1 23

Materials and Structures ISSN 1359-5997 Mater StructDOI 10.1617/s11527-014-0286-7

Prediction of material damping in timberfloors, and subsequent evaluation ofstructural damping

Nathalie Labonnote, Anders Rønnquist& Kjell Arne Malo

1 23

Your article is protected by copyright and all

rights are held exclusively by RILEM. This e-

offprint is for personal use only and shall not

be self-archived in electronic repositories. If

you wish to self-archive your article, please

use the accepted manuscript version for

posting on your own website. You may

further deposit the accepted manuscript

version in any repository, provided it is only

made publicly available 12 months after

official publication or later and provided

acknowledgement is given to the original

source of publication and a link is inserted

to the published article on Springer's

website. The link must be accompanied by

the following text: "The final publication is

available at link.springer.com”.

ORIGINAL ARTICLE

Prediction of material damping in timber floors,and subsequent evaluation of structural damping

Nathalie Labonnote • Anders Rønnquist •

Kjell Arne Malo

Received: 4 July 2013 / Accepted: 6 March 2014

� RILEM 2014

Abstract Dynamic properties of two timber floor

specimens are experimentally evaluated by the impact

method. Each specimen uses one specified type of

connectors, either screws or nails. A numerical model

is developed using constrained degrees-of-freedom for

the modeling of connectors. Numerical analyses have

been performed, and show good agreement with

experimental results. A procedure is written using

the finite element software Abaqus to predict material

damping from a strain energy approach. Estimation of

structural damping is performed as the difference

between the experimentally evaluated total damping

and the predicted material damping. The contribution

from floor members to material damping is exten-

sively investigated.

Keywords Timber floors �Material damping �Structural damping � Strain energy approach

1 Introduction

Low damping is one of the primary causes of

excessive human-induced floor vibration in buildings

[27]. Modern timber structures are prone to low

fundamental frequencies due to the generalization of

long-span architecture and ‘‘open-space’’ solutions.

These low fundamental frequencies may unfortunately

coincide with the frequency of walking excitation,

rendering amplified dynamic response. However,

compared to other building materials such as steel,

timber exhibits a great advantage in the form of higher

damping, which in general will decrease both the

duration of transient vibrations and the amplitude of

steady-state vibrations. In addition, higher damping in

floors should ensure that vibrations are predominantly

transient, and therefore more easily tolerated [16],

since both duration and amplitude were largely

recognized as influential parameters on the perception

of vibration by human subjects [5].

When the response is damping controlled, there is a

clear consensus about including damping in criteria

for assessing the performance of existing floors.

However, at present the omission of damping in

design criteria originates from the difficulty for the

practicing engineer to predict the damping character-

istics of a floor during the design process. This is

especially relevant for wood structures where the

damping characteristics to a large degree will depend

on the workmanship [32] and construction techniques

[11]. Although designers have accurate models and

N. Labonnote (&)

Materials and Structures, SINTEF Building and

Infrastructure, 7465 Trondheim, Norway

e-mail: nathalie.labonnote@sintef.no

A. Rønnquist � K. A. Malo

Department of Structural Engineering, Norwegian

University of Science and Technology, 7491 Trondheim,

Norway

Materials and Structures

DOI 10.1617/s11527-014-0286-7

Author's personal copy

tools to predict strength and stiffness, the estimation

and calculation of damping is usually more difficult

due to a general lack of knowledge of the damping

phenomena. The total damping: ntot, is commonly

divided into at least two categories:

– the material damping, nmat, which refers to internal

friction in the materials and

– the structural damping, nstruct, which may arise

from other sources such as friction between

components and/or friction due to connectors.

Hence:

ntot ¼ nmat þ nstruct: ð1ÞStructural damping nstruct is therefore partially

dependent on the workmanship, whereas material

damping nmat is only dependent on the actual material

properties. A first, yet conservative, step towards the

better prediction of damping in timber structures can

therefore be accomplished by considering material

damping nmat as a lower boundary for total damping

ntot, i.e.:

min ntotð Þ ¼ nmat: ð2ÞThe great advantage in this formulation is that

prediction models of material damping nmat have been

developed over the last few decades by means of the

strain energy approach [3, 35]. The use of available

prediction models for material damping nmat may also

result in possible estimations of structural damping

nstruct as the difference between the measurable total

damping ntot and the predicted material damping nmat:

nstruct ¼ ntot � nmat: ð3ÞThe main applications of the strain energy approach

were directed towards composite single members,

either beams or plates [2, 4, 8, 17, 24, 26, 28].

Berthelot et al. [6] developed a synthesis of damping

analysis of laminate materials, and applied the strain

energy method to a composite structure composed of

different materials. So far, there have been few similar

studies on timber members and/or timber structures,

with the exception of studies dealing with laminated

plates [21, 22, 33], among them some timber panels.

The present study implements the strain energy

method by means of finite element modeling in order

to predict the material damping nmat exhibited by

timber floors and to estimate the structural damping

nstruct.

The total damping ntot of two timber floors using

two types of connectors has been experimentally

assessed by the impact method (Sect. 2). A prediction

model for the material damping nmat using the strain

energy approach is then derived (Sect. 3), and used in

combination with a commercial finite element soft-

ware (Sect. 4). The structural damping nstruct is

furthermore estimated from Eq. (3) and different

investigations are performed on the contributions to

the material damping nmat (Sect. 5). The overall

procedure is summarized in Fig. 1.

2 Experimental design

2.1 Selected timber floors

Two timber floor specimens are tested: one with all

screw connectors, referred to as the screwed floor, and

one where connectors are all nails, referred to as the

nailed floor. Both specimens have the same layout, and

are composed of two edge joists with sec-

tion 225 mm 9 67 mm, five joists with sec-

tion 225 mm 9 48 mm, 22 mm thick particleboard

panels on top, and 13 mm thick particleboard panels

on bottom. Nominal dimensions of particleboard

panels are 600 mm 9 2,400 mm, and the timber

floors themselves are 2,400 mm 9 2,880 mm. All

dimensions sketched in Fig. 2 are nominal, and are

given in mm.

Assembling of the floors was performed according

to SINTEF Building Research Design Guides [31].

Connection between joists and sheathing was achieved

accordingly by the use of glue, in addition to

recommended timber nails (65 mm long) and recom-

mended timber screws (50–55 mm long), with a

recommended maximal center to center spacing of

300 mm.

Edge joists and joist are glulam beams of GL36c, as

defined in EN 1194 [12]. Particleboard panels are

made out of small wood particles, pressed together

under high temperature and pressure inside a matrix of

glue. Their material properties are defined in EN-

12369-1 [13]. Glulam beams are considered to be

transversely isotropic, whereas particleboard panels

are considered to be isotropic. Mean stiffness values

and characteristic densities for the glulam beams and

the particleboard panels are summarized in Tables 1

and 2 for convenience, with respect both to the

Materials and Structures

Author's personal copy

longitudinal direction (L) and the transverse direction

(T).

Temperature and relative humidity were not

explicitly controlled, but were according to standard

indoor summer conditions, i.e. 20 �C and 60 %

respectively.

2.2 Roving hammer experimental protocol

The modal hammer ‘‘heavy duty type 8208’’ from

Bruel and Kjær [7] is used to set the panel into motion

and to record the impact load. A soft tip is employed in

order to excite lower frequencies. Transient vibrations

due to modal hammer impact are recorded by one

ceramic/quartz impedance head Kistler 8770A50

Fig. 1 Summarized procedure and main outputs

Fig. 2 Lay-out and dimensions of floors

Table 1 Mean stiffness values and characteristic density val-

ues [13]

E (MPa) G (MPa) Density

(kg/m3)

Particleboard panel:

22 mm thick

1,600 770 550

Particleboard panel:

13 mm thick

1,700 830 600

Table 2 Mean stiffness values, poison ratios, and characteristic density values [9, 12]

EL (MPa) ET (MPa) GLT (MPa) GTT (MPa) mLT mTT Density (kg/m3)

Glulam beam GL36c 14,700 460 850 30 0.39 0.64 430

L Longitudinal direction, T transverse direction, TT radial-tangential plane, for the considered member

Fig. 3 Experimental measurements on timber floors by the

roving hammer method

Materials and Structures

Author's personal copy

accelerometer screwed into the top particleboard

panel, as shown in Fig. 3. The load and acceleration

time series are then digitalized and processed by a

dynamic signal analyzer. An experimental modal

analysis software provided by National Instruments

[23] is used to record and process the data by means of

the graphical development environment LabVIEW.

The sampling frequency is fixed to 1,000 Hz, and 5 s

data are recorded for each impact.

The mode shapes corresponding to each floor are

evaluated by means of the ‘‘roving hammer’’ method

[29], which consists of impacting different points,

usually organized on a grid, while the accelerometer

remains at one unique location. The grid consists of

195 measurements points, i.e. a 20 9 20 cm spaced

grid. Each measurement point is impacted twice. Both

timber floors are simply supported at only four

corners, by means of 20 cm long steel cylinders

located along the edge joists, as illustrated in Fig. 3.

2.3 Modal parameter identification

Experimental modal analysis [14] is used for determin-

ing the fundamental frequencies, the damping ratios

and the mode shapes of the two floors, all under the

fundamental assumption of small total damping values.

The frequency response function H relates the input

signal spectrum F from the hammer’s load cell and the

output signal spectrum X from the accelerometer:

HðxÞ � XðxÞFðxÞ ; ð4Þ

where x is the circular frequency in rad/s. A linear

average of the frequency response function over two

impacts is performed. Identification of transfer func-

tion models is performed by curve fitting the averaged

frequency response function with suitable analytical

expressions, so that:

Hik ¼Xn

r¼1

wiwkð Þrx2

r �x2þ 2jnrxrx� �

with

wiwkð Þr¼ residues

xr ¼ natural frequency

nr ¼ equivalent viscous modal damping ratio,

8>><

>>:

ð5Þ

where r is the mode number, n is the total number of

modes, and j¼ffiffiffiffiffiffiffi�1p

. The natural frequency and the

modal viscous damping ratio are directly extracted

from Eq. (5). The mode shape vectors Wr are extracted

as:

Wr ¼ w21

� �r

w1w2ð Þr . . . w1w13ð Þrh i

: ð6Þ

The parameter identification method is based on the

Frequency-Domain Direct Parameter Identification

fitting method, which is a frequency domain multiple

degree-of-freedom modal analysis method suitable for

narrow frequency band and well separated modes.

3 Prediction model

3.1 Analytical derivation

In 1962, Ungar and Kerwin [35] were among the first

to define damping in terms of energy:

g ¼ D

2pW; ð7Þ

where g is the hysteretic damping, D is the dissipated

energy per cycle, and W is the total energy (kinetic

plus potential) associated with the vibration. They

recognized that the definition of W as the total energy

for the considered cycle was unambiguous only for

lightly damped structures, where the total energy does

not fluctuate much throughout a cycle. They therefore

proposed to compute W as the total strain energy at

instant of maximum strain at a reference point in the

case of lightly damped structures. Adams and Bacon

[3] used Ungar and Kerwin’s suggestion, and defined

the specific damping capacity u as the ratio between

the dissipated energy DU per cycle of vibration to the

maximum strain energy U:

u ¼ 2pg ¼ DU

U: ð8Þ

The strain energy U is expressed with respect to the

stress r and strain e matrices as:

U ¼ 1

2

ZZZrTedV : ð9Þ

The strain energy U may be divided into different

energies, i.e.:

U ¼ U11 þ U22 þ U33 þ U12 þ U13 þ U23

with Uij ¼1

2

ZZZrijeijdV :

ð10Þ

Materials and Structures

Author's personal copy

When considering material damping in particular,

the dissipated energy DU during one cycle s may be

expressed in the most general way [26, 30] as:

DU ¼Z

s

ZZZ1

2~rT ~edV

� �dt ¼ 2p

ZZZ1

2~rT ~edV ð11Þ

where ~r and ~e are damped quantities. Damped

quantities have been commonly defined by dividing

the dissipated energy DU into different parts as well

[2, 20, 25], i.e.:

DU ¼ DU11 þ DU22 þ DU33 þ DU12 þ DU13

þ DU23: ð12Þ

The different dissipated energies DUij are defined

with respect to specific loss factors gij:

DUij ¼ 2pgij

ZZZ1

2rijeijdV: ð13Þ

The relationship between equivalent viscous damp-

ing n with hysteretic damping g at resonance yields

[10]:

n ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�1þ

ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ g2

p

2

s

� g2: ð14Þ

The predicted material damping nmat is finally

expressed as:

Adams and Bacon [2] and Maheri [20] defined

relevant loss factors g11, g22 and g12 as the longitudinal

loss factor, the transverse loss factor and the shear loss

factor, respectively. Pervez and Zabaras [25] consid-

ered in addition loss factors due to transverse shears:

g13 and g23.

3.2 Application to beam, plate and floor

In the present investigation, the evaluated floors are

composed of various timber members, acting either as

beams or plates. For beams, all energy quantities

defined in Eq. (10) are relevant. However, since here

both top and bottom plates exhibit a very low

thickness-to-length ratio, thin plate theory may be

introduced, which means that, if 1 and 2 are the in-

plane axes of the plate, as shown in Fig. 3, only r11,

r22, r12, e11, e22, and e12 are non-null. Consequently,

only U11, U22, and U12 are non-null for plates. The

total material damping of the floor is then defined

nmat ¼1

2

g11U11 þ g22U22 þ g33U33 þ g12U12 þ g13U13 þ g23U23

U11 þ U22 þ U33 þ 2U12 þ 2U13 þ 2U23

: ð15Þ

nmat ¼1

2Utot

X

Beamelements

g11;bU11;b þ g22;bU22;b þ g33;bU33;b þ g12;bU12;b þ g13;bU13;b þ g23;bU23;b

þX

Plateelements

g11;pU11;p þ g22;pU22;p þ 2g12;pU12;p

0BB@

1CCA; ð16Þ

Table 3 Loss factors estimated from previous studies

Loss factors

Glulam beams [18] gEL = 0.0081 gGLT = 0.1551

Particleboard panels [19] gE = 0.0200

L Longitudinal direction, T transverse direction

Materials and Structures

Author's personal copy

as:where Utot is the total strain energy of the floor, Uij,b

is the strain energy for a beam member, Uij,p is the

strain energy for a plate member.

3.3 Estimation of loss factors

Unlike existing estimations of elastic moduli for wood

[34, 37], experimental data on loss factors are very

scarce. A method for estimating loss factors for solid

wood beams, glulam beams, and various types of

timber panels has been recently provided by Labon-

note et al. [18, 19]. It is hoped that this method will be

further generalized to other types of timber products so

as to provide access to a database for loss factors that

could be used for design purposes.

The loss factors used in this study are therefore

estimated after previous experimental studies on

timber beams [18] and timber panels [19] with quality

similar to the edge joists and joists as well as the top

and bottom plates. For convenience, loss factors from

the above-mentioned studies are also reported in

Table 3.

Edge joists and joists are glulam beams, hence they

are considered as transversely isotropic. The following

loss factors: gL, gT, gLT, gTT, referred to as longitu-

dinal loss factor, transversal loss factor, in-plane shear

loss factor, transversal shear loss factor, respectively,

are necessary to implement in Eq. (16). From Table 3,

gL is estimated as gEL, and gLT is estimated as gGLT.

The remaining loss factors are assumed to be propor-

tional to stiffness. They are therefore estimated from

available data in Table 3 by taking into account the

ratio between the longitudinal elastic modulus EL and

the transverse elastic modulus ET, and the ratio

between both shear elastic moduli GLT and GTT, all

given in Table 1:

gT ¼ET

EL

gL

gTT ¼GTT

GLT

gLT:

ð17Þ

The top and bottom plates are isotropic, and in that

case, according to Eq. (16), the loss factor gE as well as

the shear loss factor gG are needed. The loss factor gE

is simply taken as the loss factor gE reported in

Table 3, whereas the shear loss factor gG is estimated

from the ratio between the elastic modulus E and the

shear modulus G, so that:

gG ¼G

EgE ð18Þ

The estimated loss factors are summarized in

Table 4.

4 Numerical analyses

4.1 Numerical models

The strain energies needed for the application of the

prediction model (16) are numerically determined, as

described in Fig. 1. The commercial software Abaqus

is used to perform finite element analyses. Particle-

board panels are modeled as two continuous plates

over the whole surface of the floor, one on top and one

at the bottom. The general linear, reduced integration,

shell element S4R is used. Edge joists and joists are

modeled using the 8-node linear brick, reduced

integration, continuum element C3D8R. Given the

very low motion induced by the impact test and the

recommended assembling process [31], connection

between timber components was assumed to be rigid

instead of semi-rigid. Joist-to-joist connection, as well

as joist-to-sheathing connection, whether involving

screws or nails, were therefore simplified by a ‘‘tie’’

constraint between adjacent surfaces. Rotational and

translational degrees-of-freedom were consequently

equal for adjacent surfaces. The mesh size is chosen to

be approximately 0.04 m, and corresponds to a

converging model.

Material properties are implemented as nominal

values, given in Table 1. Boundary conditions are

implemented by constraining selected degrees-of-

Table 4 Estimated loss factors used in the present study

Loss factors

Edge joists and joists gL = 0.0081 gT = 0.0003 gLT = 0.1551 gTT = 0.0055

Top plate and bottom plate gE = 0.0200 gG = 0.0100

L Longitudinal direction, T transverse direction

Materials and Structures

Author's personal copy

freedom along bottom plate selected surfaces,

assumed to be in contact with the steel cylinder

supports.

Numerical results are considered as undamped

results. Johnson and Kienholz [15] and later Rebillat

and Boutillon [26] assumed that for lightly damped

structures, mode shapes and fundamental frequencies

remain unchanged by the addition of damping. The

approximation was found reasonable even for values

of material damping in excess of unity [15].

Undamped numerical results are therefore considered

to be similar to damped experimental results.

4.2 Calculation of strain energy components

A procedure is written to calculate the strain energy

components Uij from Eq. (10) using Abaqus. Strain

energy components are calculated for each element,

and then summed over members: edge joist, joists, top

plate and bottom plates. For the continuum elements,

used to model edge joists and joists, the strain energy

components are calculated with respect to the strain

and stress related to the unique integration point. For

the shell elements, used to model the top and bottom

plates, the stress and strain are integrated over the

thickness of the shell section by the Gauss integration

method, with three points across the shell thickness h,

as presented in Fig. 4.

This method induces less than 2 % error on the total

strain energy per shell element. The location and

weights of the points [1] are summarized in Table 5.

5 Results and discussion

5.1 Comparison between experimental results

for nailed and screwed floors

Since the accelerometer was located on the top plate,

mode shapes recorded experimentally correspond to

the bending modes of the top plate. The observed

experimental mode shapes show similarities between

the screwed floor and the nailed floor for the two first

modes. No experimental data from higher modes are

available from measurements on the nailed floor,

unlike the screwed floor for which a third mode was

detected. Mode shapes obtained for the screwed floor

are plotted in Fig. 5, where the experimental used grid

is superimposed.

Fundamental frequencies f and corresponding

evaluated damping ratios ntot are presented in

Table 6. As expected, screw connectors make the

floor slightly stiffer than nail connectors, and the

Table 5 Gauss numerical integration constants

Point 1 Point 2 Point 3

Location xi �ffiffiffiffiffiffiffiffi3=5

ph2

0ffiffiffiffiffiffiffiffi3=5

ph2

Weight 5/18 4/9 5/18

Fig. 5 Experimental mode shapes

for the screwed floor

Table 6 Experimentally evaluated modal properties of floors

Mode 1 Mode 2 Mode 3

Nailed floor f1 = 28.5 Hz

ntot = 0.0196

f2 = 41.2 Hz

ntot = 0.0249

–

Screwed floor f1 = 29.7 Hz

ntot = 0.0194

f2 = 43.9 Hz

ntot = 0.0251

f3 = 53.0 Hz

ntot = 0.0293

Fig. 4 Gauss integration points on a shell thickness

Materials and Structures

Author's personal copy

fundamental frequencies f are observed to increase

by 4 and 6 % for the first mode and the second

mode, respectively. However, experimental estima-

tions of the total damping ntot reveal no significant

influence from the type of connector, probably due

to the additional presence of glue in the connections.

These observations have to be considered with care

since they are related to a limited number of

specimens: one for each type of connector.

5.2 Comparison between experimental

and numerical results

The three first bending modes of the top plates

observed experimentally are also studied by finite

element analyses. Comparison of experimental and

numerical fundamental frequencies shows good agree-

ment, as reported in Table 7, as well as the comparison

of mode shapes, depicted in Fig. 6.

Table 7 Comparison of numerical and experimental fundamental frequencies

Mode 1 Mode 2 Mode 3

Numerical fundamental frequency f1 = 28.6 Hz f2 = 37.7 Hz f3 = 51.5 Hz

Nailed floor (experimental) f1 = 28.5 Hz f2 = 41.2 Hz –

Screwed floor (experimental) f1 = 29.7 Hz f2 = 43.9 Hz f3 = 53.0 Hz

Fig. 6 Experimental mode

shapes (top row) and

numerical mode shapes

(bottom row)

Fig. 7 Different deformations types for each floor member (J. joist, E.J. edge joist)

Materials and Structures

Author's personal copy

Within the same range of frequency (28–53 Hz),

additional numerical modes are detected, but they are

all related to bending modes of the lower plate. This is

the reason why they were not detected experimentally.

Their study is therefore dismissed.

A more accurate visualization of the three first

bending modes, given by numerical simulation,

including detailed member deformations, is presented

in Fig. 7.

5.3 Contribution from floor members to material

damping

From the model displayed in Eq. (16), the material

damping nmat is calculated as the sum of material

damping quantities exhibited by each floor member.

The contributions from each floor member to the floor

material damping nmat are presented in Table 8 and

Fig. 8.

As expected, the top and bottom plates provide a

governing contribution to material damping, com-

pared to edge joists and joists, since they are also

subject to larger deformation, as shown in Fig. 7. For

the same reason, material damping induced by the

bottom plate is larger than material damping induced

by the top plate.

5.4 Prediction of material damping and estimation

of structural damping in floors

The material damping nmat may be estimated from Eq.

(15) for the three first vibration modes of the floors.

The structural damping nstruct, which includes damp-

ing due to friction between components and damping

due to connectors, is therefore estimated from the

difference between the measured total damping n and

the estimated material damping nmat, as expressed in

Eq. (3). The predicted material damping nmat and the

estimated structural damping nstruct are reported in

Table 9 for both types of floors: screwed floor and

nailed floor.

Very little difference between the two types of

floors is observed concerning the estimated structural

damping nstruct. This is likely due to the small

amplitude of vibrations under testing. Low amplitude

induces less friction; hence the influence of a specific

type of connectors is reduced.

From Fig. 9 and Table 9, it also appears that the

share of structural damping increases with the mode

number. This is especially clear for the third mode, e.g.

Table 8 Breakdown of material damping among floor

members

Mode

1

Mode

2

Mode

3

Edge joist 1 0.0004 0.0003 0.0001

Edge joist 2 0.0004 0.0003 0.0001

Joist 1 0.0000 0.0008 0.0007

Joist 2 0.0006 0.0014 0.0004

Joist 3 0.0014 0.0000 0.0005

Joist 4 0.0006 0.0014 0.0004

Joist 5 0.0000 0.0008 0.0007

Edge joists ? joists 0.0034 0.0050 0.0029

Top plate 0.0030 0.0031 0.0031

Bottom plate 0.0036 0.0038 0.0051

Sum plates 0.0066 0.0069 0.0082

Plates ? edge

joists ? joists = Material

damping nmat

0.0100 0.0119 0.0111

Fig. 8 Contribution to material damping from floor members (J. joist, E.J. edge joist)

Materials and Structures

Author's personal copy

for the screwed floor, where the structural damping

represents about 62 % of the total damping, whereas

structural damping represents only 48 % of the first

mode’s damping. The use of material damping as the

lower boundary of the total damping, as expressed in

Eq. (2), is therefore less accurate as the mode number

increases.

In 1971, Yeh, Hartz and Brown [36] compared the

magnitudes of different damping sources evaluated

experimentally. They however considered the material

damping, as a constant value equal to 0.0035 for any

timber structure and any vibration mode, which clearly

explains why they measured a significantly higher

ratio between material damping and structural damp-

ing (1:6) for conventional construction.

6 Conclusion

The present study describes an efficient approach for

prediction of material damping and estimation of

structural damping in timber floors. The prediction

method for material damping is derived from the strain

energy approach, and a procedure has been written

using the commercial finite element software Abaqus.

This method allows a precise estimation of the

different contributions to material damping from each

floor member. In particular it is observed that top and

bottom plates introduce larger material damping than

joists or edge joists.

Estimation of structural damping is performed as

the difference between experimentally evaluated total

damping and predicted material damping. The results

reveal a lower than expected share of structural

damping, compared to material damping. Insignificant

influence of the type of connectors is observed, and

this is probably due to the very low level of induced

motion. In addition, the contribution from structural

damping to total damping is observed to increase with

the mode number. In particular structural damping is

larger than material damping for the third mode

considered. This demonstrates that estimating a lower

boundary of the total damping by predicting the

material damping becomes more conservative as the

mode number increases.

The proposed procedure to predict material damp-

ing is dependent on the accuracy and the availability of

loss factors, but is convenient to implement and

efficient to use. However, further research is needed

regarding the influence of the type of connectors. More

timber floor specimens exhibiting different types of

joist-to-sheathing connection need to be systemati-

cally experimentally measured. Corresponding semi-

rigid connection numerical models need also to be

established and validated in order to enhance knowl-

edge on structural damping predictions in general.

Acknowledgments Bjørn Ottar Torp from Moelven

ByggModul is gratefully acknowledged for supplying the floors

used in the present study, and for his support and his time in general.

References

1. Abaqus Analysis User’s manual, version 6.9 (2010) Das-

sault Systemes Simulia Corp., Providence

2. Adams RD, Bacon DGC (1973) Effect of fiber orientation

and laminate geometry on the dynamic properties of CFRP.

J Compos Mater 7:402–428

3. Adams RD, Bacon DGC (1973) Measurement of the flex-

ural damping capacity and dynamic Young’s modulus of

metals and reinforced plastics. J Phys D 6(1):27–41. doi:10.

1088/0022-3727/6/1/308

Table 9 Predicted material damping and estimated structural

damping in floors

Mode 1 Mode 2 Mode 3

nmat—Nailed floor and

screwed floor

0.0100 0.0119 0.0111

nstruct—Nailed floor 0.0096 0.0130 –

nstruct—Screwed floor 0.0094 0.0132 0.0182

Fig. 9 Share of material damping and structural damping over

the total damping

Materials and Structures

Author's personal copy

4. Adams RD, Maheri MR (1994) Dynamic flexural properties

of anisotropic fibrous composite beams. Compos Sci

Technol 50(4):497–514

5. Alves N, Roitman N, Magluta C (1999) Dynamic response

under human movements. Mater Struct 32(1):31–37. doi:10.

1007/bf02480409

6. Berthelot J-M, Assarar M, Sefrani Y, Mahi AE (2008)

Damping analysis of composite materials and structures.

Compos Struct 85(3):189–204

7. Bruel & Kjær (2011) Product data: heavy duty impact

hammer: Type 8208. http://www.bksv.com/doc/bp2079.

pdf. Accessed 7 Feb 2011

8. Chandra R, Singh SP, Gupta K (2003) A study of damping

in fiber-reinforced composites. J Sound Vib

262(3):475–496

9. Dahl KB (2009) Mechanical properties of clear wood from

Norway spruce. Norwegian University of Science and

Technology, Trondheim

10. De Silva CW (2005) Vibration and shock handbook. Taylor

& Francis, Boca Raton

11. Dolan JD, Murray TM, Johnson JR, Runte D, Shue BC

(1999) Preventing annoying wood floor vibrations. J Struct

Eng 125:19–24

12. European Committee for Standardization (1999) NS - EN

1194 - Timber structures - Glued laminated timber -

Strength classes and determination of characteristic values.

Brussels

13. European Committee for Standardization (2001) NS-EN

12369-1 Wood-based panels: characteristic values for

structural design: Part 1: OSB, particleboards and fibre-

boards. Brussels

14. Ewins DJ (2000) Modal testing: theory, practice and

application. Research Studies Press, Baldock

15. Johnson CD, Kienholz DA (1983) Prediction of damping in

structures with viscoelastic materials. Paper presented at the

MSC Software World Users’ Conference, CA, USA

16. Kalkert RE, Dolan JD, Woeste FE (1993) The current status

of analysis and design for annoying wooden floor vibrations.

Wood Fiber Sci 25(3):305–314

17. Kam TY, Chang RR (1994) Design of thick laminated

composite plates for maximum damping. Compos Struct

29(1):57–67

18. Labonnote N, Rønnquist A, Malo KA (2013) Modified

hysteretic damping model applied to Timoshenko timber

beams. Comput Struct 121:22–31

19. Labonnote N, Rønnquist A, Malo KA (2013) Semi-analyt-

ical prediction and experimental evaluation of material

damping in wood panels. Holzforschung 67(3):333–343

20. Maheri MR (2011) The effect of layup and boundary con-

ditions on the modal damping of FRP composite panels.

J Compos Mater 45(13):1411–1422. doi:10.1177/

0021998310382314

21. McIntyre ME, Woodhouse J (1978) The influence of

geometry on linear damping. Acustica 39(4):209–224

22. McIntyre ME, Woodhouse J (1988) On measuring the

elastic and damping constants of orthotropic sheet materi-

als. Acta Metall 36(6):1397–1416. doi:10.1016/0001-

6160(88)90209-x

23. National Instruments (2011) Modal analysis. http://zone.ni.

com/devzone/cda/tut/p/id/8276. Accessed 31 Jan 2011

24. Ni RG, Adams RD (1984) The damping and dynamic

moduli of symmetric laminated composite beams: theoret-

ical and experimental results. J Compos Mater

18(2):104–121

25. Pervez T, Zabaras N (1992) Transient dynamic and damp-

ing analysis of laminated anisotropic plates using a refined

plate theory. Int J Numer Methods Eng 33(5):1059–1080

26. Rebillat M, Boutillon X (2011) Measurement of relevant

elastic and damping material properties in sandwich thick

plates. J Sound Vib 330(25):6098–6121

27. Saidi I, Haritos N, Gad EF, Wilson JL (2006) Floor vibra-

tions due to human excitation: damping perspective. Paper

presented at the Earthquake Engineering in Australia Con-

ference, Canberra, Australia, 24–26 Nov 2006

28. Saravanos DA (1994) Integrated damping mechanics for

thick composite laminates and plates. J Appl Mech

61(2):375–383

29. Schwarz BJ, Richardson MH (1999) Experimental modal

analysis. In: CSI Reliability Week. Orlando

30. Siala W, Abdennadher M, Hammami L, Haddar M (2008)

Modal damping prediction of sandwich panel with visco-

elastic thick core. In: Proceedings of the Institution of

Mechanical Engineers, Part C (J Mech Eng Sci) 222(C11):

2077–2086. doi:10.1243/09544062jmes1080

31. SINTEF Byggforsk (2011) Undergolv pa trebjelkelag. By-

ggforskserien, Byggdetaljer 522.861. SINTEF Byggforsk,

Oslo

32. Smith I, Chui YH (1988) Design of lightweight wooden

floors to avoid human discomfort. Can J Civ Eng

15(2):254–262

33. Talbot JP, Woodhouse J (1997) The vibration damping of

laminated plates. Composites Part A 28A(12):1007–1012.

doi:10.1016/s1359-835x(97)00056-0

34. Thomas W (2004) Planar shear moduli of rigidity of an

oriented strand board from bending and shear tests. Mater

Struct 37(7):480–484. doi:10.1007/bf02481585

35. Ungar EE, Kerwin EM Jr (1962) Loss factors of viscoelastic

systems in terms of energy concepts. J Acoust Soc Am

34(7):954–957

36. Yeh CT, Hartz BJ, Brown CB (1971) Damping sources in

wood structures. J Sound Vib 19(4):411–419. doi:10.1016/

0022-460X(71)90612-2

37. Yoshihara H, Tsunematsu S (2006) Feasibility of estimation

methods for measuring Young’s modulus of wood by three-

point bending test. Mater Struct 39(1):29–36. doi:10.1617/

s11527-005-9015-6

Materials and Structures

Author's personal copy