable of providing valuable shear stress results for estimating the initiation of delamination cracks, which were not previously available by linear layerwise theories. The effect of ply orientation, lamination, thickness and curvature (in the case of the shells) on modal damping is studied. In hybrid multi-damped composite beams and plates the developed mechanics encompass both damping contributions of the viscoelastic composite plies and the resistively shunted piezoelectric layers and their beneficial interaction in producing a more uniform overall damping capacity.

Vortex induced vibration of a circular cylinder in an inclined flow is a major subject in this thesis, the interaction and effect between a moving cylinder and fluid is always focused and investigated. We used a finite differences method to get the forces on cylinder, and then combined a Runge-Kutta four order approximate method to get a new position of a cylinder at next time step, repeated above procedure and we will get the solutions of a time series of cylinder response for VIV simulations. Most of papers focus on the peak amplitude and its scale due to the shedding frequency of system is near or at the fs, where fs is the shedding frequency of a uniform flow past a stationary cylinder. Except the ¡§first resonance¡¨, we found the ¡§second resonance¡¨ in the VIV simulations. The ¡§second resonance¡¨ occurs due to the natural shedding frequency of system is near or at the twice of the reduced frequency of the oscillator ¡§fs=2F1¡¨. The natural shedding frequency of a body is a key parameter, it always be discussed its effect and importance, and its value is also presented the frequency of lift force (or displacement on Y direction) of a body. On the contrary, the frequency of in-line force (or displacement on X direction) and its effect is seldom be investigated and discussed. In this study, we will discuss the effect of frequency of in-line force and the scale of ¡§first resonance¡¨ and ¡§second resonance¡¨ for VIV simulations. In order to verify the accuracy of our numerical model, this study simulated four different types for the cases of uniform flow past a circular cylinder with stationary, streamwise, transversal and rotational oscillating, respectively. The simulation results are compared with the study results of other paper by experimental and numerical methods, and the comparison show good agreement and high accuracy in the range of the in-line and lift forces on the cylinder, the main wake size behind the cylinder, the vortex shedding mode and the streamline pattern of the flow field. Furthermore, this study investigates a uniform flow past an inclined oscillating cylinder which is forcing oscillation in a range of 00 ~ 900 for the inclined angle (with respect to the X-direction of the Cartesian coordinates system). The effects of giving the different forced frequencies of a cylinder were investigated and discussed. And the application and restriction of Morison¡¦s equation will also be studied and investigated in different input conditions.

Elastic constants of single-walled carbon nanotubes (SWCNTs) and single-layer graphene sheets (SLGSs) are determined by studying their free vibration characteristics using molecular mechanics (MM) simulations with the MM3 potential and finding their equivalent continuum structures (ECSs). The computational framework has been validated by comparing the presently computed basal plane stiffness and frequencies of radial breathing modes (RBMs) with those available in the literature. We have considered armchair, zigzag and chiral SWCNTs of aspect ratios (length/ diameter in the unloaded relaxed configuration) ranging from 2 to 15. The wall thickness of ECSs of SWCNTs is determined by applying continuum theories, viz., beam, shell and 3D-linear elasticity to ECSs and equating their frequencies with those of SWCNTs obtained from the MM simulations. An expression for the wall thickness of an ECS of a SWCNT in terms of its chiral indices is deduced. The wall thickness of an ECS of a SWCNT is found to increase with an increase in its radius and to saturate at 1.37 Ã for the radius exceeding 15 Ã . Poisson's ratio for zigzag SWCNTs decreses with an increase in the tube radius, but that for armchair SWCNTs exhibits the opposite trend. For the same radius, Poisson's ratio of a chiral SWCNT is slightly more than that for an armchair tube but a little less than that for a zigzag tube. For zigzag SWCNTs, frequencies of inextensional modes of vibration saturate with an increase in the circumferential wave number but those of their ECSs do not. The MM simulations of uniaxial tensile deformations of SLGSs of aspect ratios (length/width) ~ 10 give the basal plane stiffness of ~ 340 N/m. The MM simulations of free vibrations of clamped SLGSs and the analysis of vibrations of their ECSs with a continuum theory gives a wall thickness of ~ 1 Ã for a SLGS. / Ph. D.

Master of Science / Department of Civil Engineering / Hani G. Melhem / This study reports the results of an analytical, experimental and a numerical study (proof of concept study) on a proposed method for extracting the pseudo-free-vibration response of a structure using ambient vibration, usually of a random nature, as a source of excitation to detect any change in the dynamic properties of a structure that may be caused by damage. The structural response contains not only a random component but also a component reflecting the dynamic properties of the structure, comparable to the free vibration for a given initial condition. Structural response to the arbitrary excitation is recorded by one or several accelerometers with a desired data-collection frequency and resolution. The free-vibration response of the structure is then extracted from this data by removing the random component of the response by the method proposed in this study. The features of the free-vibration response of the structure extracted by a suitable method, namely Fast Fourier Transform (FFT) in this study, can be used for change detection. Possible change of the pattern of these features is dominantly linked to the change in dynamic properties of the system, caused by possible damage. To show the applicability of the concept, besides an analytical verification using Newmark’s linear acceleration method, two steel portal frames with different flexural stiffness were made in the steel workshop of the structural laboratory for an experimental study. These structures were also numerically modeled using a finite element software. A wireless accelerometer with a sampling frequency rate of 2046 Hz was affixed on the top of the physical structure, at the same location where the acceleration was recorded for the corresponding numerical model. The physical structure was excited manually by an arbitrary hit and the response of the structure to this excitation, in terms of the acceleration on the top of the structure, was recorded. The pseudo-free-vibration response was extracted and transferred into frequency domain using FFT. The frequency with the largest magnitude which is the fundamental frequency of the structure was traced. This was repeated for several independent excitations and the fundamental frequencies were observed to be the same, showing that the process can correctly identify the natural frequencies of the structure. Similarly, the numerical model was excited and for several base excitation cases, the fundamental frequencies were found to be the same. Considering the acceptable accuracy of the results from the two numerical models in simulating the response of their corresponding physical models, additional numerical models were analyzed to show the consistency and applicability of the proposed method for a range of flexural stiffness and damping ratio. The results confirm that the proposed method can precisely extract the pseudo-free-vibration response of the structures and detect the structural frequencies regardless of the excitation. The fundamental frequency is tied to the stiffness and a larger stiffness leads to a higher frequency, as expected, regardless of the simulated ambient excitation.

Curved beams such as arches find ubiquitous applications in civil, mechanical and aerospace engineering, e.g., stiffened floors, fuselage, railway compartments, and wind turbine blades. The analysis of free vibrations of curved structures plays a critical role in their design to avoid transient loads with dominant frequencies close to their natural frequencies. One way to increase their areas of applications and possibly make them lighter without sacrificing strength is to make them of Functionally Graded Materials (FGMs) that are composites with continuously varying material properties in one or more directions. In this thesis, we study free vibrations of FGM circular beams by using a logarithmic shear deformation theory that incorporates through-the-thickness logarithmic variation of the circumferential displacement, and does not require a shear correction factor. The radial displacement of a point is assumed to depend only upon its angular position. Thus the beam theory can be regarded as a generalization of the Timoshenko beam theory. Equations governing transient deformations of the beam are derived by using Hamilton's principle. Assuming a time harmonic variation of the displacements, and by utilizing the generalized differential quadrature method (GDQM) the free vibration problem is reduced to solving an algebraic eigenvalue problem whose solution provides frequencies and the corresponding mode shapes. Results are presented for different spatial variations of the material properties, boundary conditions, and the aspect ratio. It is found that the radial and the circumferential gradation of material properties maintains their natural frequency within that of the homogeneous beam comprised of a constituent of the FGM beam. Furthermore, keeping every other variable fixed, the change in the beam opening angle results in very close frequencies of the first two modes of vibration, a phenomenon usually called mode transition. / Master of Science / Curved and straight beams of various cross-sections are one of the simplest and most fundamental structural elements that have been extensively studied because of their ubiquitous applications in civil, mechanical, biomedical and aerospace engineering. Many attempts have been made to enhance their material properties and designs for applications in harsh environments and reduce weight. One way of accomplishing this is to combine layerwise two or more distinct materials and take advantage of their directional properties. It results in a lightweight structure having overall specific strength superior to that of its constituents. Another possibility is to have volume fractions of two or more constituents gradually vary throughout the structure for enhancing its performance under anticipated applications. Functionally graded materials (FGMs) are a class of composites whose properties gradually vary along one or more space directions. In this thesis, we have numerically studied free vibrations of FGM circular beams to enhance their application domain and possibly use them for energy harvesting.

In many engineering structures transmission of vertical or horizontal forces to the foundation is a major challenge. As a first approach to model it may be assumed that the foundation behaves elastically. For generalized foundations the model assumes that at the point of contact between plate and foundation there is not only pressure but also moments caused by interaction between the springs. In this study, the exact stiffness, geometric stiffness and consistent mass matrices of the beam element on two-parameter elastic foundation are extended to solve plate problems. Some examples of circular and rectangular plates on two-parameter elastic foundation including bending, buckling and free vibration problems were solved by the finite grid solution. Comparison with known analytical solutions and other numerical solutions yields accurate results.

Orientador: Leandro Palermo Jr / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-09T15:27:34Z (GMT). No. of bitstreams: 1 Sakanaka_SandraHiromi_M.pdf: 2300706 bytes, checksum: bf530823f185b6dbee7f56dd83d01a67 (MD5) Previous issue date: 2006 / Resumo: A análise de vibração livre e de instabilidade de placas finas e placas moderadamente espessas é apresentada através do método dos elementos de contorno (MEC) considerando o efeito da deformação pela força cortante e, particularmente para o cálculo de freqüências naturais, o efeito da inércia rotatória é também considerado. A formulação da solução fundamental é baseada na teoria de Mindlin (1951) mas resultados para a teoria de Kirchhoff (1850) também podem ser obtidos [Palermo Jr. (2000)]. O presente trabalho usa a técnica da iteração inversa através do coeficiente de Rayleigh para a determinação das menores freqüências naturais e cargas críticas de instabilidade das placas. A implementação numérica emprega elementos de contorno isoparamétricos lineares contínuos e descontínuos. Elementos constantes de domínio são usados. Os parâmetros nodais são posicionados nos extremos dos elementos e os pontos de carregamento dos elementos descontínuos são deslocados para o interior a uma distância igual a um quarto do comprimento do elemento. Expressões analíticas das integrais de contorno são desenvolvidas para os casos em que o elemento contém o ponto de carregamento e integração numérica de Gauss-Legendre é feita nos outros casos. As integrais de domínio foram transformadas em integrais de contorno para cada célula e foram tratadas como cargas de superfície atualizadas através de um processo iterativo. Os resultados obtidos foram comparados com valores encontrados na literatura para demonstrar a precisão do presente trabalho / Abstract: Free-vibration analysis and static buckling loads analysis of thin and thick plates considering the shear deformation effects using the Boundary Element Method (BEM) is presented. For the calculation of natural frequencies, the rotatory inertia is also counted. The formulation of the fundamental solution considers Mindlin¿s plates but results according to the classic theory can also be obtained [Palermo Jr. (2000)]. The present article makes use of the inverse iteration with Rayleigh coefficient to determine the smallest natural frequencies and the smallest static buckling loads of the plates. The numerical implementation employed continuous or discontinuous isoparametric linear boundary elements according to the characteristics of the problem to be solved. Constant domain elements are used. Nodal parameters have been placed at the ends of the elements and the source point of the discontinuous elements were positioned at a distance equal to one quarter of the element length. Analytical expressions have been employed in the integration on elements containing the source point and Gauss-Legendre numerical integration scheme otherwise. The domain integrals containing the inertia effects or nonlinear effect have been transformed into boundary integrals for each cell and were treated as surface loads updated in an iterative process. The obtained results were compared to those in literature to demonstrate the precision of this proposal / Mestrado / Estruturas / Mestre em Engenharia Civil

Due to high specific strength and stiffness as well as outstanding energy-absorption characteristics, sandwich structures are extensively used in aircraft, aerospace, automobile, and marine industries. With the objective of finding lightweight blast-resistant sandwich structures for protecting infrastructure, we have found, for a fixed areal mass density, one- or two-core doubly-curved sandwich shell's (plate's) geometries and materials and fiber angles of unidirectional fiber-reinforced face sheets for it to have the maximum first failure load under quasistatic (blast) loads. The analyses employ a third-order shear and normal deformable plate/shell theory (TSNDT), the finite element method (FEM), a stress recovery scheme (SRS), the Tsai-Wu failure criterion and the Nest-Site selection (NeSS) optimization algorithm, and assume the materials to be linearly elastic. For a sandwich shell under the spatially varying static pressure on the top surface, the optimal non-symmetric one-core (two-core) design improves the first failure load by approximately 33% (27%) and 50% (36%) from the corresponding optimal symmetric design with clamped and simply-supported edges, respectively. For a sandwich plate under blast loads, it is found that the optimal one-core design is symmetric about the mid-surface with thick face sheets, and the optimal two-core design has a thin middle face sheet and thick top and bottom face sheets. Furthermore, the transverse shear stresses (in-plane transverse axial stresses) primarily cause the first failure in a core (face sheet). For the computed optimal design under a blast load, we also determined the collapse load by using the progressive failure analysis that degrades all elasticities of the failed material point to very small values. The collapse load of the clamped (simply-supported) sandwich structure is approximately 15%–30% (0%–17%) higher than its first failure load. Incompressible materials such as rubbers, polymers, and soft tissues that can only undergo volume preserving deformations have numerous applications in engineering and biomedical fields. Their vibration characteristics are important for using them as wave reflectors at interfaces with a fiber-reinforced sheet. In this work we have numerically analyzed free vibrations of plates made of a linearly elastic incompressible rubber-like material (Poison's ratio = 0.5) by using a TSNDT for incompressible materials and the mixed FEM. The displacements at nodes of a 9-noded quadrilateral element and the hydrostatic pressure at four interior nodes are taken as unknowns. Computed results are found to match well with the corresponding either analytical or numerical ones obtained with the commercial FE software Abaqus and the 3-dimensional linear elasticity theory. The analysis discerns plate's in-plane vibration modes. It is found that a simply supported plate admits more in-plane modes than the corresponding clamped and clamped-free plates. / Doctor of Philosophy / A simple example of a sandwich structure is a chocolate ice cream bar with the chocolate layer replaced by a stiff plate. Another example is the packaging material used to protect electronics during shipping and handling. The intent is to find the composition and the thickness of the "chocolate layer" so that the ice cream bar will not shatter when dropped on the floor. The objective is met by enforcing the chocolate layer with carbon fibers and then finding fiber materials, their alignment, ice cream or core material, and its thickness to resist anticipated loads with a prescribed level of certainty. Thus, a sandwich structure is usually composed of a soft thick core (e.g., foam) bonded to two relatively stiff thin skins (e.g., made of steel, fiber-reinforced composite) called face sheets. They are lightweight, stiff, and effective in absorbing mechanical energy. Consequently, they are often used in aircraft, aerospace, automobile, and marine industries. The load that causes a point in a structure to fail is called its first failure load, and the load that causes it to either crush or crumble is called the ultimate load. Here, for a fixed areal mass density (mass per unit surface area), we maximize the first failure load of a sandwich shell (plate) under static (dynamic) loads by determining its geometric dimensions, materials and fiber angles in the face sheets, and the number (one or two) of cores. It is found that, for a non-uniformly distributed static pressure applied on the central region of a sandwich shell's top surface, an optimal design that has different materials for the top and the bottom face sheets improves the first failure load by nearly 30%-50% from that of the optimally designed structure with identical face sheets. For the structure optimally designed for the first failure blast load, the ultimate failure load with all of its edges clamped (simply supported) is about 15%-30% (0%-17%) higher than its first failure load. This work should help engineers reduce weight of sandwich structures without sacrificing their integrity and save on materials and cost. Rubberlike materials, polymers, and soft tissues are incompressible since their volume remains constant when they are deformed. Plates made of incompressible materials have a wide range of applications in everyday life, e.g., we hear because of vibrations of the ear drum. Thus, accurately predicting their dynamic behavior is important. A first step usually is determining natural frequencies, i.e., the number of cycles of oscillations per second (e.g., a human heart beats at about 1 cycle/sec) completed by the structure in the absence of any externally applied force. Here, we numerically find natural frequencies and mode shapes of rubber-like material rectangular plates with different supporting conditions at the edges. We employ a plate theory that reduces a 3-dimensional (3-D) problem to a 2-D one and the finite element method. The problem is challenging because the incompressibility constraint requires finding the hydrostatic pressure as a part of the problem solution. We show that the methodology developed here provides results that match well with the corresponding either analytical or numerical solutions of the 3-D linear elasticity equations. The methodology is applicable to analyzing the dynamic response of composite structures with layers of incompressible materials embedded in it.

The dynamics of rigid body motion are dependent on the inertial properties of the body - that is, the mass and moment of inertia. For complex systems, it may be necessary to derive these results empirically. Such is the case for manual wheelchairs, which can be modeled as a rigid body frame connected to four wheels. While 3D modeling software is capable of estimating inertial parameters, modeling inaccuracies and ill-defined material properties may introduce significant errors in this estimation technique and necessitate experimental measurements. To that end, this thesis discusses the design of a device called the iMachine that empirically determines the mass, location of the center of mass, and moment of inertia about the vertical (yaw) axis passing through the center of mass of the wheelchair. The iMachine is a spring-loaded rotating platform that freely oscillates about an axis passing through its center due to an initial angular velocity. The mass and location of the center of mass can be determined using a static analysis of a triangular configuration of load cells. An optical encoder records the dynamic angular displacement of the platform, and the natural frequency of free vibration is calculated using several techniques. Finally, the moment of inertia is determined from the natural frequency of the system. In this thesis, test results are presented for the calibration of the load cells and spring rate. In addition, objects with known mass properties were tested and comparisons are made between the analytical and empirical inertia results. In general, the mass measurement of the test object had greater than 99% accuracy. The average relative error for the x and y-coordinates of the center of mass was 0.891% and 1.99%, respectively. For the moment of inertia, a relationship was established between relative error and the ratio of the test object inertia to the inertia of the system. The results suggest that 95% accuracy can be achieved if the test object accounts for at least 25% of the total inertia of the system. Finally, the moment of inertia of a manual wheelchair is determined using the device (I = 1.213 kg-m²), and conclusions are made regarding the reliability and validity of results. The results of this project will feed into energy calculations for the Anatomical Model Propulsion System (AMPS), a wheelchair-propelling robot used to measure the mechanical efficiency of manual wheelchairs.

Changes in load characteristics, deterioration with age, environmental influences and random actions may cause local or global damage in structures, especially in bridges, which are designed for long life spans. Continuous health monitoring of structures will enable the early identification of distress and allow appropriate retrofitting in order to avoid failure or collapse of the structures. In recent times, structural health monitoring (SHM) has attracted much attention in both research and development. Local and global methods of damage assessment using the monitored information are an integral part of SHM techniques. In the local case, the assessment of the state of a structure is done either by direct visual inspection or using experimental techniques such as acoustic emission, ultrasonic, magnetic particle inspection, radiography and eddy current. A characteristic of all these techniques is that their application requires a prior localization of the damaged zones. The limitations of the local methodologies can be overcome by using vibration-based methods, which give a global damage assessment. The vibration-based damage detection methods use measured changes in dynamic characteristics to evaluate changes in physical properties that may indicate structural damage or degradation. The basic idea is that modal parameters (notably frequencies, mode shapes, and modal damping) are functions of the physical properties of the structure (mass, damping, and stiffness). Changes in the physical properties will therefore cause changes in the modal properties. Any reduction in structural stiffness and increase in damping in the structure may indicate structural damage. This research uses the variations in vibration parameters to develop a multi-criteria method for damage assessment. It incorporates the changes in natural frequencies, modal flexibility and modal strain energy to locate damage in the main load bearing elements in bridge structures such as beams, slabs and trusses and simple bridges involving these elements. Dynamic computer simulation techniques are used to develop and apply the multi-criteria procedure under different damage scenarios. The effectiveness of the procedure is demonstrated through numerical examples. Results show that the proposed method incorporating modal flexibility and modal strain energy changes is competent in damage assessment in the structures treated herein.